Swapnil Bhalla
email: swapnil.bhalla@ntnu.no

Erlend Alfnes

Hans-Henrik Hvolby

Assessing Fit of Capacity Planning Methods for Delivery Date Setting: An ETO Case Study

Keywords: Engineer-to-order (ETO), strategic fit, delivery

The paper studies an engineer-to-order (ETO) manufacturing firm. A novel approach is used to assess the fit of capacity planning methods in the planning environment of the firm, and towards delivery date setting, which is of strategic importance for ETO firms.

Introduction

Developing product designs for specific customer orders allows manufacturers to deliver customised products that address customers' unique requirements. This manufacturing approach, known as customer-driven manufacturing, is a key concept for future factories [START_REF] Gosling | Extending customer order penetration concepts to engineering designs[END_REF][START_REF] Rudberg | Manufacturing networks and supply chains: an operations strategy perspective[END_REF][START_REF] Wortmann | Why customer driven manufacturing[END_REF]. Such a customer-driven approach to manufacturing is prevalent among enterprises producing high-value capital products, such as shipbuilding, offshore equipment manufacturing, etc. [START_REF] Hicks | A typology of uk engineer-to-order companies[END_REF][START_REF] Sriram | Taxonomy of engineer-to-order companies[END_REF]. Based on the customer order decoupling point (CODP) framework, such manufacturing contexts are characterised by a supply chain strategy or product delivery strategy known as engineer-to-order (ETO) [START_REF] Olhager | The role of the customer order decoupling point in production and supply chain management[END_REF]. While firms producing high-value products benefit from an ETO strategy, which enables them to address specific customer requirements, they also operate in relatively complex planning environments due to increased uncertainty regarding specifications of the product and production process [START_REF] Stevenson | A review of production planning and control: the applicability of key concepts to the make-to-order industry[END_REF].

Customising products for every customer's requirements leads to newness within order fulfilment activities for each customer order, which include engineering, purchasing, production, etc. The newness of order fulfilment activities for a product is managed by organising these activities as a project [START_REF] Yang | Key practices, manufacturing capability and attainment of manufacturing goals: The perspective of project/engineer-to-order manufacturing[END_REF]. A precursor to planning a project and confirmation of customer orders is the customer enquiry stage, where estimated price, project delivery date, etc. should be quoted by the manufacturer [START_REF] Stevenson | A review of production planning and control: the applicability of key concepts to the make-to-order industry[END_REF]. The acceptance of these delivery dates by potential customers are often a criterion for confirmation of customer orders [START_REF] Stevenson | A review of production planning and control: the applicability of key concepts to the make-to-order industry[END_REF]. Due to the uncertainty in product and process specifications, and the newness or nonrepetitiveness of production activities, identifying reliable production delivery dates at this stage is not a trivial task in these manufacturing environments. It is worth clarifying that while 'project delivery date' is used here to refer to the date promised to the customer for handing over the finished product, 'production delivery date' refers to the estimated date when production is expected to be completed, which precedes the project delivery date. The possibility to determine reliable production delivery dates through capacity planning in ETO (and make-to-order (MTO)) environments, is a primary criteria for applicability of production planning and control (PPC) systems in these environments [START_REF] Stevenson | A review of production planning and control: the applicability of key concepts to the make-to-order industry[END_REF].

The fit between PPC systems and corresponding planning environment, has often been emphasised as consequential to manufacturers' performance [START_REF] Berry | Linking systems to strategy[END_REF][START_REF] Lödding | Handbook of manufacturing control: Fundamentals, description, configuration[END_REF][START_REF] Vollmann | Manufacturing Planning and Control Systems[END_REF]. Motivated by the importance of this fit towards improving manufacturing performance, different frameworks for mapping planning environments have been proposed in literature [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF][START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF][START_REF] Olhager | Linking manufacturing strategy decisions on process choice with manufacturing planning and control systems[END_REF][START_REF] Schönsleben | Integral logistics management: planning and control of comprehensive supply chains[END_REF]. These frameworks for mapping planning environments are intended to be starting points for identifying suitable PPC systems.

This paper presents a case study that set out to investigate the applicability of relevant theoretical knowledge to delivery date setting practice in ETO manufacturing. Through the case study, the paper also demonstrates a novel approach for investigating how the mapping of a planning environment can be used to assess the fit of PPC methods, as called for by Buer et. al. [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF] in possibilities for future work.

The paper is organised as follows. Section 2 contextualises this paper using literature. Section 3 outlines relevant capacity planning techniques. Section 4 presents the research framework and case study. Section 5 serves as a brief conclusion to the paper.

Delivery date setting in ETO manufacturing

The strategic importance of estimating, quoting and setting production delivery dates for customised manufacturing environments such as ETO and MTO, has been emphasised often in literature [START_REF] Hicks | An analysis of company structure and business processes in the capital goods industry in the uk[END_REF][START_REF] Kingsman | Integrating marketing and production planning in make-to-order companies[END_REF][START_REF] Konijnendijk | Coordinating marketing and manufacturing in eto companies[END_REF][START_REF] Watanapa | Simultaneous price and due date settings for multiple customer classes[END_REF][START_REF] Zorzini | Customer enquiry management and product customization: An empirical multi-case study analysis in the italian capital goods sector[END_REF]. The repeatedly emphasised importance has triggered much research on the subject. However, much of the literature is found to be primarily focused on MTO contexts. Undeniably, firms operating with strategies that are a hybrid of ETO and MTO can be found in practice [START_REF] Rudberg | Manufacturing networks and supply chains: an operations strategy perspective[END_REF][START_REF] Semini | Strategies for customized shipbuilding with different customer order decoupling points[END_REF]. Nevertheless, the primary difference between the two strategies is the engineering aspect, which may introduce uncertainty into the planning environment depending on the level of customisation [START_REF] Zorzini | Customer enquiry management and product customization: An empirical multi-case study analysis in the italian capital goods sector[END_REF]. As a result, delivery date setting approaches applicable in MTO contexts may not demonstrate equivalently satisfactory performance in ETO contexts. The remainder of this section discusses some salient contributions to delivery date setting literature to contextualise the contribution of this paper.

Zorzini et. al. [START_REF] Zorzini | Due date (dd) quotation and capacity planning in make-to-order companies: Results from an empirical analysis[END_REF] studied the delivery date setting process at 15 capital goods manufacturers. They report that majority of the studied firms opted to perform aggregated capacity analysis for quoting delivery dates, as compared to detailed or no workload analysis. While the sampled firms using aggregated capacity analysis are scattered across the spectrum of customisation and complexity, Zorzini et. al. [START_REF] Zorzini | Due date (dd) quotation and capacity planning in make-to-order companies: Results from an empirical analysis[END_REF] point out that the assembly process was found to be a fixed bottleneck resource for all of these firms. However, this might not be the case for all ETO environments. It was also not found to be true for our case study context where historically, different machining resources have been observed to be the bottleneck resource for different products. Further, among the firms sampled by Zorzini et. al. [START_REF] Zorzini | Due date (dd) quotation and capacity planning in make-to-order companies: Results from an empirical analysis[END_REF], it is also not clear how firms across different levels of customisation differently manage uncertainties regarding product and process specification. Their proposed model assumes that average lead times can be estimated based on past orders, but the validity of this assumption can be expected to vary with the level of customisation and size of the product portfolio.

Ebadian et. al. [START_REF] Ebadian | Hierarchical production planning and scheduling in make-to-order environments: reaching short and reliable delivery dates[END_REF] propose a heirarchical PPC model to support delivery date setting, which assumes that incoming orders can be prioritised according to the service level desired for different customers. Carvalho et. al. [START_REF] Carvalho | Tactical capacity planning in a realworld eto industry case: A robust optimization approach[END_REF] present an optimisation approach developed for tactical capacity planning under uncertainty in an ETO firm, calling for exploration of the validity of the proposed approach in other ETO contexts. As outlined above through the discussed literature, context-specificity can be observed as a common feature among most research on delivery date setting in ETO. While these are valuable contributions to theory, generalised validity of the findings is only limited. This highlights the contingent nature of the applicability of delivery date setting methods, as also argued by Zorzini et. al. [START_REF] Zorzini | Customer enquiry management and product customization: An empirical multi-case study analysis in the italian capital goods sector[END_REF] for taking a contingency theory approach to studying customer enquiry management. Therefore, the case study presented in this paper assesses the applicability of basic theoretical methods in an ETO setting, while explicitly demonstrating the approach, which can be replicated in other ETO contexts for assessing applicability of seemingly relevant methods.

Rough-cut Capacity Planning

Capacity planning refers to "the process of determining the amount of capacity required to produce in the future" [START_REF]APICS Dictionary Fourteenth edition[END_REF]. It entails different activities at different hierarchical levels of PPC, such as strategic or long-term resource requirement planning, rough-cut capacity planning (RCCP) on a tactical or master production scheduling (MPS) level, and detailed capacity requirements planning (CRP) at the material requirements planning (MRP) level [START_REF]APICS Dictionary Fourteenth edition[END_REF]. As emphasised frequently in literature, delivery date setting is most commonly observed on a tactical level of PPC [START_REF] Carvalho | Tactical capacity planning in a realworld eto industry case: An action research[END_REF][START_REF] Hans | A hierarchical approach to multi-project planning under uncertainty[END_REF][START_REF] Stevenson | A review of production planning and control: the applicability of key concepts to the make-to-order industry[END_REF][START_REF] Zorzini | Due date (dd) quotation and capacity planning in make-to-order companies: Results from an empirical analysis[END_REF], and therefore, RCCP methods can be classified as most relevant for delivery date setting. This section briefly presents three basic RCCP methods that are later assessed for their fit to the case environment and for their capability to support delivery date setting. The methods are explained using descriptions from Vollman et. al. [START_REF] Vollmann | Manufacturing Planning and Control Systems[END_REF] and the APICS dictionary [START_REF]APICS Dictionary Fourteenth edition[END_REF].

Capacity planning using overall factors (CPOF). Using overall factors for RCCP is a relatively simple approach where the MPS is used as the starting point. The scheduled quantities of end products in different time buckets serve as basis for estimating the capacity requirements for different work centres, by applying historical percentages to the total number of hours for producing the item. This essentially gives the estimated workload requirement from different work centres for producing the scheduled quantities, without consideration of the actual timing of the capacity requirement projections. The advantages offered by this approach are minimal data requirements and computational simplicity.

Capacity planning using capacity bills (CPCB). Using capacity bills follows a similar computational procedure as CPOF, but differs in the data requirements. Instead of using historical percentages for different work centres, as in CPOF, CPCB requires bill-of-material (BOM) and routing data with labour-hour or machine-hour data for each operation. Not unlike CPOF, CPCB also does not consider the production lead times, and capacity requirements are not timephased.

Capacity planning using resource profiles (CPRP). Among the three basic RCCP techniques, using resource profiles for capacity planning is the most sophisticated. It takes production lead times into account, and provides timephased projections of capacity requirements. Using the MPS, BOM and routing data, capacity requirements are estimated as in CPCB. These estimates are further utilised to develop time-phased projections by offsetting the capacity requirements.

Case study

The case company is a supplier of equipment for the maritime industry. The main products and spare parts for previously sold products constitute the manufacturing activities, which are undertaken at the same facility. Their products can be broadly classified into four types, where every type has various sub-types and size alternatives that essentially serve as templates for tailoring the product designs to specific customer requirements. The cumulative production volume of different product types is typically below 500 units per year. Presently, at the customer enquiry stage, production delivery dates are determined using a method that is a hybrid of CPOF and CPRP methods. The product templates and experience from past projects are used to estimate the total workload for a project and consequently, workloads for different work centres. These workloads are then offset in time to get time-phased projections of capacity requirements, and delivery dates are estimated based on these projections. Maintaining delivery precision for the production department has been challenging, and has worsened in recent years with widening of the product portfolio and variations in the product mix of demand.

Methodology

The purpose of the case study was to better understand the challenges in setting delivery dates in ETO environments. As it was revealed during earlier collaboration that the case company recognise delivery date setting as one of the challenging managerial tasks, the firm served as an appropriate context for this case study. The case sample presented in this paper is limited to a single indepth case study due to space constraints and can be expanded in the future to test generalisability of the findings. Figure 1 shows the underlying research framework for the case study process, which can be utilised in future studies to assess fit of planning activities or PPC systems towards planning environments.

Assessing fit

The case company is mapped using Buer et. al.'s [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF] framework, where characteristics of a planning environment are classified into product, market and manufacturing process related variables. The fit of the RCCP methods is then assessed towards the clustered environmental variables and delivery date setting, based on a combination of literature synthesis and logical assumptions, as shown in Table 1. The planning environment is characterised as follows.

Product-related variables. CODP placement: ETO-MTO; level of customisation: some specifications are allowed; product variety: high; BOM complexity: 3-5 levels; product data accuracy: low-medium; level of process planning: fully designed process.

Market-related variables. P/D ratio < 1; demand type: customer order allocation; source of demand: customer order; volume/frequency: few large customer orders per year; frequency of customer demand: unique-sporadic; time distributed demand: annual figure; demand characteristics: dependent; type of procurement ordering: order by order procurement; inventory accuracy: medium. The market-related variables can be further distinguished into demand-related (from P/D ratio to demand characteristics) and supply-related variables (type of procurement and inventory accuracy).

Manufacturing process characteristics. Manufacturing mix: mixed products; shop floor layout: fixed-position -cell; type of production: single-unit -smallseries; throughput time: months -weeks; number of major operations: high; batch size: equal to customer quantity; frequency of production order repetition: infrequent repetition; fluctuations of capacity requirements: medium; planning [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF] render CPOF unreliable for the case environment. This is consistent with CPOF's success criteria of flat BOM [START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF][START_REF] Vollmann | Manufacturing Planning and Control Systems[END_REF].

CPCB reflects a poor fit to the product characteristics. This is primarily due to relatively low product data accuracy, which is detrimental to the use of CPCB [START_REF] Fogarty | Production and inventory management[END_REF]. Product data entails detailed BOM and routing data, the availability and reliability of which, are integral to the success of CPCB [START_REF] Burcher | Effective capacity planning[END_REF].

CPRP reflects a poor fit to the product characteristics. Performance of CPRP, like CPCB, relies on the availability and reliability of detailed BOM, routing data and time standards, accuracy of which is significantly low during RCCP. Customisation and high product variety indirectly contribute to this [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF].

Market characteristics

CPOF reflects a poor fit to the market characteristics, and more specifically, to the demandrelated variables such as customer-allocated and customer order-originated demand, low frequency and uniqueness of demand. While a P/D ratio < 1 is a favourable situation for the fit of CPOF [START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF], the overall fit is rendered poor by other majority of variables.

CPCB reflects a poor fit to the market characteristics, and specifically, to demand-related characteristics. However, these characteristics affect the fit of CPCB indirectly rather than directly. Dependent demand influences time distribution of demand [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF], which in turn influences the CODP placement [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF], and leading to the unavailability of BOM and route during RCCP.

CPRP reflects a poor fit to the market characteristics of the planning environment. Demand-related characteristics that cause CPCB to be a poor fit to the planning environment, also cause CPRP to have a poor fit. None of the discussed RCCP methods are influenced by supplyrelated characteristics, as on-hand stocks of components are not considered in any of them [START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF].

Process characteristics

CPOF reflects a poor fit to the manufacturing process due to environmental characteristics such as nonhomogeneous manufacturing mix [START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF], production in single-unit or small series, long throughput times, relatively high number of operations and planning points, and infrequent repetition of production orders.

CPCB reflects a poor to neutral fit to the process characteristics of the planning environment. Lack of homogeneity in the manufacturing mix does not cause any particular challenges in using CPCB, as it uses detailed bill of resources [START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF]. Large number of major operations is expected to negatively influence the CPCB's reliability. CPRP reflects a neutral to good fit to the manufacturing process characteristics of the planning environment. A high number of major manufacturing operations is expected to increase the importance of offsetting the capacity requirements in time for reliable projections, thus qualifying CPRP to have the best fit.

DD setting

Using CPOF for RCCP is expected to provide unreliable delivery dates, as it does not offset capacity requirements in time.

Using CPCB for RCCP is expected to provide unreliable delivery dates, as it does not offset capacity requirements in time.

Using CPRP is expected to give reliable delivery dates, as it offsets capacity requirements in time to get time-phased projections. points: medium; set-up times: medium; sequencing dependency: medium; part flow: one-piece/lot-wise; material flow complexity: medium; capacity flexibility: low; load flexibility: medium.

Conclusion

The studied case environment demonstrated an overall low applicability of the theoretical RCCP methods. It can be concluded that the fit of RCCP methods to the planning environment is relatively less influenced directly by the manufacturing process as compared to the market and product characteristics. The case study also revealed that existing mapping frameworks [START_REF] Buer | Strategic fit of planning environments: Towards an integrated framework[END_REF][START_REF] Jonsson | The implications of fit between planning environments and manufacturing planning and control methods[END_REF][START_REF] Olhager | Linking manufacturing strategy decisions on process choice with manufacturing planning and control systems[END_REF][START_REF] Schönsleben | Integral logistics management: planning and control of comprehensive supply chains[END_REF] lack 'production monitoring accuracy' as an environmental variable. Production monitoring accuracy refers to the accuracy of data that is used to monitor actual production with respect to planned production. The availability and reliability of this data was found to play a vital role in the success of the delivery date setting process by providing information about available capacity in different planning periods, and was found to be a factor in the low delivery precision observed at the case company. More comprehensive investigation of the influence of production monitoring data on delivery date setting is a possibility for future work.

Fig. 1 .

 1 Fig. 1. Research framework underlying the case study

Table 1 .

 1 Assessing fit of RCCP methods towards planning environment and delivery date setting.

		Overall factors	Capacity bills	Resource profiles
		CPOF reflects a poor fit
	Product characteristics	to the product charac-teristics. Values of mu-tually causative variables such as CODP, customisa-tion, product variety, BOM complexity and data accu-racy


Mihai Neagoe
email: mihai.neagoe@utas.edu.au

Hans-Henrik Hvolby

Sadegh Taskhiri

Paul Turner

Understanding the Impact of User Behaviours and Scheduling Parameters on the Effectiveness of a Terminal Appointment System Using Discrete Event Simulation

Keywords: Transport management, supply chain collaboration, user requirements, congestion management

This research improves understanding of the impact of specific types of truck driver behaviour and temporal scheduling on the effectiveness of a terminal appointment system. A discrete event simulation model of a bulk cargo marine terminal is developed to analyse parameters related to driver behaviour (punctuality and proportion of planned appointments) and temporal scheduling (appointments per time window and time window spacing) on truck flows and turnaround times at the terminal. The model is based on an Australian wood chip export marine terminal currently experiencing significant truck congestion. The terminal operator and stakeholders have expressed interest in the implementation of an appointment system to address this issue. The modelling presented in this research was used to inform their investigation into developing an appointment system solution.

Simulation results indicate that the proportion of planned appointments, used as a proxy for the appointment system use, has a significant impact on truck turnaround times. Greater truck arrival punctuality only marginally improves truck turnaround times. Interestingly most optimization approaches continue to focus on improving punctuality through service rules or financial penalties in order to achieve optimal turnaround times. However, the additional cost in terms of complexity or assumptions for optimal solutions against non-optimal approaches are rarely weighed in terms of dividends of the marginal improvements generated. By involving terminal users (drivers and transporters) in the design of an appointment system and its scheduling parameters, terminal operators can significantly improve appointment system use and effectiveness by increasing the probability of positive users' behaviours.

Introduction

Terminal appointment systems are one of the most effective methods to manage congestion and communicate with multiple users at marine terminals. The system's performance in terms of truck turnaround times and equipment use efficiency can be affected by the systems' parameters and by the behaviours of the terminal users. System parameters can include the lead time for selecting an appointment time, appointment window length [START_REF] Chen | Managing truck arrivals with time windows to alleviate gate congestion at container terminals[END_REF], number of appointments per time-window [START_REF] Torkjazi | Truck appointment systems considering impact to drayage truck tours[END_REF][START_REF] Huynh | Robust Scheduling of Truck Arrivals at Marine Container Terminals[END_REF], appointment spacing, and truck servicing rules [START_REF] Li | Disruption management for truck appointment system at a container terminal: A green initiative[END_REF] . User behaviours can be modelled by the probability that drivers miss appointments, arrive un-appointed [START_REF] Huynh | Robust Scheduling of Truck Arrivals at Marine Container Terminals[END_REF], or their arrival punctuality [START_REF] Li | Disruption management for truck appointment system at a container terminal: A green initiative[END_REF][START_REF] Ramírez-Nafarrate | Impact on yard efficiency of a truck appointment system for a port terminal[END_REF]. The system parameters are often determined by optimization approaches, either linear programming [START_REF] Chen | Managing customer arrivals with time windows: a case of truck arrivals at a congested container terminal[END_REF], queuing theory [START_REF] Guan | Modeling Gate Congestion of Marine Container Terminals, Truck Waiting Cost, and Optimization[END_REF] or through simulation [START_REF] Huynh | Improving efficiency of drayage operations at seaport container terminals through the use of an appointment system[END_REF]. Some user behaviours are seen as disruptions to the optimal system solution that must be dealt with. Authors recommend the use of penalty systems to enforce compliance with the appointment system schedules [START_REF] Ramírez-Nafarrate | Impact on yard efficiency of a truck appointment system for a port terminal[END_REF] while others introduce more complex truck service rules to maintain a high level of system efficiency [START_REF] Li | Disruption management for truck appointment system at a container terminal: A green initiative[END_REF]. Although enforcement and system rules approaches have merit in moderating users' behaviours they suffer from a series of shortcomings:

• The information required for complex system rules may be difficult to collect in realtime, making implementations in real-life scenarios challenging; • Neither approach (enforcement nor system rules) is based on understanding of the underlying causes behind the users' behaviours. This can lead to unexpected outcomes such as system misuse [START_REF] Morais | Terminal Appointment System Study[END_REF]. • Users' involvement in decisions regarding the system's parameters and functionality is typically limited [START_REF] Huynh | Truck Appointment Systems[END_REF] . The potential consequences of the lack of involvement in decision making is explained by Ackoff [START_REF] Ackoff | The art of problem solving[END_REF]: "In problems, the solution to which involve the reactions of others, their participation in the problem-solving process is the best protection against unexpected responses […] A failure to consult others who have a stake in our decision is often seen as an act of aggression".

This research therefore introduces a discrete event simulation model of a bulk cargo marine terminal is developed to analyse parameters related to driver behaviour (punctuality and proportion of planned appointments) and temporal scheduling (appointments per time window and time window spacing) on truck flows and turnaround times at the terminal. The modelling results are then used to support the involvement of terminal users prior to the implementation of an appointment system to understand their requirements, consequences on the users' behaviours and the consequences of the users' behaviours on the effectiveness of the system.

The Wood Chip Export Terminal Field Site

The marine terminal on which the modelling work is based is an Australian wood chip export facility. Wood chips are processed from logs in facilities located in close proximity of the terminal, and delivered to the terminal. Wood chips are stored at the terminal and subsequently loaded on dry bulk cargo ships belonging to international pulp and paper producers. The terminal receives approximately 1.6 million tons of wood chips and handles roughly 52,000 truck deliveries per year. The terminal's customers outsourced the transportation task between their production sites and the terminal to a stable base of transport contractors. This setup creates a small and relatively closed transport system. At the terminal, trucks are first weighed at a weigh-bridge. Next trucks drive to an on-dock staging area where they wait for one of two unloading ramps become available. Once a ramp is available, trucks are unloaded, then drive to a weigh-bridge to be weighed once more. The terminal and supply chain setup have been explored in greater detail in previous work [START_REF] Neagoe | Exploring congestion impact beyond the bulk cargo terminal gate[END_REF].

The terminal was experiencing truck significant congestion. The consequences of congestion ranged from increased costs for transporters, increased supply chain uncertainty for terminal customers, and additional staff and maintenance scheduling for the terminal operator. The stakeholders were considering a range of potential options to mitigate congestion and expressed interest in an appointment system to manage truck flows at the terminal. The researchers developed a simulation model to further understanding regarding the potential consequences of different system parameters and behaviours can have on truck waiting and turnaround times and ultimately inform the stakeholders' investigation into the development of an appointment system solution.

Data Collection and Simulation Model

Data on truck arrivals were collected from the terminal weigh-bridge database and geolocation data from GPS units mounted on several trucks. These data were supplemented by on-site observations by the research team and discussions with stakeholders. The GPS data were used in conjunction with geo-fences setup around terminal infrastructure that quantified the duration of truck visits at every stage. The truck arrival frequency and geo-fence visit durations data were analysed with Arena Input Analyzer to generate distributions. Approximately 7 months of truck arrival data and 3 months of geo-location data were used. The fitted distributions formed the input for the discrete-event simulation model. The simulation model, presented in Table 1, comprises of two stages: the truck arrival generator and the truck processing. The lack of complexity in the model's design is purposeful, as the model and results primarily served as a discussion point with the terminal's and its users' staff which had a diverse demographic and socio-economic backgrounds. The use of a relatively simplistic model aimed to improve its accessibility to a broader audience. The model is implemented in Python programming language.

In the first stage, the truck arrivals are generated. The planned arrivals parameter indicates the percentage of appointed arrivals and walk-ins. The arrival time of the truck is then calculated based on whether or not the respective truck has an appointment. A time-window spacing coefficient is applied on each one-hour interval (e.g. a 6-minute spacing means that within a 60-minute interval, the first 6 minutes do not have any appointments). The truck arrival list is then sorted in ascending order of arrival times and fed to a generator function which creates truck objects with payload, capacity, product characteristics. In the second model stage, the truck objects are then processed by the terminal object. The two-stage approach is required as trucks are served on a first-come, firstserved basis, irrespective of their appointment time. While other priority rules are considered in the literature [START_REF] Li | Disruption management for truck appointment system at a container terminal: A green initiative[END_REF], The first-come, first served approach was considered in this model for its lower level of complexity. The second stage is largely based on modelling presented in previous work [START_REF] Neagoe | Exploring the Role of Information Systems in Mitigating Gate Congestion Using Simulation: Theory and Practice at a Bulk Export Terminal Gate[END_REF]. The weigh-out and unloading ramp service times are stochastically determined from distributions fitted from GPS data. The weigh-in in stage is held constant at 1 minute/truck. the drive times from the weigh-bridge and unloading ramp and back are held constant at 1 and 2 minutes respectively. The total truck processing times including the waiting are the summarized and output.

The second simulation stage follows closely the unloading process observed by the research team at the terminal and described in Section 2. The simulation model and its logic have been presented and discussed with terminal staff to improve the accuracy and validity of the representation.

Scenario Analysis: System Parameters and User Behaviour

The four factors included in the scenario analysis were driver behaviours (punctuality, missed and unplanned appointments) and system parameters (appointments per time window and appointment buffers). These factors were adapted from the appointment systems literature. The factors included are:

• Number of appointments per time window. Two values were included for each one-hour time window, 6 (low frequency) and 8 appointments (high frequency). In the cases where all appointments were unplanned, an inter-arrival time distribution that would provide similar arrival frequency was used. • Time window spacing. Each time window contains the same number of appointments but has a starting buffer period. The three values included were 0-, 6-, and 12minutes/time window. • Planned/Unplanned arrivals. The proportion of planned and unplanned arrivals was varied in 25% increments between 0% (all un-appointed arrivals) and 100% (all appointed arrivals). • Arrival punctuality. Punctuality was modelled by adding a stochastic component to each appointed arrival time. Three normal distributions were used to simulate truck arrival punctuality, similar to the approach presented in [START_REF] Ramírez-Nafarrate | Impact on yard efficiency of a truck appointment system for a port terminal[END_REF]: (1) High: 95% of arrivals are within +/-5 min. from appointment time {N(0, 2.5)}, (2) Medium: 68% of arrivals are within +/-5 min. from appointment time {N(0, 5)}, (3) Low: 38% of arrivals are within +/-5 min. from the appointment time {N(0,10)}, The scenario analysis included combinations of the 4 factors and resulted in 74 scenarios. Each scenario was run 20 times and each iteration simulated a year of operations.

Modelling Results

The results of the simulation model in terms of average truck turnaround time for the scenarios tested are presented in Fig. 1. The scenario where an average of 6 trucks per hour arrive uncoordinated resembles the situation empirically observed at the terminal (yellow diamond symbol). The modelled turnaround time in this scenario was approximately 23.5 minutes per truck. This turnaround time figure is similar to the empirically observed average turnaround time. The turnaround time in this scenario includes an average waiting time of 6 minutes per truck, the majority of which accrued waiting for an unloading ramp to become available. The sequential nature of the processes at the terminal means that reductions in turnaround time arise primarily from a reduction in waiting times. Since the terminal's infrastructure is fixed, most benefits accrued from the reduction in waiting and turnaround times directly benefit terminal users.

The change from a low to high frequency truck arrivals generates a 20% increase in throughput, from 1.6 to 2 million tons. The change in truck arrival frequency is represented in Fig. 1 by the change in symbol colours, from yellow to blue. This increase is also met with a doubling of truck turnaround times, most likely due to throughput getting closer to the terminal's maximum physical capacity. In the higher arrival frequency scenarios, an improvement in turnaround times of 25 to 30%, is generated if at least 25% of arrivals are scheduled. The turnaround time improvement gradually decreases as a higher percentage of trucks arrive appointed. When all trucks arrive with appointments, the expected turnaround time improvement is between 37 and 46% compared to the scenario where all appointments are unplanned, depending on arrival punctuality. In the low arrival frequency scenarios, the marginal improvement with each increment of planned appointment proportion remains relatively constant, between 3 and 5%, depending on the arrival punctuality. The impact of low arrival punctuality increases with the proportion of appointed truck arrivals. Punctuality is represented in Fig. 1 by the change of symbol type and darkening colour tones. Low punctuality halves the effectiveness of the appointment system compared to high punctuality in virtually all low arrival frequency scenarios. In high arrival frequency scenarios, the impact of low punctuality is less considerable, between 16-20% compared to high punctuality. Time window spacing (not depicted in Fig. 1) has limited impact on truck turnaround time averages. The introduction of 6-or 12-minute spacing between each time window increases turnaround times by 2% compared to no spacing. The next section discusses the simulation results in the context of the extant literature and of the potential applications.

Discussion and Future Research

Simulation results indicate that truck turnaround times increase non-linearly with throughput which corroborates literature findings [START_REF] Neagoe | Exploring congestion impact beyond the bulk cargo terminal gate[END_REF][START_REF] Guan | Container terminal gate appointment system optimization[END_REF]. Particularly in the high frequency arrival scenarios, a small proportion of known, even less punctual, arrivals, can have a significant impact on turnaround times, similar to [START_REF] Chen | Terminal appointment system design by non-stationary M(t)/E k/c(t) queueing model and genetic algorithm[END_REF]. Finally, the impact of arrival punctuality, while an important influencing factor for turnaround times, was not the most important determining factor in turnaround times.

Modelling results revealed that the factor with the most influence on turnaround times was the use of the system. If the potential achievable reduction in turnaround times through the use of the terminal appointment system is not fully appreciated by its users, it is likely that the system use will not be as high as expected. This situation can create a vicious circle in which low use reduces the impact of the appointment system on turnaround times therefore leading to lower system use. Therefore, it is paramount to involve users in the design of appointment systems and particularly in determining its operating parameters to encourage system use. While not directly considered in this paper, it is important to acknowledge that the appointment system usability and adoption, among other factors can also influence the system use. Design for usability should also be central in design workshops.

The impact of arrival punctuality was important but considerably less than that of appointment system use. Much of the extant literature focuses on optimizing costs [START_REF] Chen | Managing truck arrivals with time windows to alleviate gate congestion at container terminals[END_REF][START_REF] Guan | Container terminal gate appointment system optimization[END_REF] in which case, low truck arrival punctuality can increase terminal and user costs and consequently, the optimal solution. By focusing solely on optimal solution, however, its potential cost in complexity or assumptions compared to near-optimal solutions is rarely weighed against the additional benefits an optimal solution can generate. To ensure compliance from this perspective, variations in service rules [START_REF] Li | Disruption management for truck appointment system at a container terminal: A green initiative[END_REF] or financial penalties have been proposed. However, the literature rarely considers whether the impact of disruptions caused by driver behaviours are sufficiently significant to warrant the introduction of complex service rules and financial penalties variations while risking to reduce the appointment system use.

Future research aims to use the findings from the scenario analysis in conducting participatory design workshops with the terminal operator and its users. The collaboration with the terminal operator is part of an ongoing multiple case-study investigation on mechanisms and technologies to address maritime terminal land-side congestion. The simulation and participatory design approach will be extended to the other case studies to seek replicating the results or identifying differentiating factors.

Conclusion

This research introduced a discrete event simulation model of a bulk cargo marine terminal is developed to analyse parameters related to driver behaviour (punctuality and proportion of planned appointments) and temporal scheduling (appointments per time window and time window spacing) on truck flows and turnaround times at the terminal. Modelling findings highlight the importance of involving terminal users in the design of the appointment system and its parameters to ensure its use and consequently its effectiveness in reducing truck turnaround times. Arrival punctuality appears to have less impact than the appointment system use. However, the lack of punctuality is typically financially penalized which tends to cause tensions between terminals and transporters. Shifting focus from enforcing punctuality towards ensuring use of system may assist have a more positive impact on turnaround times.

In the context of this research it is important to acknowledge some of its limitations. The model scope is limited to the terminal gate and unloading operations as insufficient data were available to generate a model of the entire chain. Bulk cargo marine terminal operations are typically less complex than those observed in container terminals, on which the majority of the terminal appointment systems literature is based. It is likely that insights generate in this research can be, at least in part, transferrable to other bulkcargo and container marine terminals.

This research is part of an ongoing project undertaken in Australia funded by the Australian Research Council through the Industrial Transformation Research Program.

Fig. 1 .

 1 Fig. 1. Simulation model scenario analysis results in terms of average truck turnaround times, truck arrival punctuality, and percentage of planned arrivals

Table 1 .

 1 Simulation model stages and steps

	Step	Stage 1 -Truck Arrival Generator
	1.1	Random choice of appointed/un-appointed arrival;
	1.2 A	If un-appointed arrival: arrival time = previous truck arrival time +
		inter-arrival time (gamma, k = 1.49, θ = 6.97);
	1.2 B	Else appointed arrival: arrival time = previous app. time + spacing +
		appointment interval + punctuality;
	1.3	Sort truck list based on truck arrival times;
	1.4	Generate truck object (payload, capacity, product and arrival times);
	Step	Stage 2 -Truck Processing
	2.1	Next truck object from arrival list;
	2.2	Weigh-in at Weigh-bridge (1 min);
	2.3	Drive to Unloading area (1 min);
	2.4 A	If any unloading ramp free and available: Unloading
		lognormal (m = 5.16, s = 3.97);
	2.4 B	Else no unloading ramp free and available: Accrue waiting time;
	2.5	Drive to Weigh-bridge -2 min;
	2.6 A

If weigh-bridge free: Weighing -normal (µ = 3.46, s = 1.68); 2.6 B Else weigh-bridge not free: Accrue waiting time; 2.7 Calculate total service and waiting times for truck;


Xuehong Gao
email: gao2016@pnu.edu

A Stochastic Optimization Model for Commodity Rebalancing under Traffic Congestion in Disaster Response

Keywords: Commodity Rebalancing, Emergency Logistics, Stochastic Optimization, Traffic Congestion

After a large-scale disaster, the emergency commodity should be distributed to relief centers. However, the initial commodity distribution may be unbalanced due to the incomplete information and uncertain environment. It is necessary to rebalance the emergency commodity among relief centers. Traffic congestion is an important factor to delay delivery of the commodity. Neither the commodity rebalancing nor traffic congestion is considered in previous studies. In this study, a two-stage stochastic optimization model is proposed to manage the commodity rebalancing, where uncertainties of demand and supply are considered. The goals are to minimize the expected total weighted unmet demand in the first stage and minimize the total transportation time in the second stage. Finally, a numerical analysis is conducted for a randomly generated instance; the results illustrate the effectiveness of the proposed model in the commodity rebalancing over the transportation network with traffic congestion.

Introduction

In the last decade, large-scale natural disasters have occurred frequently. Such natural disasters pose serious threats to the sustainable development of society, economy, and ecology. A large number of people are impacted significantly and a lot of assets are damaged severely. Upon these disasters, relief centers should be determined and emergency commodity should be distributed to these relief centers to provide basic life support [START_REF] Akgün | Risk based facility location by using fault tree analysis in disaster management[END_REF][START_REF] Chen | The regional cooperation-based warehouse location problem for relief supplies[END_REF][START_REF] Gao | A Hybrid Genetic Algorithm For Multi-emergency Medical Service Center Location-allocation Problem In Disaster Response[END_REF]. However, because the initial commodity distribution may be unbalanced due to the incomplete information and uncertain environment, each relief center may have a surplus or a shortage. In such a situation, the surplus should be redelivered to other unmet relief centers to make the efficient use of the commodity. In the transportation process to rebalance the commodity, traffic congestion is considered, because large-scale disasters usually trigger huge demand and service in the disaster area, which makes the mobile network operators no longer able to provide demand and service sufficiently. Hence, tasks to rebalance the commodity over the transportation network with traffic congestion are very difficult to accomplish under demand and supply uncertainties. Against the backdrop of difficulties, the aim of this study is to formulate this commodity rebalancing problem with stochastic elements considering traffic congestion and solve it using mathematical programming. The rest of this paper is organized as follows. Section 2 reviews previous studies and highlights the main differences from the previous studies. Section 3 provides a problem description, a stochastic optimization model, and a solution method. Then, the application of the proposed model in a numerical instance is shown where the results are presented and discussed in Section 4. Finally, Section 5 concludes this study with contributions and further directions.

2

Literature review

Humanitarian logistics research has attracted growing attention as human suffering and economic loss continue to increase. In the past, many studies mainly surveyed on the humanitarian logistics for disaster management. Caunhye, Nie [START_REF] Caunhye | Optimization models in emergency logistics: A literature review[END_REF] reviewed optimization models in emergency logistics, which were divided into the following parts: facility location, relief distribution, casualty transportation, and other operations. Galindo and Batta [START_REF] Galindo | Review of recent developments in OR/MS research in disaster operations management[END_REF] reviewed recent OR/MS research in disaster operations management and provided future research directions. Here, the related studies are reviewed on the commodity distribution, commodity rebalancing (also referred to as redistribution), and humanitarian logistics under the consideration of traffic congestion in disaster response. Dessouky, Ordonez [START_REF] Dessouky | Rapid distribution of medical supplies[END_REF] argued two important issues to solve facility location and vehicle routing problems that could ensure the rapid distribution of medical supplies in a logistics network. Jotshi, Gong [START_REF] Jotshi | Dispatching and routing of emergency vehicles in disaster mitigation using data fusion[END_REF] developed a robust methodology for dispatching and routing emergency vehicles in a post-disaster environment with the support of data fusion. Chen and Yu [START_REF] Chen | Network based temporary facility location for the Emergency Medical Services considering the disaster induced demand and the transportation infrastructure in disaster response[END_REF] applied an integer programming and a network-based partitioning to determine temporary locations for on-post EMS facilities after the disaster. Al Theeb and Murray [START_REF] Al Theeb | Vehicle routing and resource distribution in postdisaster humanitarian relief operations[END_REF] presented a mathematical programming model to deliver goods, disaster victims, and volunteer workers through a road network. Gao and Lee [START_REF] Gao | A Stochastic Programming Model for Multi-commodity Redistribution Planning in Disaster Response[END_REF] proposed a stochastic programming model to facilitate the multi-commodity redistribution process under uncertainty. Gao and Lee [START_REF] Gao | A two-stage stochastic programming model for commodity redistribution under uncertainty in disaster response[END_REF] proposed a two-stage stochastic programming model to design a multimodal transportation network for multi-commodity redistribution. Traffic congestion is one of the most important factors to delay humanitarian logistics and contribute to increasing the time of delivery and the number of injuries after disasters [START_REF] Campos | A method for evacuation route planning in disaster situations[END_REF]. Transportation time may also be affected by traffic congestion on the roads due to various reasons [START_REF] Jotshi | Dispatching and routing of emergency vehicles in disaster mitigation using data fusion[END_REF]. Feng and Wen [START_REF] Feng | A fuzzy bi-level and multi-objective model to control traffic flow into the disaster area post earthquake[END_REF] pointed out that the roadway systems usually got different levels of damage, and thus the roadway capacity was reduced, which caused traffic congestion after a severe earthquake. Nagurney, Flores [START_REF] Nagurney | A Generalized Nash Equilibrium network model for post-disaster humanitarian relief[END_REF] proposed a network model which consisted of multiple nongovernmental organizations who sought to supply multiple demand points with relief items post a disaster to reduce the convergence and even congestion. To estimate the traffic congestion, the travel time function suggested in the traditional Bureau of Public Roads (BPR) curve [START_REF] Roads | Traffic assignment manual for application with a large, high speed computer[END_REF] provides the relationship between the link travel time and the volume of traffic on a highway network, which is shown in the following functional form:

𝐹𝐹(𝑥𝑥) = 𝐹𝐹 0 • [1.0 + 𝛼𝛼 • � 𝑥𝑥 𝐶𝐶 � 𝛽𝛽 ]. (1)
where 𝐹𝐹(𝑥𝑥) is the link travel time when the link-flow rate is 𝑥𝑥, 𝐹𝐹 0 is the free flow travel time, 𝐶𝐶 is the practical link capacity, and 𝛼𝛼 ≥ 0, 𝛽𝛽 ≥ 0 are parameters. This BPR function is widely used in the transportation planning field [START_REF] Florian | Traffic equilibrium methods[END_REF].

In spite of many studies that have been dedicated to humanitarian logistics after the disasters, few of them concern the commodity rebalancing process. To fill this research gap, this study focuses on the commodity rebalancing problem that incorporates traffic congestion. The novelty and contribution can be summarized as follows. A stochastic mixed-integer nonlinear programming model is proposed to formulate this commodity rebalancing problem, which has never been studied before. Then, a linearization method is also proposed to reformulate the nonlinear model so that it can be solved in the optimization solver CPLEX. Finally, a numerical instance is carried out and some managerial insights are obtained.

3

Problem and Methodology

Problem Statement

A transportation network which consists of a number of roads and relief centers is considered in this study. An initial commodity distribution has been delivered to these relief centers. Upon the disaster, the surplus commodity at some relief centers needs to be redelivered to other unmet relief centers. It is difficult to determine how much of commodity should be delivered and received at each relief center, which makes the supply and demand uncertain. In this study, a scenario-based approach is applied for uncertain elements, which are represented in terms of a number of discrete realizations of stochastic quantities. Generally, in a demand or supply relief center, there is a set of scenarios 𝛯𝛯. For a particular scenario 𝜉𝜉 ∈ 𝕊𝕊, there is a probability of occurrence 𝒫𝒫(𝜉𝜉), such that 𝒫𝒫(𝜉𝜉) ≥ 0 and ∑ 𝒫𝒫(𝜉𝜉) = 1

𝜉𝜉∈𝕊𝕊

. In this study, two assumptions are made: (i) each relief center is a separate unit in term of the possible quantities of demand or supply; (ii) the available paths with background traffic-flow rates are given.

In light of the above requirements, this study develops a two-stage stochastic mixedinteger nonlinear programming model for the commodity rebalancing problem. The objective functions are to minimize the expected total weighted unmet demand in the first stage and minimize the total transportation time in the second stage.

Model Formulation

The problem is modeled using the following notations. Vehicle number from relief centers 𝑠𝑠 to 𝑑𝑑. The completed formulation is given as the following two-stage stochastic mixedinteger nonlinear programming model. In the first stage, the objective function is defined as follows

𝛹𝛹 1 = ∑ ∑ 𝑝𝑝 𝑑𝑑 𝜉𝜉 𝜉𝜉∈𝕊𝕊 • 𝑍𝑍 𝑑𝑑 • max {𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 𝑑𝑑∈𝒟𝒟 , 0} + ∑ ∑ 𝑝𝑝 𝑠𝑠 𝜉𝜉 • 𝜉𝜉∈𝕊𝕊 𝑍𝑍 𝑠𝑠 • max {𝑑𝑑 𝑠𝑠 -𝑜𝑜 𝑠𝑠 𝜉𝜉 , 0} 𝑠𝑠∈𝒮𝒮 (2)
To remove the MAX function in (2) and realize the MAX function, the following two auxiliary binary variables are introduced into the model.

𝓅𝓅 𝑑𝑑 𝜉𝜉 = � 1 if 𝑟𝑟 𝑑𝑑 is smaller than 𝑖𝑖 𝑑𝑑 𝜉𝜉 0 otherwise ∀ 𝑑𝑑 ∈ 𝒟𝒟, 𝜉𝜉 ∈ 𝕊𝕊, (3)
𝓆𝓆 𝑠𝑠 𝜉𝜉 = � 1 if 𝑑𝑑 𝑠𝑠 is greater than 𝑜𝑜 𝑠𝑠 𝜉𝜉 0 otherwise ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝜉𝜉 ∈ 𝕊𝕊. (4)
Then, the commodity rebalancing problem can be formulated as a deterministic optimization model:

Min 𝛹𝛹 1 = ∑ ∑ 𝑝𝑝 𝑑𝑑 𝜉𝜉 • 𝜉𝜉∈𝕊𝕊 𝑍𝑍 𝑑𝑑 • (𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 ) 𝑑𝑑∈𝒟𝒟 • 𝓅𝓅 𝑑𝑑 𝜉𝜉 + ∑ ∑ 𝑝𝑝 𝑠𝑠 𝜉𝜉 • 𝜉𝜉∈𝕊𝕊 𝑍𝑍 𝑠𝑠 • (𝑑𝑑 𝑠𝑠 -𝑜𝑜 𝑠𝑠 𝜉𝜉 ) • 𝓆𝓆 𝑠𝑠 𝜉𝜉 𝑠𝑠∈𝒮𝒮 (5) s.t. ∑ 𝑑𝑑 𝑠𝑠 𝑠𝑠∈𝒮𝒮 = ∑ 𝑟𝑟 𝑑𝑑 𝑑𝑑∈𝒟𝒟 , (6)
�𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 � + 𝑀𝑀 ≥ 𝑀𝑀 • 𝓅𝓅 𝑑𝑑 𝜉𝜉 ∀ 𝑑𝑑 ∈ 𝒟𝒟, 𝜉𝜉 ∈ 𝕊𝕊, (7)
�𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 � + 𝑀𝑀 ≥ 𝑀𝑀 • 𝓆𝓆 𝑠𝑠 𝜉𝜉 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝜉𝜉 ∈ 𝕊𝕊, (8)
�𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 � ≤ 𝑀𝑀 • 𝓅𝓅 𝑑𝑑 𝜉𝜉 ∀ 𝑑𝑑 ∈ 𝒟𝒟, 𝜉𝜉 ∈ 𝕊𝕊, (9)
�𝑑𝑑 𝑠𝑠 -𝑜𝑜 𝑠𝑠 𝜉𝜉 � ≤ 𝑀𝑀 • 𝓆𝓆 𝑠𝑠 𝜉𝜉 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝜉𝜉 ∈ 𝕊𝕊, (10)
𝑆𝑆 𝑠𝑠 ∆ ≤ 𝑑𝑑 𝑠𝑠 ≤ 𝑆𝑆 𝑠𝑠 ∇ ∀ 𝑠𝑠 ∈ 𝒮𝒮, (11)
𝑅𝑅 𝑑𝑑 ∆ ≤ 𝑟𝑟 𝑑𝑑 ≤ 𝑅𝑅 𝑑𝑑 ∇ ∀ 𝑑𝑑 ∈ 𝒟𝒟, (12)
where objective function [START_REF] Galindo | Review of recent developments in OR/MS research in disaster operations management[END_REF] aims to minimize the expected total weighted unmet demand at relief centers. Constraint (6) guarantees the balance of outgoing and incoming shipments. Constraints ( 7)- [START_REF] Gao | A Stochastic Programming Model for Multi-commodity Redistribution Planning in Disaster Response[END_REF] guarantee that relief centers only account for the unmet demand. Given a general positive number to 𝑖𝑖 𝑑𝑑 𝜉𝜉 -𝑟𝑟 𝑑𝑑 , 𝓅𝓅 𝑑𝑑 𝜉𝜉 is 1, whereas 𝓅𝓅 𝑑𝑑 𝜉𝜉 is 0.

Constraints [START_REF] Gao | A two-stage stochastic programming model for commodity redistribution under uncertainty in disaster response[END_REF] and ( 12) define the decision variables. After the first-stage decision variables are obtained, the second-stage problem can be formulated as follows.

Min 𝛹𝛹 2 = ∑ ∑ 𝑇𝑇 • 𝑛𝑛 𝑠𝑠𝑑𝑑 + ∑ ∑ 𝐷𝐷 𝑠𝑠𝑠𝑠 𝑉𝑉 • �1 + 𝛼𝛼 • � 𝑛𝑛 𝑠𝑠𝑠𝑠 +𝐵𝐵 𝑠𝑠𝑠𝑠 •𝑇𝑇 𝐶𝐶 𝑠𝑠𝑠𝑠 •𝑇𝑇 � 𝛽𝛽 � 𝑑𝑑∈𝒟𝒟 𝑠𝑠∈𝒮𝒮 𝑑𝑑∈𝒟𝒟 𝑠𝑠∈𝒮𝒮 • 𝑛𝑛 𝑠𝑠𝑑𝑑 (13)
𝑛𝑛 𝑠𝑠𝑑𝑑 ≥ 0 & integer ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟, ( 20
) 𝑤𝑤 𝑠𝑠𝑑𝑑 ≥ 0 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟. ( 21
)
where the objective function ( 13) aims to minimize the total transportation time. Constraint ( 14) ensures the total outgoing shipment cannot exceed the available amount at relief center 𝑠𝑠. Constraint [START_REF] Roads | Traffic assignment manual for application with a large, high speed computer[END_REF] ensures that the total incoming shipment should be greater than or equal to the demand at relief center 𝑑𝑑 . Constraint ( 16) guarantees transportation balance. Constraints ( 17) and ( 18) restrict assigned vehicles should be able to deliver the commodity by satisfying both weight and volume capacities. Constraint (19) ensures that assigned vehicles cannot exceed the route capacity. Constraints (20) and ( 21) are nonnegative constraints of variables.

Solution Method

The second-stage objective function is nonlinear when the BPR function is considered.

To linearize the second-stage objective function, two more auxiliary parameters are introduced in this study. The first one is the maximum units of the commodity in one vehicle, which is represented as G = min( 𝐶𝐶𝐶𝐶 𝐶𝐶 ,

𝐶𝐶𝑉𝑉 𝑉𝑉

). The other one is the number of vehicles 𝑥𝑥 from relief centers 𝑠𝑠 to 𝑑𝑑, which is represented as 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 . Because the vehicle number must be an integer, the discrete solution space can be built. The consecutive integer numbers are used to represent the potential solution.

𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 ∈ �0, 1, 2 … , 𝑥𝑥, … , min �(𝐶𝐶 𝑠𝑠𝑑𝑑 -𝐵𝐵 𝑠𝑠𝑑𝑑 ) • 𝑇𝑇, min � 𝑑𝑑 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G ��� ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟. (22)
And an auxiliary binary variable is used to represent the second-stage decision variables.

𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 = � 1 if 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 vehicles are used from relief centers 𝑠𝑠 to 𝑑𝑑. 0 otherwise. (23)
Then, the BPR function can be rewritten as follows.

𝜓𝜓(𝑛𝑛 𝑠𝑠𝑑𝑑

𝑥𝑥 ) = �1 + 𝛼𝛼 • � 𝑛𝑛 𝑠𝑠𝑠𝑠 𝑥𝑥 +𝐵𝐵 𝑠𝑠𝑠𝑠 •𝑇𝑇 𝐶𝐶 𝑠𝑠𝑠𝑠 •𝑇𝑇 � 𝛽𝛽 � • 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟. (24)
With the new BPR function, the second-stage model can be rewritten as follows.

Min 𝛹𝛹 2 = ∑ ∑ ∑ [T • 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 + 𝐷𝐷 𝑠𝑠𝑠𝑠 𝑉𝑉 • 𝜓𝜓(𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 )] • 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 𝑑𝑑∈𝒟𝒟 𝑠𝑠∈𝒮𝒮 , (25) s.t.
∑ 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 • 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 ≤ min � 𝑑𝑑 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G � ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟, (26)
∑ 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 • 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 ≤ (𝐶𝐶 𝑠𝑠𝑑𝑑 -𝐵𝐵 𝑠𝑠𝑑𝑑 ) • 𝑇𝑇 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟, (27)
∑ 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 = 1 min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟, (28)
∑ ∑ 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 • 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 • G min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 𝑠𝑠∈𝒮𝒮 ≥ 𝑟𝑟 𝑑𝑑 * ∀ 𝑑𝑑 ∈ 𝒟𝒟, (29)
∑ ∑ 𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 • 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑥𝑥 • G ≤ min [(𝐶𝐶 𝑠𝑠𝑠𝑠 -𝐵𝐵 𝑠𝑠𝑠𝑠 )•𝑇𝑇,min� 𝑠𝑠 𝑠𝑠 * G , 𝑟𝑟 𝑠𝑠 * G �] 𝑥𝑥=0 𝑑𝑑∈𝒟𝒟 𝑑𝑑 𝑠𝑠 * ∀ 𝑠𝑠 ∈ 𝒮𝒮, (30)
𝑛𝑛 𝑠𝑠𝑑𝑑 𝑥𝑥 ≥ 0 & integer ∀ 𝑠𝑠 ∈ 𝒮𝒮, 𝑑𝑑 ∈ 𝒟𝒟. ( 31
)
where objective function (25) represents the total transportation time. Constraints ( 26) and ( 27) restrict the total number of vehicles on each route. Constraint (28) restricts that only one solution is selected from the set of potential solutions. Constraint (29) restricts that the pre-determined demand should be met. Constraint (30) restricts the outgoing commodity cannot exceed the pre-determined supply. Constraint (31) defines the decision variable.

Numerical analysis

To illustrate the validity of the proposed model and solution approach, a numerical analysis with a randomly generated instance is carried out and the related results are reported. In this numerical instance, 12 relief centers and the commodity of food are considered. In BRP function, α=0.15 and β=4.0 are used to estimate the travel time under traffic congestion. The planning period 𝑇𝑇 equals to 1. Relief-center weight values are integers generated randomly in the interval [START_REF] Gao | A Stochastic Programming Model for Multi-commodity Redistribution Planning in Disaster Response[END_REF]30]. The minimum and maximum quantities of demand and supply are integer numbers and drawn randomly from the intervals [START_REF] Galindo | Review of recent developments in OR/MS research in disaster operations management[END_REF][START_REF] Roads | Traffic assignment manual for application with a large, high speed computer[END_REF] Table 1 shows that 6 relief centers are considered as supply relief centers. The parameters and decision variables at relief centers are also given in Table 1. It is obvious that the incoming and outgoing quantities of commodities are closely related to the weighted values, demand, and supply at relief centers. Generally, a demand relief center with a large weighted value and great demand receives more to meet its high-pressure need. A supply relief center with a small weighted value and great supply shares more with other relief centers. For instance, the fifth demand relief center with weighted value 30 receives more food than the first demand relief center with weighted value 30. The second supply relief center with a weighted value of 28 shares less and maintains a higher food inventory level. To obtain a better insight into the behavior in the transportation process with traffic congestion, the obtained first-stage decision variables are expanded ten times. After that, the vehicle assignment between relief centers is obtained and shown in Table 2

Conclusion and future research

This paper presents a two-stage stochastic mixed-integer nonlinear programming model for the commodity rebalancing considering traffic congestion under uncertainties of demand and supply. A method to linearize the model is developed so that it can be solved in the CPLEX solver. A numerical analysis is applied to demonstrate the applicability of the solution method for the proposed model. In the end, the problem of interests from the following aspects can be explored in future studies. It is interesting to consider the multi-commodity rebalancing cases. It is a significant topic to extend the model to the multi-period rebalancing process. Another future consideration is to extend this work to the budget-based uncertain cases. These questions will be considered in further research.

  0 and a volume of 1.0. The vehicle has weight and volume capacities (10, 10). Besides, the vehicle has loading/unloading time 2 and speed 1. The distance between relief centers comes from the intervals [20, 60]. The background traffic-flow rates are randomly generated on the interval [0.4, 0.8]. The practical capacity of each route is randomly generated in the interval [60, 100]. All the models are implemented in IBM ILOG CPLEX Optimization Studio (Version: 12.6).

Table 1 .

 1 . Results of incoming and outgoing food at relief centers in the first stage

	Relief center			𝒮𝒮						𝒟𝒟
	ID	1	2	3	4	5	6	1	2	3	4	5	6
	𝑍𝑍 𝑠𝑠 , 𝑍𝑍 𝑑𝑑	16 28 19 16 19 13 30 30 17 22 30 26
	𝑆𝑆 𝑐𝑐𝑠𝑠 ∆ /𝑅𝑅 𝑐𝑐𝑑𝑑 ∆ 𝑆𝑆 𝑐𝑐𝑠𝑠 ∇ ∇ /𝑅𝑅 𝑐𝑐𝑑𝑑 𝑑𝑑 𝑠𝑠 * /𝑟𝑟 𝑑𝑑 *	11 26 21 28 26 22 20 21 21 28 30 28 20 9 5 12 12 12 13 13 12 9 6 5 21 13 18 21 17 19 18 18 18 20 21 14

Table 2 .

 2 Results of vehicle assignment between relief centers in the second stage

	𝑛𝑛 𝑠𝑠𝑑𝑑		1	2	3	𝒟𝒟	4	5	6
		1	--	32	10		--	--	--
		2	--	--	--		--	26	--
	𝒮𝒮	3 4	----	----	--26		36 4	--12	----
		5	30	--	--		--	4	--
		6	6	4	--		--	--	28


Federica Acerbi
email: federica.acerbi@polimi.it-

Silvia Assiani
email: silvia.assiani@polimi.it

Marco Taisch
email: marco.taisch@polimi.it

A methodology to assess the skills for an Industry 4.0 factory

Keywords: Industry 4.0, Skills, Assessment Model, Maturity Model

The rapid change that is affecting the society together with the rising of new technologies are impacting the manufacturing sector as well. Moreover, this change has also an impact on the skills that operators and managers should master. Companies, on their own, must be always updated in order to keep high their competitive advantage. For these reasons, we carried out this study which aims at searching for a new methodology to assess the current level of companies' workforce in terms of skills needed for taking advantage from the Industry 4.0 paradigm. Starting from an analysis of skills assessment methods, we created DREAMY4Skills, a skills 4.0 assessment model focused on the specific job profile within a company operating in the manufacturing sector. This model is based on a maturity model which enables to make companies be aware of their current status in terms of skills and thus it helps companies in implementing a transformation path to pursue a continuous improvement strategy. This work has two purposes, on one side we would like to have a model useful in practical terms to enable the skills 4.0 assessment held by the workforce, on the other side there is the scientific purpose which is to create another small brick in the literature.

Introduction

Nowadays, we are living in a world where everything is transforming. The rising of new technologies is re-shaping the entire society and even humankind. Along with the Fourth Industrial Revolution, the Industry 4.0 (I4.0) concept has risen and this has been transforming the traditional manufacturing sector by enabling more efficient and flexible production systems. The rising of I4.0 enabling technologies [START_REF] Gerbert | Industry 4.0: The Future of Productivity and Growth in Manufacturing Industries[END_REF] is bringing many advantages but some challenges must be considered [START_REF] Wmf | THE 2018 WORLD MANUFACTURING FORUM REPORT Recommendations for the Future of Manufacturing[END_REF].

The requests of competencies are changing rapidly, and, since the relevance of human capital is commonly recognized as "competitive weapon" [START_REF] Becker | The Age of Human Capital[END_REF], today in order to be competitive both new hard skills and soft skills are needed [START_REF] Acerbi | A Research on Hard and Soft Skills Required to Operate in a Manufacturing Company Embracing the Industry 4.0 Paradigm[END_REF]. Companies must develop clear plans for expenditures, but they should also take into account that the increase in productivity and the consequent expected revenue growth will shorten the payback time to a few years. So, in order to really take advantage of this revolution firms must balance investments in human capital and in technologies.

Considering both the relevance of human capital and the change of the necessary skills to be competitive in the manufacturing sector, leveraging on different studies on skills 4.0, as [START_REF] Pinzone | Jobs and Skills in Industry 4.0: An Exploratory Research[END_REF], the paper [START_REF] Acerbi | A Research on Hard and Soft Skills Required to Operate in a Manufacturing Company Embracing the Industry 4.0 Paradigm[END_REF] identified a wide spectrum of both hard and soft skills necessary to operate in an I4.0 factory. Moreover, a clustering of them in new or evolved job profiles was developed. From that work, a skills 4.0 assessment model was built in this paper. In fact, companies are interested in understanding their current status in order to act in the proper way to undertake an improvement path. As stated by Watts Humphrey [START_REF] Humphrey | Managing the software process[END_REF] "If you don't know where you are, a map won't help". In this study, skills assessment methods were analysed together with maturity models to identify the best way to measure the level of workforce skills and thus, enabling companies to act accordingly to their current status. According to us, those models already developed by academics and consulting companies were not fully completed or were not focused on skills for the I4.0. Thus, we decided to develop DREAMY4Skills, a skills 4.0 assessment model focused on the specific job profiles characterising a current manufacturing company. This paper will be divided into 5 sections: 1) introduction, 2) description of the methodology of the study that is based on a literature review, two focus groups and a pilot assessment; 3) a literature review on skills assessment models, and maturity models; 4) the description and development of the DREAMY4Skills model; 5) limitations and conclusions.

Methodology

In this section, we define the main steps that we undertook in order to perform the studies and develop DREAMY4Skills.

Considering the worldwide necessity to align the workforce skills with the investments in new technologies, we perform a detailed analysis on skills assessment models in order to identify a new way to enable companies operating in the manufacturing sector to have a picture on their workforce current status. For this purpose, a systematic literature review was performed. In order to collect material regarding the methods most used to evaluate workforce, we searched about both hard and soft skills on the main scientific database by using the following keywords "soft skills", "hard skills", "assessment models", and "assessment methods". Among all the papers emerged from the research and looking at their references, we selected the most relevant ones in order to understand how our evaluation could have been performed.

Once we understood which instruments are present in the literature, we decided to analyse which tools are put in place by some consulting companies.

The skills assessment models analysed were not completely effective for our purpose since none of them was explicitly developed to assess skills 4.0. Furthermore, maturity models have been found suitable to assess manufacturing companies' processes within I4.0 context. For these reasons, we performed a deeper analysis of maturity models in order to evaluate whether it was suitable for people as well. The keywords used for this part of the analysis were: "maturity model", "capability maturity models", "People capability maturity model" and then the terms above were combined with "Industry 4.0". To the results obtained from this research, we added a model suggested by academic experts [START_REF] Carolis | A methodology to guide manufacturing companies towards digitalization[END_REF], focused on the assessment of the readiness of companies' processes in terms of processes 4.0.

Then, in order to validate and to verify the feasibility and usability of our study, we organized two focus groups: one with academic experts and one with industrial experts.

Finally, we submitted our model to an Italian firm to do a pilot assessment. The results are shown in chapter 4.3.

3

Literature review

Skills assessment models

In the academic world, many skills assessment models are described and studied. They focused on soft skills or hard skills few of them covered both the thematics. Considering hard skills, the majority of the models are those developed in the clinical field like [START_REF] Van Der Vleuten | Assessment of clinical skills with standardized patients: State of the art[END_REF]- [START_REF] Mandel | Self-assessment of resident surgical skills: Is it feasible?[END_REF]. The majority of them assesses whether a task is performed or not by using yes/no checklists, others do not report how the assessment is performed. Moreover, these studies did not drill down explaining which are the technical skills that the workforce should have, and there is no distinction between different job profiles.

As regards soft skills, the majority of those analysed presents a self-assessment model through a questionnaire with answers based on the Likert scale [START_REF] Wilson-Ahlstrom | From Soft Skills to Hard Data: Measuring Youth Program Outcomes[END_REF], [START_REF] Oecd | Take the Test sample Questions from OECD's pisa assessments programme for international student assessment[END_REF], that biased the results. Finally, the assessment of a mix of technical skills and soft skills, but still in the clinical field, is studied by [START_REF] Arora | Self vs expert assessment of technical and non-technical skills in high fidelity simulation[END_REF].

There is a lack of studies about skills assessment models in the industrial field and Consulting companies' tools were investigated too in order to have a more practical view of the topic. They were mainly focused on specific and restrict subjects not regarding the I4.0 paradigm, as for example [START_REF] Consiglio | Dalle competenze professionali ai risultati di successo. Un caso organizzativo di applicazione della BFC map[END_REF]- [START_REF] R-Group S.R.L | Il Manuale dei profili professionali di competenza[END_REF], but the methodology was interesting because they proposed a multi-source assessment in order to reduce at minimum the subjectivity.

In spite of this, some attempts to assess both soft and hard skills were conducted. An example is "Toolbox Workforce management 4.0" [START_REF] Galaske | Workforce Management 4.0 -Assessment of Human Factors Readiness Towards Digital Manufacturing[END_REF] where an assessment of skills in an I4.0 context is proposed. The main limitation found was the fact that it considers a generic set of skills that is not differentiated according to the different job profiles. An interesting point instead is that, it is based on a maturity model and for this reason, we decided to further investigate the potentialities that these types of models can have to complete our work.

Maturity models

A wide literature about maturity models has been written starting from the latest '70 until today. Even if they are applied with many different purposes, the structure is quite common to all of them. The main purposes for which the maturity models usually are utilised are [START_REF] Pöppelbuß | What makes a useful maturity model? A framework of general design principles for maturity models and its demonstration in business process management[END_REF]:

─ Descriptive: the final goal is to describe the current status of an organization and it can be used as a diagnostic tool; ─ Prescriptive: the final goal is to identify the desired level of maturity for then providing guidelines for the improvement and courses of actions are suggested; ─ Comparative: the final goal is to perform an internal or external benchmark on the basis of historical data.

The common characteristics shared among the maturity model analysed are:

─ the number of levels, that varies from 3 to 6 (the most commons are those composed of 5 levels); ─ there is a logical progression among the levels, thus to reach subsequent levels of maturity, all the previous levels must be covered; ─ the main goal is always to enable an improvement. Some models were focused on the process assessment, others were focused on workforce management, and considering also the work done by [START_REF] Galaske | Workforce Management 4.0 -Assessment of Human Factors Readiness Towards Digital Manufacturing[END_REF], we thought that the structure of these models, in particular, those with a descriptive purpose, could have been exploited for the skills assessment too. In fact, they allow obtaining a picture of the current status of the entity under analysis. They also support the continuous improvement, by giving specific details, step by step, on the next goal to be achieved. For these reasons, they could be useful to enable companies to design the correct training strategy for each person. Thus, in the end, we took inspiration from [START_REF] De Bruin | Understanding the Main Phases of Developing a Maturity Assessment Model[END_REF], that proposed a framework with a detailed description, step by step, on how to create a maturity model.

4

DREAMY4Skills methodology

In this section, the focus is on the description of DREAMY4Skills and on its development steps including the creation of the questionnaire needed to gather data.

DREAMY4Skills: Skills 4.0 assessment model

DREAMY4Skills, whose development is reported in section 4.2, is a skills 4.0 assessment tool based on maturity models which aims to evaluate the competencies, in terms of both hard and soft skills, owned by managers and operators employed in manufacturing companies embracing I4.0 paradigm. It is composed by five maturity levels, described below, characterizing the competencies level owned by each worker.

(v) Proficient: The worker is totally able to manage the emerging technologies and he/she is open to improving his/her capabilities being always updated. He/she is able to use tablets and PC and the software that are commonly installed on them autonomously and in complex situations by supervising the others in case of need.

(iv) Competent: The worker is able to manage autonomously the majority of the emerging technologies and he/she is open to improving his/her capabilities trying to be always updated. He/she is able to use tablets and PC quite autonomously and also the software that are commonly installed on them.

(iii) Practiced: The worker has few notions about the emerging technologies and he/she is able to use some of them. Usually, he/her is not intentioned to update his/her current status of his/she capabilities unless it is of his/her own interest or it is necessary for his/her career or to keep his/her job occupation. The worker has a working knowledge about tools like PC, tablet and the software that are commonly used.

(ii) Aware: The worker has few notions about the emerging technologies even if he/she has never used any of them. Moreover, he/she is not intentioned to update his/her current status of his/her capabilities unless it is of his/her own interest. The worker is aware of the existence of common tools like PC and tablet but he/she does not know how to use them.

(i) Basic: The worker is not aware of the majority of the new technologies and he/she has not a behaviour inclined to modify his current status. He/she has no idea about the existence of common tools like PC or tablet neither of their usage.

In order to perform the assessment, ad hoc questionnaires are provided to managers and operators according to the job profile. Thanks to their answers, it is possible to evaluate their competencies level and thus to highlight their strengths and weaknesses. A final report with some indications about the next objectives that should be achieved is provided to the company. This enables the company to define the right training plan.

DREAMY4Skills development

Being inspired by [START_REF] De Bruin | Understanding the Main Phases of Developing a Maturity Assessment Model[END_REF], we started by defining the scope, essentially for the development of a maturity model since it will be the basis for all the subsequent decisions. The scope is assessing the workforce maturity to embrace Industry 4.0.

In the design phase, we defined the general characteristics of the model for the accomplishment of the goal set. These are the following:

─ the audience that we address are the companies; ─ the method of application is a self-assessment supported by third party analysts; ─ the drivers of application are an internal need or a stimulus from an external analyst; ─ the respondent of our questionnaire are both managers and workforce; in fact, in order to perform the assessment, we gather data from their answers; ─ the application of the model will be based on multiple entities since the questionnaire will be submitted to many people within different process areas. Moreover, the geographical application will be defined on the basis of the company needs and localization of its facilities.

In terms of maturity levels, we defined 5 levels: basic, aware, practiced, competent, proficient as reported above in section 4.1.

In the populate phase, we defined what it is necessary to be measured and how the measurement is performed. The definitions of the job profiles under assessment are based on the integration between the identification of the hard skills essential for that process area together with the soft skills that we found to be fundamental in general to embrace properly the I4.0 paradigm and basic knowledge about ICT. This last dimension should be part of the hard skills, but considering their absolute importance in this context we decided to examine it as a stand-alone category. Therefore, the assessment is performed by following these three analysis dimensions.

In order to gather data from the workforce, we created a questionnaire tailored to each job profile. The first section of the questionnaire is dedicated to soft skills, the second one to the ICT literacy and these two parts are submitted to all the job profiles without any differences. The third one is focused on hard skills that are specific for each job profile, therefore this section is developed ad hoc for each job profile according to its characteristics.

To select the structure and formulate the normative answers we were inspired by [START_REF] Carolis | A methodology to guide manufacturing companies towards digitalization[END_REF], [START_REF] R-Group S.R.L | Il Manuale dei profili professionali di competenza[END_REF]. We used normative answers, instead of checklists or similar methods, to properly describe a specific level without being subjective, as the model analysed in section 3.1, and increasing the level of standardization. The person answering the questionnaire selects which sentence better describes his/her behaviour, attitude or thoughts.

In the test phase, we organized two different focus groups. The first one was held with academic experts the team "Jobs&Skills" of Polimi together with the author of the DREAMY. The team "Jobs&Skills" was of fundamental importance in order to validate our questionnaire and the skills defined by us as skills4.0 since their past studies were focused on this topic. The author of DREAMY, on the other side, was fundamental for the validation of our model as a whole since she provided suggestions on the possible criticalities of our first version of the model.

A second focus group was organized with industrial exponents in order to verify the formulation of each question and the related normative answers.

Once the model has been created and tested, it was submitted to a sample of companies in order to verify its usability.

DREAMY4Skills application

In order to validate our model, we applied it to a real case. We sent the questionnaire to a company and its personnel provided us with the answers. To report the final results, we used a radar chart. In fact, using a radar chart (see Fig. 1) that shows all the job profiles together, it is possible to better see their differences. As far as soft skills, all the job profiles are around the third level, the main differences are due to higher knowledge of foreign languages and higher interest in continuous learning showed by managerial roles with respect to the more operative ones.

As regard ICT literacy the results highlight that, as expected, those profiles with lower knowledge are warehouse and production operators being around the third level. These are people who currently do not use PCs and tablets during their working activities. Instead, the profiles reaching the fourth level in ICT literacy are the data scientist followed by the managers. While the best performer is the IT-OT integrator.

Looking at hard skills, the data analysed show that the majority of the job profiles has an evident gap. Also in this case, given that we are talking about new technologies like smart devices, operative profiles have a bigger gap than managerial ones and the best performer is the IT-OT integrator. This assessment allowed us to understand the current status of skills owned by the workforce and thus we developed a report to explain to the company the meaning of the scores giving them a detail description about the current level of each profile.

Finally, we suggested them, as forthcoming targets, the improvement needed to reach the upper level by underlining the strengths and weaknesses of each person.

Limitations and Conclusions

The model provides a picture of the current status of companies' workforce enabling their continuous improvement.

In order to apply it in an effective way, some communication efforts are required to companies because the assessment must be seen by the workforce as something positive for their professional growth and not as an internal investigation conducted by human resources to evaluate good/bad performances of a person.

Moreover, to guarantee the alignment between the assessment method and the technological advancement, the model should be kept always updated in terms of both job profiles considered and skills included in the analysis.

To conclude, the proposed model has a descriptive purpose, therefore the main follow-up that we envisage is to make it become prescriptive, by providing companies guidelines to achieve their next goal once the current situation has been assessed.

Fig. 1 .

 1 Fig. 1. Radar chart showing the results of the case study