David Guerrero⁺

Patrick Niérat⁺

Jean-Claude Thill

IFSTTAR Gustave Eiffel

Connecting short and long distance perspectives in freight transportation: Introduction to a Special

Keywords: freight transportation, transport chain, supply chain, resilience, city logistics, transport terminals, first mile/last mile

Research on short and long distance freight transport artificially separates the segments of transport chains, which are interrelated and which might be better viewed as a continuum.

The eight papers of this special issue aim to bridge this gap. The major disruptions in global supply chains of the last years brought to light the vulnerability of the transport system and the need for a more integrated approach for effective transport policies. This special issue explores some of the challenges facing freight transport in three research areas: supply chain studies, transport networks and warehouse location. It also identifies avenues for further research.

Why a special issue on the relationship between short and long distance in freight transportation?

Within social sciences, scholars have tried to understand how cargo is moved, in many different ways, theoretically, descriptively, and through empirical modeling. This diversity of approaches partly results from a growing demand from society to understand various facets of freight and freight shipping. But it also reveals the state of fragmentation of this community of research practice, where researchers interested in related issues of cargo movement are simply not talking to each other. In transportation studies, this diversity is associated with two broad traditions through which cargo movement is studied. One of these, inter-urban or long distance transport, is often viewed as a 'dirty activity' (Hall and Hesse, 2013). A dominant feature of this line of research is to articulate patterns in freight flows in relation to the evolution of transport systems [START_REF] Rodrigue | Transportation and spatial cycles: evidence from maritime systems[END_REF], to the global impacts of cargo movement --such as economic development [START_REF] Banister | Transport investment and the promotion of economic growth[END_REF])--and to the evolving conditions that favor modal shift (Woodburn, 2003). The tradition of urban freight/ city logistics, on the other hand, is concerned more with local issues such as congestion, noise or local air pollution (see, for example, [START_REF] Figliozzi | Analysis of the efficiency of urban commercial vehicle tours: Data collection, methodology, and policy implications[END_REF], Holguin-Veras et al, 2006[START_REF] Anderson | Urban logistics--how can it meet policy makers' sustainability objectives[END_REF].

We argue this division is unhelpful because it artificially separates segments of a same transport chain, which are interrelated and might be better viewed as a continuum [START_REF] Robinson | The hinterland-foreland continuum: concept and methodology[END_REF]. For example, the optimal location of logistics activities within an urban area is often viewed as a problem of distance minimization to a barycenter [START_REF] Dablanc | The impacts of logistics sprawl: How does the location of parcel transport terminals affect the energy efficiency of goods' movements in Paris and what can we do about it?[END_REF]. That is, it implies that logistics activities are exclusively focused on local deliveries, which may in fact be far from reality [START_REF] Sakai | Logistics chain modeling for urban freight: pairing truck trip ends with logistics facilities[END_REF], Giuliano & Kang, 2018).

Taking into account what happens outside and between urbanized regions (inter-urban flows) can lead to a better understanding of the factors governing the location of terminals within the city itself (Niérat, 1997). This lack of integration between short and long distance perspectives is not specific to urban freight research. For example, within maritime transport, while many works underline the benefits related to the achievement of economies of scale on the maritime segment (Cullinane & Khanna, 1999), less work explains how this advantage is dramatically lessened by the bottlenecks around ports or on hinterland connections (Monios and Wilsmeier, 2016[START_REF] Merk | Container ship size and port relocation[END_REF][START_REF] Guerrero | Impacts of transport connections on port hinterlands[END_REF]. The current crisis of global supply chains, which has resulted in major problems such high freight rates, supply chain disruptions and inflation, largely results from problems at the level of inland transport segment, such the shortage of chassis and drivers, and the temporary lack of containers [START_REF] Ng | Strategies for chassis dislocation management at container ports: repositioning and yard consolidation[END_REF][START_REF] Toygar | Investigation of empty container shortage based on SWARA-ARAS methods in the COVID-19 era[END_REF]. Although inland connections only represent a small fraction of the overall transport distance, they are particularly costly and therefore crucial for the competitiveness of entire transport chains.

Of course, the lack of integration between long and short distance perspectives is not just an academic issue. It reflects broader competing/conflicting interests, for example between city governments, on the one hand, and regional and national authorities, on the other. While the former generally try to avoid the negative consequences of the bottlenecks of long distance transport in large urban areas [START_REF] De Lara | This Port Is Killing People": Sustainability without Justice in the Neo-Keynesian Green City[END_REF] the latter are rather concerned with the efficiency and consistency of national/regional transport systems [START_REF] Mckinnon | Life without trucks: the impact of a temporary disruption of road freight transport on a national economy[END_REF].

These interfaces between long and short distance are critical, as many of the problems, such congestion, take place here [START_REF] Steinbach | Port congestion, container shortages, and US foreign trade[END_REF]. Therefore, a coherent regulation of the different segments of the transport chain remains a challenge for public policy (Reme-Harnay, 2022).

In the last decades, while considerable gains in efficiency have been achieved on medium and long distance transport, last mile/first mile segments have lagged behind. Freight flows have become more fragmented, favoring the use of road transport and small vehicles for frequent deliveries [START_REF] Guilbault | Transport and logistics demand: new input from large surveys of shippers in France[END_REF]. This exacerbates the negative impacts of freight activities in urban areas such congestion and pollution, and has become a sensitive issue for local policy makers. In response to growing urban freight problems, studies and surveys on urban freight have been encouraged or promoted by local authorities, particularly since the 1990s. Meanwhile, the research field of urban freight/urban logistics has progressively penetrated academic journals, eventually consolidating as a research field on its own (Browne et al, 2019, Wolpert and[START_REF] Wolpert | Status quo of city logistics in scientific literature: systematic review[END_REF].

Consequently, today it becomes necessary to increase the dialogue between researchers in short and long distance freight transport. Even if some have developed both approaches (see, for example Barthel and Woxenius, 2004[START_REF] Behrends | Urban freight transport sustainability-the interaction of urban freight and intermodal transport[END_REF][START_REF] Nemoto | Intermodal transport and city logistics policies[END_REF], researchers have seldom discussed the potential incongruities between these perspectives. This is rather surprising given the international research networks that have emerged on urban freight during the last two decades. One could argue that the main challenge for the dialogue between short and long distance approaches is the lack of data. Or one could argue that the expectations about the outputs that research on short and long distance freight would generate are very different. But by avoiding the potential conflicts between approaches, the possibilities for cross-fertilization are missed [START_REF] Bissell | Geographies of the passenger[END_REF].

To foster the agenda of integrative science along the supply chain, including long-and shorthaul shipping, and to encourage this dialogue, we proposed in this special issue a list of shared themes that would be familiar to scholars working on both long distance (e.g., intermodality, terminal systems, routing and allocation problems) and short distance researchers (e.g., location of logistics activities, optimization of urban deliveries, urban freight policies).

The Special Issue contributions

This special issue of eight papers addressed this agenda through a range of themes, including supply chain organization, transport connectivity and the location of terminals.

The articulation between long and short distance freight transportation is critical in supply chain organization. Button (2020) presents a case study on the Africa's floriculture air-cargo supply chain which shows that flower growing is geographically concentrated around airports, so as to minimize first-mile transport costs and shipping time in a context of poorly developed transport infrastructure. Market size appears to be crucial for the development of efficient air supply chains, encouraging competition between airlines and providing market power for large shippers to obtain better fares. Given the highly perishable nature of flowers, supply chains are technically challenging, and highly dependent on passenger flights, which are particularly vulnerable to disruptions such as during the Covid-19 pandemic.

For other agricultural products, like wine, first-mile logistics from rural areas are also particularly challenging. [START_REF] Guerrero | Challenging the shipper's location problem in port studies: An analysis of French AOC wine shipments to the US[END_REF] analyze the port choice and routing decisions for French AOC wines to the US, using disaggregated shipment data on individual shipments and a discrete choice model. They highlight the key role played by freight forwarders in the consolidation of wine in containers. When a container is loaded with wines from several AOC regions, the effect of inland distance on port choice is less prominent than for containers exclusively carrying wines from a single region. This suggests that port-choice decisions may result from a more complex trade-off including the location of wine regions and the overall geographical organization of freight forwarders. This work also raises an issue about the quality of O/D data in transport studies, and suggests a novel method based on the identification of O/D through wine names.

A second theme analyzes the connectivity in maritime transport chains, including ports and hinterlands. Three papers discuss the ways in which port systems develop in different parts of the world, and the main challenges for connecting local and distant markets. Ducruet (2020a) reviews the evolution of maritime networks studies in geography and other sciences, and discusses potential research pathways for future work. He shows that during the second half of the 20 th Century transport geography studies were mainly focused on the land connections of ports (hinterlands), largely overlooking the maritime side. This changed during the past two decades with the emergence of a maritime networks subfield within transport geography, fostered by advances in complex networks analysis and progress in data availability. It is suggested that to become more than a "purely quantitative experiment", maritime networks should be seen as parts of larger systems including shippers and the territories served by maritime transport.

Accordingly, Ducruet et al. (2020b) analyzed the relationship between the population of port cities and the containerized services between those cities, using a gravity-model. Their results show that, despite the development of networks in containerized transport, population size and distance still matter a lot in the organization of maritime networks. The study also measures the correlation between port throughput, on one side, and the population of port-cities and port-regions, on the other side. It shows that while the relationship between port throughput and local population has decreased, it has increased with regard to regional population. This finding supports the idea that the inland scope of port system extends beyond the vicinity of the ports to a wider regional scale, as suggested by Notteboom and Rodrigue (2005). [START_REF] Jung | Sea-land interdependence and delimitation of port hinterland-foreland structures in the international transportation system[END_REF] also explore the interdependence between forelands and hinterlands, using disaggregated data on containerized shipments from Europe to the US. In doing so, they implemented within the scope of trans-Atlantic containerized commerce the seminal ideas on hinterland-foreland continuum [START_REF] Robinson | The hinterland-foreland continuum: concept and methodology[END_REF]) and port triptych [START_REF] Vigarié | Ports de commerce et vie littorale[END_REF][START_REF] Charlier | Ports and hinterland connections[END_REF]) advanced over three decades ago. Jung and Thill's approach, based on network science algorithms of meso-scale analysis, is particularly original because it provides for the first time, clusters of ports and regions simultaneously based on the inland and maritime routes followed by shipments. These clusters differ from the ones exclusively based on inland routes identified by previous studies [START_REF] Guerrero | Deep-sea hinterlands: Some empirical evidence of the spatial impact of containerization[END_REF]. Interestingly, some of the 9 regional clusters identified in Europe include several countries (France and Belgium, Germany and the Netherlands), confirming that the functional areas of ports go beyond national borders. Papers in this theme underscore the need to transition our analytical thinking to encompass the entire logistics chain spanning the landsides and the seasides to avoid the mischaracterization of shipping networks and structures they form.

The third theme relates to the location of logistics activities, taking into account their geographical orientation towards local or distant markets. [START_REF] Guerrero | On the spatial scope of warehouse activity: An exploratory study in France[END_REF] study the spatial scope of large warehouses through a national survey describing their operational characteristics. They show, on one hand, that the warehouses located in the Greater Paris and in a few large urban areas and more oriented towards international markets. On the other hand, they find that the warehouses located in inner Paris are more oriented to local deliveries than those located on the outskirts of the Greater Paris and in the other large cities.

Also in the Greater Paris, Robichet and Niérat (2021) analyze a large dataset of pick-ups and deliveries for a large parcel deliver carrier to determine the optimum location of its terminals. The predicted locations, resulting from the minimization of distance to clients, that are outside Inner Paris. Therefore, when a firm operates several terminals, the location outside inner Paris is not necessarily suboptimal. This result shows that logistic sprawl is not always synonymous with increasing the distance traveled for the first and last mile, neither, by extension, with increasing pollution. [START_REF] Sakai | Logistics facilities for intra and inter-regional shipping: Spatial distributions, location choice factors, and externality[END_REF], using an extensive shipment survey, in the Tokyo Metropolitan Area, analyze locations and goods vehicle trips for four types of logistics facilities. These types are defined on the basis of the geographical scope of the shipments generated by these logistics facilities: intra or inter urban. An interesting finding of this study is that an important share of the logistics facilities located within the Tokyo Metropolitan Area, are not oriented to intra-urban deliveries and pick-ups. Therefore, their location outside inner Tokyo does not lead to longer trip distances. The three papers in this theme highlight the need of taking into account the geographical scope of shipments for the study of the optimal location of warehouses and question the validity of approaches exclusively based on distance to a barycenter.

Conclusion and research agenda

This special issue covered a wide range of topics on short and long distance perspectives in freight transportation, through the themes of supply chain organization, transport connectivity and the location of logistics activities. Interestingly, most of the papers were mostly focused either on long distance or short distance but only few of them dealt simultaneously with both perspectives. This simultaneous treatment of long and short distance is mainly found in the papers on the theme of warehouse location and the relationship of urban/non urban scope of shipments. In the papers focused on long-distance transportation, although there is an effort to integrate several transport segments, there is not much information linking the ends of the chain to the middle parts. Maybe this difficulty stems from the lack of datasets that combine first and last mile data because both ends typically occur in different jurisdictions. The linkage data is often broken somewhere in the middle of transport chains.

Connecting intra and inter-urban freight markets through the prism of urban hierarchy offers new possibilities to study these relationships. Specifically, through an analysis of commodity flows it is possible to study the freight advantages or disadvantages of firms located in large urban areas. A recent study based on the Japanese Commodity Flow Survey has showed that shipping cargo from small to large urban areas is less costly than in the reverse direction (Guerrero et al., 2021). A related strand concerns the relative benefits of hub-and-spoke network structures on the landside and their primary drivers, when cargo is traded internationally. The study of the relevance of intermodal solutions may also be viewed from an urban perspective, by focusing on the ways in which short distance segments of intermodal transport determine the competitiveness of the whole transport chain [START_REF] Nierat | Market area of rail-truck terminals: Pertinence of the spatial theory[END_REF][START_REF] Behrends | Burden or opportunity for modal shift?-Embracing the urban dimension of intermodal road-rail transport[END_REF]. Another important aspect of these interconnections are the operational constraints within terminals, and how workers add fluidity to the constraints of different transport modes. There are several works paving the way on this labor perspective in transport geography, such the study of subcontracting in global logistics (Gutelius, 2015) or the work conditions within intermodal terminals (Munduteguy, 2012). Another important perspective relates to the relationships between transport companies in the short and long distance segments. A recent study comparing subcontracting practices in urban and interurban transportation, shows that transport firms operating urban parcel delivery services are more economically vulnerable than those operating in inter-urban transportation (Reme-Harnay, 2022).

[perhaps one final sentence calling for further research]


Zhengmin Zhang

Gong
email: gong@em-lyon.com

Qian Shen

Multi-Fidelity Simulation-Based Optimisation for Large-Scale Production Release Planning in Wafer Fabs

Keywords: Queuing Theory, Multi-fidelity Simulation-based Optimisation, Wafer Fabs, Production Release

This paper focuses on large-scale production release planning problems in wafer fabs. Due to the complexity and dynamic characteristic of production lines, it is useful to develop simulation models to evaluate different production plans and select the optimal one. However, detailed simulation requires large computational costs, especially for large-scale problems. Therefore, we provide a multi-fidelity optimisation with ordinal transformation and optimal sampling (MO2TOS) based on the multiple population evolutionary algorithm to accelerate computational efficiency and address large-scale release planning problems for wafer fabs. In the low-fidelity approximation process of the proposed approach, we employ open queuing theory to estimate cycle times. The experimental results confirm that the low-fidelity model shows a high consistency with the high-fidelity model and the proposed multi-fidelity optimisation method is effective at solving large-scale release planning problems.

Introduction

The manufacturing of wafer fabs is a highly complex and time-consuming process because of massive process steps and complex process requirements [START_REF] Chung | Job releasing and throughput planning for wafer fabrication under demand fluctuating make-to-stock environment[END_REF]. Thus, it is difficult to provide an effective production release plan for the production line. In wafer fabs, the production release planning problem seeks an optimal or near-optimal solution to optimise the output and the work-in-process of a production system by determining the release rate of each product type. Some basic approaches, such as mathematical programming [START_REF] Asmundsson | Tractable nonlinear production planning models for semiconductor wafer fabrication facilities[END_REF][START_REF] Leachman | Semiconductor production planning[END_REF], simulation-based optimisation [START_REF] Zhang | Semiconductor wafer fabrication production planning using multi-fidelity simulation-based optimisation[END_REF][START_REF] Thuerer | On the combined effect of due date setting, order release, and output control: an assessment by simulation[END_REF], and analytical modelling [START_REF] Chung | Job releasing and throughput planning for wafer fabrication under demand fluctuating make-to-stock environment[END_REF][START_REF] Schneckenreither | Order Release Planning with Predictive Lead Times: A Machine Learning Approach[END_REF], have been developed to address production release planning problems. Simulation-based optimisation [START_REF] Chen | Stochastic Simulation Optimisation (An Optimal Computing Budget Allocation)[END_REF][START_REF] Xu | Industrial strength COMPASS: A comprehensive algorithm and software for optimisation via simulation[END_REF] refers to the approaches that search for the optimal solution by using simulation models to directly evaluate the objective values of candidate solutions. Compared with mathematical modelling, this technology can provide accurate estimates of given production plans.

Besides, simulation-based optimisation plays an important role in digital twins and has huge advantages in the application of the digital twin platform [START_REF] Zhang | Improved multi-fidelity simulation-based optimisation: application in a digital twin shop floor[END_REF].

However, simulation-based optimisation consumes high computational costs because of its high-precision modelling capability [START_REF] Asmundsson | Production planning with resources subject to congestion[END_REF]. Real-world production planning problems require considerable computational time to run the entire solution space by the simulation model [START_REF] Fowler | Modeling and Analysis of Semiconductor Manufacturing[END_REF]. Therefore, simulation models are often used to verify the solution quality of mathematical models [START_REF] Bang | Hierarchical Production Planning for Semiconductor Wafer Fabrication Based on Linear Programming and Discrete-Event Simulation[END_REF][START_REF] Kopp | Qualification Management in Wafer Fabs: Optimisation Approach and Simulation-Based Performance Assessment[END_REF][START_REF] Ziarnetzky | Simulation-based performance assessment of production planning formulations for semiconductor wafer fabrication[END_REF]. Some approaches [START_REF] Missbauer | Order release planning by iterative simulation and linear programming: theoretical foundation and analysis of its shortcomings[END_REF][START_REF] Kim | Synchronized production planning and scheduling in semiconductor fabrication[END_REF][START_REF] Kim | Extended model for a hybrid production planning approach[END_REF] address the order release planning problems by iterative simulation and linear programming. Nevertheless, these methods may take a long time to converge if the initial release plan is ineffective or the convergence process is not stable. Therefore, the research question of this paper is: How to solve large-scale production release planning problems in wafer fabs effectively by simulation-based optimisation?

This research therefore designs a multi-fidelity optimisation with ordinal transformation and optimal sampling (MO2TOS) based on the multiple population evolutionary algorithm for production release planning problems. The proposed method is developed based on the MO2TOS proposed by Xu et al. [START_REF] Xu | MO2TOS: Multi-Fidelity Optimisation with Ordinal Transformation and Optimal Sampling[END_REF]. The high-fidelity model is developed using the discrete-event simulation and the low-fidelity model is established as a mathematical expression based on the queuing theory. In the proposed MO2TOS, we provide a multiple population evolutionary algorithm to accelerate the solution space searching and obtain the approximate solution space. Compared with other methods, this proposed method obtains the same optimal solution as MO2TOS when solving large-scale problems, and saves about 90% of computational time.

Problem Formulation and Modelling

Consider the following scenario: 𝑘 (𝑘 = 1 … 𝐾) types of products are produced by 𝑚 (𝑚 = 1 … 𝑀) workstations of a wafer production line that demand exceeds supply. Product 𝑘 have 𝑟 (𝑟 = 1 … 𝑅 𝑘 ) alternative processing routes, each route has 𝐿 𝑘,𝑟 operations. 𝑀 𝑘,𝑟,𝑙 represents the workstation for the 𝑙th operation of product k with processing route r. Products of different types have similar processing flows but not exactly the same. Any processing routes may have re-entrant flows. The demand 𝑑 𝑘 of product k is known, the optimal release rate and the routing allocation scheme for each product type need to be calculated to increase productivity. We need to find the optimal release plan for different products and obtain the optimal routing allocation plan for each product type with different processing routes. The objective of the problem is to complete the customer's requirements as soon as possible and minimise the maximum work-in-process of workstations in the production line. To maintain balanced production, we put forward the following two assumptions: 1. The release rate of each product in a planning period is stable and changeless. 2. Under any release plan, the product demand capacity cannot exceed the production capacity of the machine. Otherwise, the system cannot reach a steady state and may lead to infinite accumulation of work-in-process.

We provide a mathematical model to describe the proposed problem on the basis of the above assumptions. The objective function are as follows:

𝑀𝑖𝑛(𝑤1 • 𝑚𝑎𝑘𝑒𝑠𝑝𝑎𝑛 + 𝑤2 • 𝑤𝑜𝑟𝑘_𝑖𝑛_𝑝𝑟𝑜𝑐𝑒𝑠𝑠) (1)
𝑚𝑎𝑘𝑒𝑠𝑝𝑎𝑛 = 𝑚𝑎𝑥 𝐹(𝑘, 𝑟, 𝑝, 𝐿 𝑘,𝑟 ), ∀𝑘, 𝑟, 𝑝, 𝑚

𝑤𝑜𝑟𝑘_𝑖𝑛_𝑝𝑟𝑜𝑐𝑒𝑠𝑠 = 𝑚𝑎𝑥( ∑ ∑ ∑ 𝑊𝐼𝑃(𝑘,𝑟,𝑝,𝑚) 𝑅 𝑘 𝑟=1 𝐾 𝑘=1 ⌈𝐹(𝑘,𝑟,𝑝,𝑙)⌉ 𝑝=1 ⌈𝐹(𝑘,𝑟,𝑝,𝑙)⌉ ), ∀𝑚 (2)
Subject to:

∑ ∑ 𝑦 𝑘,𝑟 𝑝 𝑅 𝑘 𝑟=1 ⌈𝐹(𝑘,𝑟,𝑝,𝑙)⌉ 𝑝=1 ≥ 𝑑 𝑘 , ∀𝑘, 𝑚 (4)
𝑥 𝑘,𝑟 𝑝 , 𝑦 𝑘,𝑟 𝑝 , 𝐹(𝑘, 𝑟, 𝑝, 𝑙), 𝑊𝐼𝑃(𝑘, 𝑟, 𝑝, 𝑚) ≥ 0, ∀𝑘, 𝑟, 𝑝, 𝑚

Equations ( 1)-( 3) represents the objectives of this problem, 𝑤1 and 𝑤2 means the weights of two objectives. 𝐹(𝑘, 𝑟, 𝑝, 𝑙) means the complete time for the 𝑙th operation of product k with processing route r released in period p. 𝑊𝐼𝑃(𝑘, 𝑟, 𝑝, 𝑚) is the cumulative work-in-process for product k with processing route r at workstation m in period p, where 𝑊𝐼𝑃(𝑘, 𝑝, 𝑚) = ∑ 𝑊𝐼𝑃(𝑘, 𝑟, 𝑝, 𝑚)

𝑅 𝑘 𝑟=1

. Constraint (4) provides the minimum production quantity for each product. 𝑦 𝑘,𝑟 𝑝 represents the external release material quantity for product k with processing route r in period p. 𝑦 𝑘,𝑟 𝑝 , 𝐹(𝑘, 𝑟, 𝑝, 𝑙) and 𝑊𝐼𝑃(𝑘, 𝑝, 𝑚) are decision variables linked with 𝑥 𝑘,𝑟 𝑝 (external release material quantity for product k with processing route r in period p). In the proposed mathematical model, we need to derive the relationship between 𝑥 𝑘,𝑟 𝑝 and other decision variables.

MO2TOS Based on the Multiple Population Genetic Algorithm

Low-Fidelity Approximation Based on Queuing Theory

We )), 𝑛 ≠ 𝑚 [START_REF] Chen | Stochastic Simulation Optimisation (An Optimal Computing Budget Allocation)[END_REF] Therefore, λ 𝑚 𝑝 (𝑘, 𝑟) can be described as:

λ 𝑚 𝑝 (𝑘, 𝑟) = λ 0,𝑚 𝑝 (𝑘, 𝑟) + λ 𝑛,𝑚 𝑝 (𝑘, 𝑟), ∀𝑚, 𝑘, 𝑟, 𝑝 (8)
λ 𝑚 𝑝 is then given by:

λ 𝑚 𝑝 = ∑ ∑ λ 𝑚 𝑝 (𝑘, 𝑟) 𝑅 𝑘 𝑟=1 𝐾 𝑘=1 , ∀𝑚, 𝑝 (9)
Therefore, the utilisation of workstation m can be provided as:

𝜌 𝑚 𝑝 = 𝜏 𝑚 • λ 𝑚 𝑝 , ∀𝑚, 𝑝 (10)
We refer the approximation method of a GI/G/1 system in Whitt [START_REF] Whitt | The Queueing Network Analyser[END_REF] to estimate the expected waiting time of each product lot in any workstations.

𝐸𝑊 = 𝜏𝜌(𝐶 𝑎 2 +𝐶 𝑠 2 )𝑔 2(1-𝜌) (11)
Where 𝑔 is defined as:

𝑔(𝜌, 𝐶 𝑎 2 , 𝐶 𝑠 2 ) = { exp [- 2(1-𝜌) 3𝜌 (1-𝐶 𝑎 2 ) 2 𝐶 𝑎 2 +𝐶 𝑠 2 ] , 𝐶 𝑎 2 < 1 1 , 𝐶 𝑎 2 ≥ 1 (12)
𝜏 denotes the service time for a product, 𝜌 means the utilisation of this server, 𝐶 𝑎 2 represents the squared coefficient of variation of the arrival interval distribution at this server, while 𝐶 𝑠 2 is the squared coefficient of variation for the service-time distribution. 𝐶 𝑎 2 is the variance of the renewal interval divided by the square of its mean, and 𝐶 𝑠 2 is the variance of the service time divided by the square of its mean.

In our low-fidelity approximation model, 𝑊(𝑘, 𝑟, 𝑝, 𝑙) can be represented by the expected waiting time EW. Accordingly, 𝐹(𝑘, 𝑟, 𝑝, 𝑙) can be recorded as: 𝐹(𝑘, 𝑟, 𝑝, 𝑙) = 𝑃 𝑘,𝑟,𝑙 + 𝑊(𝑘, 𝑟, 𝑝, 𝑙)

According to the Little's law:

𝑊𝐼𝑃(𝑘, 𝑝, 𝑗) = 𝑊(𝑘, 𝑟, 𝑝, 𝑙) • λ 𝑚 𝑝 (14)
𝐹(𝑘, 𝑟, 𝑝, 𝐿 𝑘,𝑟 ) means the makespan of product k released in period p. Because the release rate in each period is the same, we can consider 𝐹(𝑘, 𝑟, 1, 𝐿 𝑘,𝑟 ) as the cycle time for product k with processing route r. Thus, 𝑦 𝑘,𝑟 𝑝 can be estimated according to the following formula:

𝑦 𝑘,𝑟 𝑝 = 𝑥 𝑘,𝑟 𝑝 + 𝐹(𝑘, 𝑟, 1, 𝐿 𝑘,𝑟 )

Framework of MO2TOS Based on the Multiple Population Genetic Algorithm

The steps of MO2TOS based on the multiple population genetic algorithm (MPGA) are exhibited in Fig. 1. Traditional MO2TOS uses the low-fidelity model to estimate all the results of the solution space. Then, it selects high-quality solutions by the ordinal transformation and optimal sampling strategy, and uses the high-fidelity simulation model to calculate these solutions and choose the optimal solution. However, the solution space of large-scale production planning problems may be more than several million. Even if we use the low-fidelity model to run the entire solution space, the computational costs and runtime are not negligible. To reduce computational burden, we design a multiple population evolutionary algorithm to accelerate the solution space search efficiency based on the original MO2TOS. We choose a multiple population evolutionary algorithm because solution spaces of production problems are generally multi-peak, and multiple population evolutionary algorithms are conducive to jumping out of local optimal and accelerating the convergence process.

Computational Experiments

We simplify the actual wafer production system and develop some typical wafer production lines to test and estimate the effectiveness of the proposed method. The simplified cases retain the characteristics of batch processing, machine failures and mixedflow production in actual wafer fabs. First, we develop a small-scale production release planning case to verify the accuracy of the low-fidelity model. We calculate the solution space via the high-fidelity simulation model and the low-fidelity model. Fig. 2 plots the output of the solution space after ordinal transformation. According to Fig. 2, we find the consistency of the output of the solution space using two models is obvious, which proves the proposed low-fidelity approximation method is feasible. Therefore, the low-fidelity model we proposed in this paper is feasible.

Fig. 2. Output of the solution space after ordinal transformation

We further develop a large-scale production release planning case and employ the proposed method to solve the case. We first examine the optimisation performance of the proposed multi-population genetic algorithm. Fig. 3 shows the convergence curves of the optimal results for the same case when the same low-fidelity budget (10000) is allocated. From Fig. 3, we conclude that the proposed algorithm has stable optimisation capability in solution space searching process. We compare the proposed method with the high-fidelity simulation optimisation (HFSO) method and MO2TOS used by Zhang et al. [START_REF] Zhang | Semiconductor wafer fabrication production planning using multi-fidelity simulation-based optimisation[END_REF]. HFSO selects specific amount of solutions randomly according to the high-fidelity simulation budget, uses only the high-fidelity model to run all the selected solutions, and searches for the optimal solution according to the results. The MO2TOS method solves the entire solution space by using a low-fidelity model, selects high-fidelity samples using ordinal transformation and optimal sampling, and runs the high-fidelity samples to find the optimal solution. The MO2TOS based on the multi-population genetic algorithm differs from MO2TOS in the first phase. It uses the multi-population genetic algorithm combined with a low-fidelity model to solve the solution space.

Table 1. The optimal results for the large-scale release planning case.

High-fidelity budget

The optimal result Runtime (s) 1 provides the optimal results with different methods for the large-scale release planning case. We can conclude: 1. The more fidelity budgets are allocated, the longer the run time is required. 2. Regardless of the amount of high-fidelity budget allocated, HFSO is worse than the compared methods. 3. The method proposed in this paper can find the optimal solution when the high-fidelity budget is only 200, and save about 90% of the computing time than MO2TOS when solving large-scale problems.

The studied actual wafer production system uses a static lead time release planning model in Manufacturing Requirements Planning (MRP) to develop release plans at present. This model is oversimplified because it considers lead times as workloadindependent constants. The static lead time is usually estimated from historical data and experience. This method releases the materials corresponding to the demand of each cycle directly according to the static lead time, which often causes a large amount of work-in-process accumulation. Consider the proposed case as an example, the optimal result of this method is 134.515, which is 18.733% worse than the method proposed in this manuscript.

This method is suitable for real-world wafer fabs that demand exceeds supply. First, managers need to know the demands of multiple planning periods in the future and roughly estimate the upper and lower limits of release rates based on demands. Then, managers can use the proposed low-fidelity estimation method to estimate the revenues of different release plans and obtain the appropriate solution set. Next, they can use the high-fidelity discrete simulation model to run these plans and select the optimal one.

Fig. 1 .

 1 Fig. 1. MO2TOS based on the multiple population genetic algorithm

Fig. 3 .

 3 Fig. 3. The convergence curve of the optimal results

Table

		HFSO	MO 2 TOS	MO2TOS	HFSO MO 2 TOS MO 2 TOS
				& MPGA			& MPGA
	200	128.048	113.475	113.292	425	2221	358
	400	120.651	113.447	113.292	1351	2874	824
	600	121.166	113.292	113.292	3028	3944	1672
	800	124.113	113.292	113.292	4908	5503	2785
	1000	120.061	113.292	113.292	7948	7569	4906
	1200	117.943	113.292	113.292	10244	10348	7149

This method can greatly reduce computation time and is suitable for large-scale problems. Note that due to some uncertain events or parameters in actual production scenarios, this method may need to update release plans periodically to keep the simulation model consistent with the actual production system.

Conclusions

In this research, we present a MO2TOS based on the multi-population evolutionary algorithm to address large-scale production release planning problems in wafer fabs.

The low-fidelity estimation model is an open queue approximation model and the highfidelity simulation model is established based on discrete-event simulation. We test a large-scale case to evaluate the proposed method. The proposed method is compared with the MO2TOS framework proposed by Zhang et al. [START_REF] Zhang | Semiconductor wafer fabrication production planning using multi-fidelity simulation-based optimisation[END_REF] and the high-fidelity simulation optimisation method. Experiment results show that the proposed method can obtain the same optimal solution as Zhang et al. [START_REF] Zhang | Semiconductor wafer fabrication production planning using multi-fidelity simulation-based optimisation[END_REF] and save computing time.

In the future, we will consider how to improve the estimation accuracy and speed of the low-fidelity model simultaneously. Moreover, we will study how to let high-fidelity model estimation results feedback to the low-fidelity model and reduce estimation gaps between the low-and the high-fidelity models.


Tian Zhang
email: tian.zhang@ensam.eulazhar.homri@ensam.eu

Lazhar Homri

Jean-Yves Dantan
email: jean-yves.dantan@ensam.euali.siadat@ensam.eu

Ali Siadat

Conceptual maps of reliability analysis applied in reconfigurable manufacturing system

Keywords: Reconfigurable Manufacturing System, Reliability Analysis, Conceptual map, Mean Time Between Failure

Reliability has always been an important factor for any manufacturing companies. An appropriate level of reliability in a manufacturing system could mean less maintenance cost, higher efficiency and steadier production state. Because each machine in a manufacturing system has its individual level of reliability, reliability on the system level would depend largely on how the machines are configured. In traditional efforts on reconfigurable manufacturing system (RMS) reliability assessments, mean time between failure (MTBF) is usually adopted as reference index of reliability. Also, in existing research efforts of applying reliability analysis in manufacturing system, reliability is merely a single and over-simplified index in the framework. But there exist various forms of reliability inside a RMS, and the complexity of this concept would keep increasing with the development of new technology in manufacturing industry. To analyze reliability in RMS in a more comprehensive way, we built conceptual maps as first step for research agenda --from the perspective of general layer, reliability analysis and RMS.

Introduction

Most of the existing research efforts on the reliability of manufacturing systems are analysis on system topology, and the reliability attributes of the components are relatively less considered. Analytical method and computer simulation method are the two main directions when analyzing reliability of a manufacturing system. Among various analytical methods, Fault tree analysis (FTA) and Failure mode and effect analysis (FMEA) are quite usually applied for systems with relatively smaller scale in earlier research [START_REF] Baig | Reliability analysis using fault tree analysis: a review[END_REF]. With the development of modern industrial technology, more methods are gradually being proposed and applied into analyzing the reliability of the systems, such as Petri net and Markov chain [START_REF] Wu | Extended object-oriented petri net model for mission reliability simulation of repairable pms with common cause failures[END_REF][13]. In the system reliability as-sessment of large complexity, simulation method such as Monte Carlo combined with various algorithms plays an important role [START_REF] Pan | An effificient reliability method combining adaptive support vector machine and monte carlo simulation[END_REF].

It is important to adapt reliability analysis to the specific case of Reconfigurable Manufacturing Systems (RMS) .RMS fits the current market trend, which is varying quite fast and cost limit. Although cost is a constraint, quality is a big issue at the same time. Taking china as an example, a national strategic plan "Made in China 2025" mentioned quality as a key focus [START_REF] Li | China's manufacturing locus in 2025: With a comparison of "Made-in-China 2025" and "Industry 4.0[END_REF]. Thus, to fit the fast-varying market with the cost and quality requirement, reliability analysis in RMS is important. Succinctly saying, when compared with regular manufacturing system, RMS would involve more module interactions/ interfaces due to the nature of the system. In an RMS, reliability not only matters on the modules of tools, machines and system, but also between these modules. Thus, it is more reasonable to distinguish the reliability of an RMS from a regular manufacturing system RMS is a machining system which can be created by incorporating basic process modules including both hardware and software that can be rearranged or replaced quickly and reliably [START_REF] Koren | Reconfifigurable manufacturing systems: Principles, design, and future trends[END_REF]. The basic features of an ideal RMS include modularity, integrability, customized flexibility, scalability, convertibility and diagnosability, in which diagnosability is the ability to automatically read the current state of a system for detecting and diagnosing the root-cause of output product defects, and subsequently correct operational defects quickly. Diagnosability has two application directions during manufacturing process. One is the diagnosability of machine failures, and another is the diagnosability of non-conforming products. The latter is quite necessary when one considers the frequent rearrangements happening in an RMS which causes higher uncertainties of product qualities than that happening in a traditional manufacturing system. Regarding the hardware equipment, fast diagnosability could be realized by reconfigurable inspection machine (RIM). Then control methods, statistic methods and signal processing techniques could be led-in for further analysis on sources of reliability and quality problems. Therefore, diagnosability -among the main 6 features mentioned above -has the strongest linkage with reliability analysis in RMS.

In traditional efforts on RMS reliability assessments, mean time between failure (MTBF) is usually adopted as the reliability performance reference index. Besides MTBF, several similar index such as failure rate (reciprocal of MTBF), mean down time and availability were also adopted in extensive research [START_REF] Kumar | Maintenance free operating period --an alternative measure to mtbf and failure rate for specifying reliability[END_REF]. But there were doubts whether this is suitable for industrial applications. Calculation of MTBF requires that failure mode being based on exponential distribution, which does not always fit the real case, especially not for a RMS case.

For an RMS, the characteristic of reconfiguration could be realized in many forms. As shown in Fig. 1, reconfigurations could be on layout, machine tools or planning, either simultaneously or separately according to specific assumptions. Hence, reliability could be interpreted in many ways with different form of reconfigurations not limited to the only index -MTBF.

Based on the considerations and discussions above, we proposed to interpret the idea of reliability in a more reasonable and comprehensive way. The problem formalization is as follows:

To address the increasing complexity of manufacturing systems, we try to include various forms of reliability inside a reconfigurable manufacturing system, its machines and products during the whole period of time: from the beginning of manufacturing to product's end of life. In this paper, our main contribution is constructing conceptual maps as an informational basis for an issue we proposed.

Fig. 1. Reconfiguration in various forms

To clarify the proposed research issue, we made an example with automobile for illustration as shown in Fig. 2. The whole life of the automobile, from manufacturing to usage were included in our research time span. When the automobile order arrives, the production requirements would occur automatically, thus we make selection of the configurations, which could be presented as the period called "usage of RMS". During this step, performance index of a system such as scalability is also renewed. Then the manufacturing process starts, during which the state of the system is diagnosed, along with the reliability such as MTBF for a maintainable automobile manufacturing system. After the automobile has been verified by the quality control and put into usage, environmental factors such as road quality, maintenance of the engine and usage weather etc. could all influence the final reliability of the automobile.

In the following part of this paper, chapter 2 includes the discussion of existing related works and highlighted two firmly related papers to our research issue; chapter 3 presents the conceptual maps we built for the research issue; and chapter 4 includes conclusion and future research perspectives.

Relevant research

After formalizing our problem, we did a literature searching in Web of Science. The searching condition was set very strictly, and we applied snowballing method for more related papers. We ended up with 25 papers as the review paper database, in which there were 2 papers highly related to the issue we proposed. This number proves the scarcity of reliability analysis in RMS, in which reliability is taken as a main criterion. Yet as we have mentioned in chapter 1, reliability plays a rather important role in current manufacturing systems, especially in systems with reconfigurable characteristics. Therefore, it is quite important to build conceptual maps for this issue as a start. Papers highly related to the proposed issue: -《A multi-objective reliability optimization for reconfigurable systems considering components degradation》 [START_REF] Zhao | A multi-objective reliability optimization for reconfifigurable systems considering components degradation[END_REF] The authors proposed an integrated method to improve reliability of the reconfigurable manufacturing system, with cost-efficiency as constraint. The problem in this paper is a multi-objective optimization, in which objectives are to maximize system reliability and minimize total cost or performance lost. In this article, reconfiguration is realized through rearranging and replacing components, which accords to the reconfigurable layout branch in Fig. 1.

-《Research and optimization of reconfigurable manufacturing system configuration based on system reliability》 [START_REF] Xiong | Research and optimization of reconfifigurable manufacturing system confifiguration based on system reliability[END_REF] The authors presented a hybrid parallel-series model with waiting system characteristics, in which reliability is set as the criterion. Also, other system performances including productivity, and cost by combining system engineering theory are adopted for evaluation. Same as the former paper, reconfiguration form also accords to the reconfigurable layout branch in Fig. 1 in this research.

These two papers share the same form of reconfiguration, and both worked on algorithms to solve the performance optimization. But the difference is in the 1st research, the optimization is multi-objective but in the 2nd research, reliability is the only objective in optimization.

Construction of conceptual maps

A conceptual map is a graphical tool that depicts suggested relationships between concepts [START_REF] Hager | Designing & delivering: Scientifific, technical, and managerial presentations[END_REF]. It is commonly used by instructional designers, engineers, technical writers, and others to organize and structure knowledge. It could help organize the complicated relations between concepts, which fits our need since the definition of the reliability and quality in our research is of multiple layers. Reliability analysis and quality control enable a manufacturing company to precisely control the manufacturing process from two key aspects. The advantage of CM is its stimulation of idea generations, which could aid in brainstorming of potential research topics. But as the same time, it can only be seen as a first step in a scientific research and there could be individual differences when it comes to the definition of one same word. This often happens when the researchers are from different countries, or even sometimes different labs.

By constructing conceptual maps, we intended to aid researchers by increasing clarity of reliability analysis and RMS concepts and thus, the probability of successful implementation. At the same time, it will help clarifying for our own research topic in the later works. CM is preferred to be built with reference to a few particular questions that researchers would like to answer as a start. The focus question we ask is consistent to the research issue we proposed: How do we conduct reliability analysis on RMS in a more reasonable and comprehensive way?

The elements in CM are concepts, propositions, cross-links and hierarchical frameworks [START_REF] Novak | The theory underlying concept maps and how to construct them[END_REF]. Concept is defined as a perceived regularity in events or objects, or records of events or objects, designated by a label. Cross-links helps connect two concepts from various segments of the CM, it is often where the creative leaps would occur. Propositions are statements about some object or event in the universe, either naturally occurring or constructed. Propositions contain two or more concepts connected using linking words or phrases to form a meaningful statement.

In the following parts, we are going to present the CM of the 2 concepts "reliability analysis " and ""reconfigurable manufacturing system" separately and then combine the two concepts for a more general CM. The former two CMs are buit the 2 main questions: why and how? "Why" leads to the concepts that's related to the reason why this main concept is built and "how" leads to the concepts those are more related to the methods and approaches.

As shown in Fig. 3, reliability analysis could be broadly interpreted as analysis on the ability for a system to perform its intended function [START_REF] Xie | Computing system reliability: models and analysis[END_REF]. As discussed in the former contents, the importance of reliability in a system is nonnegligible, especially with the increasing of size and complexity of systems. With functionality of manufacturing operations becoming more essential, there is also a growing need for reliability analysis. Definition of reliability could be adapted into many forms based on the essence of the systems. Reliability could be presented by many indexes, the common definition of reliability function is R(t), and also there could be MTTF, maintainability-which could also be presented by mean time to repair (MTTR), mean time between failure (MTBF), failure rate and availability. The techniques in RA that's quite often applied are reliability block diagrams, network diagrams, fault tree analysis (FTA) and Monte Carlo simulation. FTA has the advantage of describing the fault propagation in a system, but it might not come into effect in a system with highcomplexity and maintenance characteristic. Monte Carlo simulation could be applied to evaluate MTBF when the possible distribution function is already given.

It is noteworthy that the concepts in Fig. 3 could keep unchanged or change according to the system type (regular/ reconfigurable manufacturing system). To identify those concepts which might be significantly impacted by system type, we highlighted them in Fig. 3 by deep color. (When one concept is highlighted, all the concepts located on its branches could be affected by system type logically.) When a system is reconfigurable rather than dedicated, there would certainly involve more possible failures due to its higher system complexity. Yet when compared to overly complicated flexible manufacturing system, it could contain less failures -either in law of the failure, causes of failure or consequences of failure. Thus, the reliability for regular and reconfigurable manufacturing system would vary identically. And as shown in Fig. 3, the hardware system, software system and machines for processing could all be special for a reconfigurable manufacturing system when compared with regular ones. We constructed the CM of RMS as shown in Fig. 4. The parts where RMS is different from a regular manufacturing system have been highlighted by darker color in the figure . RMS was introduced as a response to volatile global markets that instigated large uncertainty in product demand [START_REF] Koren | The emergence of reconfigurable manufacturing systems (rmss)[END_REF]. RMS has the reconfigurable characteristics, and they are commonly concluded to 6 features for enabling rapid responsiveness [START_REF] Andersen | Understanding changeability enablers and their impact on performance in manufacturing companies[END_REF]. The feature customized flexibility enables the system to manufacture part families. One of the main reason RMS is different from dedicated manufacturing system (DMS) or flexible manufacturing system (FMS) is its focus on producing part families. Integrability could be realized either on the system level or machine level. At the machine level, reconfigurable machine tools (RMT) could be applied; at the system level, machines are seen as modules that could be integrated through transport systems. Diagnosability is the feature closely related to reliability, it could be detection on either product quality or system reliability. In the phase of problem formalization, both these two elements are taken into consideration in the model. Typically, RMS contains computer numerically controlled (CNC) machines and in-line inspection stations. RMS could be the study object in many applications: configuration selection, planning and scheduling, product family formation, layout configuration analysis and configuration design. In configuration design, it could be applied to level of systems, machines or other modules such as transportation/controlling equipment etc. [START_REF] Fotsoh | Towards a reference model for configuration of reconfigurable manufacturing system (rms)[END_REF], which concords with the feature of integrability. As show in the Fig. 5, combination of the conceptual maps includes general concepts for our research issue -applying reliability analysis in reconfigurable manufacturing system, in which we show the factors that attributes to the comprehensive research characteristics. Attributions to comprehensiveness of our research have two parts: the variety of reliability indexes and the variety of the studied layers. And the scope of time, which has not been added into the map, is also an attribution to comprehensiveness.

Conclusion

The conceptual maps we have developed are based on the study literatures of RMS and reliability. The validation of the conceptual map could be realized in 2 ways in future work. One way is to validate by comparing conceptual maps generated by others. The other way is to observe the behavior in a relevant situational context. This could be summarized as application validity approach [START_REF] Albert | Empirical Empirical validation of concept maps: Preliminary methodological considerations[END_REF]. The aim of this study was to clarify the conceptual ambiguity when applying reliability analysis in reconfigurable manufacturing systems. In support of this aim, we provided a visual representation of this topic in the form of conceptual maps in chapter 3. While the map provides a necessary first step towards clarification, the results could be continuously improved based on up-to-date findings in those fields.

The construction of the conceptual maps is a basis for our research agenda. In future work, we could keep developing the methodology and models for the research issue we proposed. As mentioned in chapter 3, each cross-link in the conceptual maps could imply a potential research topic. Besides the issue we proposed, how the usage period together with manufacturing period impact on the reliability of products could also be an interesting direction for researching.

Fig. 2 .

 2 Fig. 2. Research issue with automobile as an example

Fig. 3 .

 3 Fig. 3. Conceptual map of reliability analysis in a system

Fig. 4 .

 4 Fig. 4. Conceptual map of reconfigurable manufacturing system

Fig. 5 .

 5 Fig. 5. Combination of the conceptual maps


Rashid Anzoom
email: ranzoom2@illinois.edu

Rakesh Nagi
email: nagi@illinois.edu

A Framework To Assess Risk of Illicit Trades Using Bayesian Belief Networks

Keywords: Illicit Trade, Risk Assessment, Bayesian Belief Networks

Recent years have seen the initiatives against illicit trades gain significant traction at both national and global levels. A crucial component in this fight is correct assessment of the risks posed by different trades across different regions. To aid in this cause, we provide a risk prediction framework based on Bayesian Belief Networks. It involves the development of a causal model incorporating variables related to the rise/decline of the illicit trade volume. The influence of these variables are determined by training on available data that are allowed to update over time. Implementation on a sample case study shows relatively low prediction accuracy of our model. Factors constraining its performance are analyzed and possible ways to avert them are discussed. We expect this framework to act as a decision support tool to the policymakers and strengthen them in the fight against illicit trades.

Introduction

The sustained growth and diversification of illicit trades remain a substantial threat worldwide [START_REF] Anzoom | A review of research in illicit supplychain networks and new directions to thwart them[END_REF]. Recent statistics report the annual turnover of these trades to be in the order of 2.2 trillion US dollars, which corresponds to approximately 8-15% of the global GDP [START_REF] Mashiri | Illicit trade, economic growth and the role of customs: A literature review[END_REF]. Efforts to control/disrupt illicit trade are heavily constrained by the scarcity of resources (e.g., workforce, finance), emphasizing the importance of allocating them efficiently. Before planning for disrupting illicit trade, though, we need reasonable estimates of the proliferation risks of different trades in distinct regions of the world.

One could base this estimation process on the available statistics; however, such an approach is risky since data on illicit supply chains are rare and suffer from multiple shortcomings (including incompleteness, unclear boundary specification, low dynamics) [START_REF] Anzoom | A review of research in illicit supplychain networks and new directions to thwart them[END_REF]. An alternate strategy involves discerning factors that affect the rise or decline of these trades, as well as their degree of influence which we assume to be probabilistic. Available information on these variables will then lead to the estimation of risk. In this paper, we introduce a framework to conduct this assessment in a systematic manner. In particular, we employ Bayesian Belief Networks (BBN) modeling, which is widely known for dealing with probabilistic inference in complex systems [START_REF] Pourret | Bayesian Networks: A Practical Guide to Applications[END_REF].

Prior to discussion of the proposed approach, we review previous works related to our research problem. Existing literature on this topic is mostly qualitative in nature: identifying specific and general risk factors for different trades [START_REF] Anzoom | A review of research in illicit supplychain networks and new directions to thwart them[END_REF]. A few quantitative models have been proposed to predict individual trade risk/volume. For instance, growth of narcotics market was modeled as a function of a small number of variables (e.g., utility, risk, enforcement level, economic status) [START_REF] Baveja | A sequential model for cracking down on street markets for illicit drugs[END_REF][START_REF] Caulkins | Interdiction's impact on the structure and behavior of the export-import sector for illicit drugs[END_REF]. Researchers have also employed BBN models in some of these works. An expert-driven model is presented at [START_REF] Koen | An expert-driven causal model of the rhino poaching problem[END_REF] to predict the occurrence of poaching event of rhinos. Data-driven models aimed to predict deforestation, which is related to illegal logging [START_REF] Silva | A spatio-temporal Bayesian network approach for deforestation prediction in an Amazon rainforest expansion frontier[END_REF][START_REF] Mayfield | Use of freely available datasets and machine learning methods in predicting deforestation[END_REF]. Alternate methodologies used here include artificial neural network and Gaussian process. Apart from these, BBN has also been used to detect activities in illicit trades (e.g., prediction of fraudulent food products) [START_REF] Soon | Application of Bayesian network modelling to predict food fraud products from china[END_REF]. Using separate prediction models for each trade category might not be convenient for the policymakers. Perhaps with that in mind, The Economist Intelligence Unit [START_REF]The Economist Intelligence Unit Limited: The global illicit trade environment[END_REF] developed a country-wise risk index to indicate the prevalence risk of illicit trades. However, the index is linear in nature and defined by expert opinion. Furthermore, it does not distinguish different trade categories and focuses on the regional factors only. Thus, there is need to develop a model that can predict the risk of individual trade categories at different regions as well as provide an aggregated risk score for a particular area or trade. Our framework aims to build a customized model with these features.

The remainder of this paper is organized as follows. Section 2 describes the steps in developing and implementing the framework. Section 3 presents a case study for demonstrating our framework. Our discussion concludes in Section 4 through a critical review of the approach and a brief discussion of future avenues.

Risk assessment framework

The framework to assess the risk of illicit trades consists of five steps as shown in Figure 1. The following subsections discuss these steps sequentially.

Identification of factors related to illicit trades

The discussion on the causes behind the inception and continuation of illicit trades can be found in several places of the literature. Some of the established factors include poor socio-economic conditions, operational risk or lack thereof, the potential return on investment, etc. We divide these factors into two sets: region-specific and trade-specific. The Economist Intelligence Unit (EIU) considered 20 features of the first category to predict regional suitability for illicit trades [START_REF]The Economist Intelligence Unit Limited: The global illicit trade environment[END_REF]. The second set, on the other hand, denotes the expected supply chain performance in a business. We propose to incorporate the drivers of the

Step 1

Identification of relevant factors

Causality tests Dimensionality reduction techniques

Step 2 Step 3

Modeling of BBN

Data collection and curation

Imputation of missing data Data quality assessment

Step 4

Learning of model parameters

Expert elicitation Probabilistic inference

Step 5 illicit supply chain in this set (e.g., ease of production/acquisition, storage, concealment and transportation, access to resources, profitability, money laundering, corruption). Beyond this, one can always incorporate additional variables through causality tests, i.e., statistical hypothesis testing. Ordiano [START_REF] Ordiano | A method for estimating driving factors of illicit trade using node embeddings and clustering[END_REF] recently demonstrated another approach using node embedding and clustering. For customization, it is also possible to filter out some variables through dimensionality reduction techniques (see [START_REF] Van Der Maaten | Dimensionality reduction: A comparative review[END_REF] for details).

Prediction, evaluation, and update

Comparison between ground truth and prediction result Model validation Adjustment of model parameters

Modeling of a Bayesian belief network

Following the selection of variables, we move forward to modeling. Our adopted approach, BBN, is a directed acyclic graphical model of causal relationships based on probability theory [START_REF] Ben-Gal | Bayesian networks[END_REF]. In the constructed graph, nodes denote the variables of interest; while edges represent the causal relationship (dependence) between them. In our case, we can consider five sets of nodes: region-specific factors (A), trade-specific factors (T ), trade statistics (S), data reliability (D), and trade risk (R). Trade statistics denote the types of data available regarding illicit trades (e.g., instances reported, transaction volume, number of arrests), while data reliability indicates the confidence in the data at hand. The trade risk is predicted as a probabilistic function of all these variables. In terms of equation, this can be written as follows: P (S|A, T, R, D) = P (A)P (T )P (R|A, T )P (D)P (S|R, D).

(

) 1
In a simpler model, nodes within a set are considered conditionally independent of each other. For a better representation of reality, one can conduct multivariate regression analyses or causality tests among the variables. Given data availability, it is also possible to learn the model structure using several algorithms [START_REF] Scanagatta | A survey on Bayesian network structure learning from data[END_REF]. Two other salient node attributes in this model are the type and state of nodes. The model supports both discrete and continuous nodes, although the former is preferred. Continuous nodes have to go through discretization by some interval points. The methods for such discretization can be user-specified or algorithmic/data-driven (supervised or unsupervised) [START_REF] Beuzen | A comparison of methods for discretizing continuous variables in Bayesian networks[END_REF]. Once we specify all these issues, our model is ready to learn the parameters.

Data collection and curation

As mentioned earlier, the deceptive nature of illicit trades makes it difficult to collect reliable data on them. A discussion on the existing data sources is provided in [START_REF] Anzoom | A review of research in illicit supplychain networks and new directions to thwart them[END_REF]. Among the five mentioned sources, organizational databases remain the most useful ones for our analysis since they follow a standard format and are regularly updated. Still, it cannot be said that the available statistics accurately represent reality. This is why it is important to include in our model information regarding the quality and the reliability of the used data. The four major dimensions of data quality are accuracy, completeness, consistency, and timeliness [START_REF] Pipino | Data quality assessment[END_REF]. In the BBN, the set of nodes representing the data reliability aspect represents the state of these quality dimensions. In terms of trade statistics, one can use different types of data as nodes or apply fusion at the information level to obtain an aggregated measure.

Learning the model parameters

In this step, we train our model with the existing dataset to learn the parameters, i.e., to learn the conditional probabilities (CP). While we intend to derive these probabilities straight from the data, it is not unusual for some information to be limited in amount or to be simply unavailable. In such cases, researchers have often used expert opinions for conditional probability elicitation [START_REF] Mkrtchyan | Methods for building conditional probability tables of Bayesian belief networks from limited judgment: An evaluation for human reliability application[END_REF]. Considering this, we implement an inference method that is adaptable to such scenarios, including the combination of expert opinion and evidential information, as well as incomplete or small dataset. Further information regarding these algorithms can be found at [START_REF] Ji | A review of parameter learning methods in Bayesian network[END_REF] and [START_REF] Mkrtchyan | Bayesian belief networks for human reliability analysis: A review of applications and gaps[END_REF].

Prediction, evaluation, and model update

Given the parameters and prior probabilities of the variables would provide the risk of a specific trade in a particular region as per Equation [START_REF] Anzoom | A review of research in illicit supplychain networks and new directions to thwart them[END_REF]. If the ground truth data (actual trade risk/statistic) becomes available, one can compare it with the predicted results through different metrics (e.g., confusion matrix, kfold cross-validation, spherical payoff) [START_REF] Marcot | Metrics for evaluating performance and uncertainty of Bayesian network models[END_REF].

Most of the databases we use are updated on an annual basis. Incorporating these new pieces of evidence will update the model regularly, improving its adaptability. It is even possible to assign variable weights to cases as well as unlearn previous instances [START_REF] Nielsen | Bayesian Networks and Decision Graphs[END_REF].

Finally, should the prediction error become significantly high, it becomes necessary to scrutinize the model. In this case, techniques like sensitivity analysis, cross-validation, and scenario analysis can provide insight regarding the model [START_REF] Chen | Good practice in Bayesian network modelling[END_REF].

Case study

To illustrate the framework introduced in Section 2, we present a sample case study to compute the proliferation risk of illicit trades for different countries.

Step 1 We begin with the decision to include 4 trade-specific and 14 region (country)-specific factors influencing illicit trades. The region-specific factors are divided into four categories (trade transparency, supply and demand, governmental policy, and customs environment) as described in [START_REF]The Economist Intelligence Unit Limited: The global illicit trade environment[END_REF]). As a consequence, we introduce a node for each of them in the BBN. Two more nodes are introduced to represent the country environment and ease of trade, which influence the node trade risk. For data reliability, we only consider one node (completeness) since the age for all data is the same. Finally, we have nodes representing two types of trade statistics (trade volume and number of cases), taking the tally of nodes to 28. he selection of these variables was based on data availability, although information regarding the trade-specific factors was not found. For the sake of model completeness, we assign values to them based on our judgment, e.g., transportation of narcotics is considered to be easy because of its size while transportation of arms is considered difficult.

Step 2 With the selection of the variables complete, we move to build the model. Most of the variables are represented by scores and thus continuous in nature. Availability of data allows a reasonable discretization of continuous nodes. In this model, we employ the equal frequency strategy, which assumes the quartiles as cutpoints. Considering the minimum and maximum possible value of the factors, up to two more cutpoints can be included. The interval between these cut-points represents the states of the discretized nodes. Links between the nodes are assumed to be predetermined, so we do not run any causality test or structural learning. The complete structure of the causal model is visible in Figure 2. For ease of discernment, the node-sets are color-coded and a legend is provided. Step 3 Our next step involves collection and preprocessing of relevant data. Information related to the factors are found on 15 separate databases, the majority of which are listed in [START_REF]The Economist Intelligence Unit Limited: The global illicit trade environment[END_REF]. Besides that, information on law enforcement capability, institutional quality, and corruption is extracted from the World Internal Security and Police Index1 , the GCI (Global Competitiveness Index) database, and the World Economic Forum Global Competitiveness Report2 . On the other hand, the UNODC (United Nations Office on Drugs and Crime) database3 provides statistics on illicit trades. No data is found on trade-specific factors, as mentioned earlier. All of the sources used fall under the category of open organizational databases. However, heterogeneity exists in their structure and the volume of data they provide. For example, UNODC provides 27 year-long data regarding drug seizure, while EIU provides tracking competence for only 2 years. Furthermore, each database holds additional information besides the desired ones. For inference of the conditional relationships between the factors, one would need data for all attributes in one single database. We achieve this by collecting the latest available records (including statistics of two trades: narcotics and arms trade) across 160 countries and merging them into a country database. We also compute the completeness and timeliness of the data. The attribute with the highest completeness was the cybersecurity index (95.63%), while the lowest was the supply-demand (45%). The lowest, highest and median tuple (countrywise) completeness was 33%, 92.6%, and 59%, respectively. The overall relationship completeness was 72.31%.

Step 4 For learning the conditional probabilities, we feed this data into NET-ICA 4 , a software specializing in BBN modeling and analysis. Netica uses three methods to learn the conditional probabilities: count, expectation maximization (EM), and gradient descent method. The last two are used for inferring from an incomplete database, which applies to our case. The available data set was divided into two sets (learning and testing) for validation. The learning set is used to train the model, while the testing set is used for evaluating our prediction. For comparison, we train the model using both EM and the gradient descent method. Once trained, the model assumes values for the conditional probabilities. An example is shown in Figure 3. Here, we show the influence of tracking capability and the Kyoto Addendum on the trade transparency score.

Step 5 Once the training is complete, our focus shifts to assessing the accuracy of prediction. Since the actual proliferation risk is not known, the test is done on the trade statistics instead. Results show EM to be more accurate (38.46%) than gradient descent (28.85%). The scores for quadratic loss, logarithmic loss, and spherical payoff are 0.825, 3.66, and 0.457. The accuracy is still quite low for a prediction model, but considering the incompleteness of data, simpler model structure, and the inherent difficulty of assessing illicit trades, we consider this value to be reasonable. The omission or imputation of incomplete tuples is expected to improve this accuracy.

Sensitivity analysis measures the degree to which variation in posterior probability distribution of the target node (risk index) is explained by other variables, i.e., how influential different nodes are in predicting risk index [START_REF] Li | Sensitivity analysis of a Bayesian network[END_REF]. In this case (discrete node), the measure is entropy reduction. Table 1 shows part of our results, listing the individual factors with higher influence. As expected, trade volume and the number of cases have the greatest influence on trade risk. The next two in the list are ease of storage and transportation, which explains the higher spread of narcotics trade over arms in general. The last factor, cybersecurity preparation, is a bit surprising since the transactions are mostly done physically. This might be an issue worth investigating in the future. Once these results are validated, one can predict the risk with greater confidence. We have left the trade risk here as a categorical variable. That said, it is also possible to consider it as an index of continuous nature. The same methodology can be applied for different scales of regions (continent, country, state/district), given, of course, that data for different regions are made available.

Conclusion

The ability to predict trade proliferation risk is expected to have great value in the fight against the illicit economy. However, it requires handling a multitude of challenges. This paper discusses the main ideas behind building such a prediction model, and demonstrates the challenges of building one through a case study. The first issue requiring attention is the scarcity and limited availability of data since it has significant impact on the prediction performance. None of the trade-specific factors in the model are clearly defined in the literature. Development of measures for them would be a good idea for future research. For reliability assessment, timeliness of data merits inclusion. However, the measure of volatility (duration of data validity) in the case of illicit supply chain needs to be set a priori. Caution should also be exercised while choosing the method for discretizing continuous variables. In the equal-frequency method, updating the parameters would alter the probability distributions to some extent but the quartiles remain the same, thus affecting the expected value. Finally, if data updated annually become sufficiently available, one should consider detecting dynamics both within and between different variables over time. Dynamic Bayesian networks should be a good choice to carry out this work. These recommendations would be implemented in our future works to overcome the aforementioned limitations and build a workable model with higher prediction accuracy and greater insights.

Fig. 1 .

 1 Fig. 1. The five main steps for our illicit trades risk assessment framework.

Fig. 3 .

 3 Fig. 3. Conditional Probability of Trade Transparency Score Given Track and Trace Performance and Kyoto Accordance status (Display from NETICA).

  The BBN model for the case study, built using NETICA.

	Fig. 2.			Difficult 0 +	Moderate 100	Easy 0 +	Ease_of_Sourcing		Difficult 0 +	Moderate 100	Easy 0 +	Ease_of_Production		Difficult 18.4	Moderate 0 +	Easy 81.6	Ease_of_Storage				Difficult 18.4 Difficult 13.4	Moderate 0 + Moderate 10.0	Easy 81.6 Easy 76.6	Ease_of_Transportation Trade_Ease			7.33 ± 8.1	29.5 to 100 0 +	10.25 to 29.5 24.8	4.76 to 10.25 19.2	1.23 to 4.76 25.6 32.5 ± 19	0 to 1.23 30.4 90.3 to 100 0.35	63.3 to 90.3 Tax_Burden 5.48	51.85 to 63.3 13.1	Supply_Demand 4.95 to 5.64 5.64 to 6.75 0 to 6.3 6.75 to 7 6.3 to 38.95 23.7 23.5 0 + 4.69 ± 1.2 38.95 to 51.85 0.84 70.4 9.85	4.18 to 4.95 24.9	1.89 to 4.18 27.9	0 to 1.89 0 +	Organized_Crime_Perception	4.25 ± 1.1	3.52 ± 1.1 5.09 ± 1.3 6.5 to 7 0 +	4.09 to 5.77 27.7 5.98 to 8.16 20.4 4.93 to 6.5 26.5	3.47 to 4.09 18.1 5.09 to 5.98 20.0 4.09 to 4.93 25.3	3.07 to 3.47 25.3 4.48 to 5.09 30.1 3.53 to 4.09 27.8	1.41 to 3.07 28.9 2.97 to 4.48 29.5 1.71 to 3.53 20.3	0 to 1.41 0 + 0 to 2.97 0 + 0 to 1.71 0 +	Institution_Quality FATF_Compliance IPR_Score
							3370 ± 5900	6050 to 25000 15.7 173000 ± 410000	1669.5 to 6050 18.9 1.8032e6 to 2.5e6 0 +	359.5 to 1669.5 16.4 85937 to 1.8032e6 17.0	24.25 to 359.5 16.4 5680 to 85937 24.7	3 to 24.25 25.8 763.115 to 5680 24.8	0 to 3 6.80 0 to 763.115 33.6	Cases Volume				High 43.7	Moderate 26.8	Low 29.5		Trade_Risk				44.6 ± 28	72.35 to 99 11.9	61.7 to 72.35 21.7	50.23 to 61.7 21.8	8.6 to 50.23 22.7	0 to 8.6 21.7		Country_Environment				57.8 ± 30	92.2 to 100 10.8	85.48 to 92.2 13.7	78.15 to 85.48 12.7	61.325 to 78.15 14.6	13 to 61.325 37.6	0 to 13 10.6	Govt_Policy	3.78 ± 1.3 0.502 ± 0.3	6.4 to 7 0 + 0.931 to 1 1.04	4.7 to 6.4 26.2 0.786 to 0.931 24.0	3.4 to 4.7 26.7 0.527 to 0.786 27.1	2.7 to 3.4 24.8 0.201 to 0.527 22.9	1.7 to 2.7 22.3 0.04 to 0.201 19.8	0 to 1.7 0 + 0 to 0.04 5.21	Corruption Cybersecurity_Preparation
																	0.725 ± 0.16	0.93 to 1 0 +	0.89 to 0.93 21.4	0.74 to 0.89 31.6	0.59 to 0.74 27.6	0.33 to 0.59 19.4	0 to 0.33 0 +	Completeness							58.8 ± 30	96.3 to 100 10.6	76.7 to 96.3 18.2	67.3 to 76.7 20.3	52.85 to 67.3 19.4	7.5 to 52.85 20.0	0 to 7.5 11.6	Customs_Environment	0.613 ± 0.18	0.9 to 7 0 +	0.73 to 0.9 31.9	0.59 to 0.73 23.7	0.48 to 0.59 19.6	0.255 to 0.48 24.8	0 to 0.255 0 +	Law_Enforcement
	Data Reliability	Trade Statstics	Factors Related To Trade Transparency	Factors Related To Ease of Trade		Factors Related To Govt Policy		Factors Related To Customs Environment		Factors Related To Supply and Demand					Absentee 33.7	Signatory 66.3		Kyoto_Accordance					46.9 ± 28 3.04 ± 0.83	0 to 1.2 9.02 0 to 1.63 1.2 to 42.35 30.9 1.63 to 2.45 42.35 to 56 11.8 2.45 to 2.78 56 to 67.75 23.7 2.78 to 3.27432 67.75 to 85.1 19.4 3.27432 to 5 85.1 to 100 5.20 0 + 21.4 23.5 26.5 28.6	Transparency_Trade Track_Trace			Absent 28.2	Developing 9.31	Operational 62.5	AEO_Programme	1.17 ± 0.61	1.77 to 2 22.1	1.23 to 1.77 33.3	0.67 to 1.23 17.1	3.3 ± 0.75 0 to 0.67 27.5	4.41 to 10 1.02 15.4 ± 22 Automation	3.67 to 4.41 26.5 75 to 100 1.83	3.17 to 3.67 28.6 7 to 75 28.3	2.8 to 3.17 20.4 3 to 7 27.2	2.03 to 2.8 23.5 1 to 3 40.9	0 to 2.03 0 + 0 to 1 1.76	Clearence_Time Shipment_Inspection

Table 1 .

 1 Sensitivity of Trade Risk To Other Node Findings.

	Node

Mutual info (entropy) Percent Variance of belief

	Trade volume	0.33	21.3	0.429
	Cases	0.082	5.26	0.012
	Ease of storage	0.019	1.24	0.004
	Ease of transportation	0.019	1.24	0.004
	Track and trace	0.009	0.601	0.001
	Cybersecurity preparation	0.006	0.419	0.01

http://www.ipsa-police.org/

http://reports.weforum.org/global-competitiveness-index-2017-2018/

https://dataunodc.un.org/

https://www.norsys.com/netica.html