Manuel Rippel
email: mrippel@ethz.ch

Johannes Schmiester

Paul Schönsleben

How to Support Plant Managers in Strategizing Volume-Oriented Changeability in Volatile and Uncertain Times -Deriving Requirements for a Practice-Oriented Approach

Keywords: Uncertainty, Volatility, Resilience, Volume-oriented Changeability, Strategizing, Demand-responsive Supply Chain

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Introduction

The environment of production plants is characterized by increasing demand volatility and uncertainty, which also comprises major disruptions due to extreme events, like grey or black swans [START_REF] Akkermans | Searching for the Grey Swans: The Next 50 Years of Production Research[END_REF][START_REF] Taleb | The Black Swan: The Impact of the Highly Improbable[END_REF]. As the frequency and extent of those fluctuations and extreme events as well as the number of unknown risks in an uncertain world is increasing, it is hardly possible to use common forecasting methods anymore. Assumptions and derived decisions regarding configuring production resources of plants often turn out to be wrong. A multitude of scientific approaches and concepts have been developed, and these often focus on technical-related topics [START_REF] Kampker | Analysis of sociotechnical structures in order to increase the changeability of producing companies[END_REF]. The concept of volume-oriented changeability (VoC) was introduced [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF][START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF] with the target of synchronizing capacities and costs with demand fluctuations. VoC can be regarded as a specific subset of the broad concept of changeability [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF]. It should provide added value for plant managers or managers in charge as project managers to strategize and/or implement procedures to economically and competitively handle implications of demand volatility and uncertainty. The plant level including the interface towards corporate management is still being widely neglected in the research on responsiveness of organizations and organizational units towards volatility and uncertainty. Existing scientific approaches are either designed for the company level [START_REF] Friedli | Technologiemanagement -Modelle zur Sicherung der Wettbewerbsfähigkeit[END_REF], supply chain level [START_REF] Petit | Ensuring Supply Chain Resilience: Development of a conceptual Framework[END_REF], manufacturing network level [START_REF] Lanza | Strategic Planning of Global Changeable Production Networks[END_REF], or on the factory level, which mainly focuses on topics with high relevance for operations and logistics closely related to the shop floor [START_REF] Kampker | Analysis of sociotechnical structures in order to increase the changeability of producing companies[END_REF][START_REF] Wiendahl | Changeable Manufacturing -Classification, Design and Operation[END_REF][START_REF] Nyhuis | Wandlungsfähige Produktion. Heute für morgen gestalten[END_REF]. There is a lack of attention in literature to providing practically relevant and applicable approaches and tools that address important fields and occurring obstacles within strategizing VoC of production plants. These obstacles (summarized in chapter 2) were identified in recently conducted action research cases (in eight production plants in six countries over two years) regarding strategizing abilities of production plants in the face of demand volatility and uncertainty. They were evaluated by Rippel et al. [START_REF] Rippel | Why do plant managers struggle to synchronize production capacity and costs with demand in face of volatility and uncertainty? -Obstacles within strategizing volume-oriented changeability in practice[END_REF]. Based on this findings and the same action research cases, this paper derives requirements for an approach for strategizing the ability of production plants to economically and competitively handle volatility and uncertainty. The purpose is to provide the key parameters for subsequent research on an academically sound and practice-oriented approach.

Revealing obstacles within strategizing VoC

Obstacles, classified as target-immanent or approach-immanent, were identified and evaluated by Rippel et. al [START_REF] Rippel | Why do plant managers struggle to synchronize production capacity and costs with demand in face of volatility and uncertainty? -Obstacles within strategizing volume-oriented changeability in practice[END_REF] and summarized in the following: Business cycle-continuous profitability (O1) considers the arising trade-off between stability of unit costs (advantageous: high share of variable costs) in decline phases and exploitation of fixed costs degression effects (advantageous: high share of fixed costs) in growth phases. Multi-period competitiveness (O2) addresses that risks are transferred to third parties in order to handle volatility and uncertainty, which comes at a price. The "risk premiums" might exist in a non-transparent form due to their indirect and long-term nature (e.g., innovativeness or attractiveness of the company as employer). Multi-dimensional performance (O3) reveals that the synchronization of costs and capacities with demand volumes has implications for other target dimensions of technical, social and financial natures. These implications can be supportive or obstructive to existing strategies and implied target dimensions. Vigorous effectiveness (O4) refers to the extent and speed as essential factors within VoC. Accordingly, the scope should not be limited to production functions but include support and administrative functions of the plant. Furthermore, plants lose time to actually interpret the changes of the business environment but then might decide and act too rigorously due to time pressure and accumulating manufacturing costs. Practice-oriented applicability (O5) indicates that many approaches lack applicability in practice due to their partly single-disciplinary nature, unfeasible requirements in terms of required data and effort due to the frequently enormous complexity. Besides, many assumptions and forecasts are required but might include fragile and erroneous input in face of uncertainty with unknown risks.

Deriving requirements for strategizing VoC in practice

Based on the identified obstacles, requirements for a practically relevant and effective approach for strategizing VoC are derived and incipient hypotheses of possible solutions are given in the following.

3.1

Purpose-oriented requirements

The category "purpose-oriented" comprises three requirements which details the purpose of the underlying target of VoC, which is synchronizing capacity and costs with demand fluctuation. Solution concreteness. Approaches should explicitly address challenges, obstacles and solutions for handling volume fluctuations in production plants and contributing to a demand-responsive supply chain. Instead of generally covering various change drivers and dimensions, solutions specifically for volume fluctuations have to be defined. Thereby, plant managers should be guided by what necessarily and concretely needs to be considered in order to preventively implement measures and adapt structures, behavior and activities. For doing so, an approach should suggest relevant and important fields of action to be considered and possible enablers and levers. Solution concreteness mainly contributes to tackling the obstacles O4 and O5.

Financial explicitness. This requirement incorporates the relevance of financial considerations within managerial decision making. Beyond providing the technical possibilities to scale capacity in case of demand in-/decrease, approaches have to stress financial impacts both regarding additional costs for VoC potentials but also the target effectiveness, namely the degree of synchronization between capacities and production costs and resulting stability of unit costs and profit margins. Besides costs and capacity, the cash-flow of a production plant is endangered in the considered market environment. As fixed costs often comprise fixed cash outflows and investments into fixed structures imply amounts of bound capital, fluctuating cash inflows driven by demand volatility put severe pressure on the plant's liquidity. An approach should clearly differentiate between and make transparent the above named types and significance of financial impacts (i.e., cash-flow effective and/or profit-&-loss effective), since the effect might vary [START_REF] Taschner | Business Cases -Ein anwendungsorientierter Leitfaden[END_REF]. An approach should reflect and define a project-specific understanding, priorities and expectations (of involved stakeholders) as well as ambition level regarding profitability and competiveness related to cash-flow and/or profit-&loss impacts. This should set clear guidance for the solution search within the strategizing project and finally assess the target achievement. In particular, financial explicitness addresses the obstacles O4 and O2.

Uncertainty-adequate. The approach to be developed should sufficiently incorporate the characteristics and constraints of uncertainty, which are considered in this paper as "the insufficiency or imperfection of knowledge or information critical to decisionmaking, concerning the past, present or future events, or conditions within and surrounding an organizational system" [13, p. 401]. Within this paper and the VoC concept, we assume that neither objective nor subjective probabilities are present, which makes rational decision-making nearly impossible [START_REF] Haberfellner | Systems Engineering. Grundlagen und Anwendung[END_REF]. This requirement sets the most challenging criteria since it is questioning common approaches to model and to evaluate benefits of changeability. Significant limitations exist in modeling the system, and these reduce the practical relevance in the end. The ensuing results might incorporate an illusion of accuracy and certainty [START_REF] Gigerenzer | Risk Savvy: How to Make Good Decisions[END_REF]. According to Gigerenzer, "When we face a complex problem, we look for a complex solution. And when it doesn't work, we seek an even more complex one. In an uncertain world, that's a big error. Complex problems do not always require complex solutions." [15, pp. 14] Therefore, a robust approach should incorporate simple and heuristic elements where possible and reasonable. The requirement "uncertainty-adequate" would address obstacles O5, O2 and O1.

System boundary-dependent requirements

Within the system boundary-dependent requirements, the focus is to define which system elements, interfaces and interdependencies have to be investigated and where design possibility exists within the considered system "production plant" [START_REF] Haberfellner | Systems Engineering. Grundlagen und Anwendung[END_REF]. Strategic plant level. Taking account the underlying problem mentioned above, strategic management at the production plant is likely to be the hierarchical level in charge of responding effectively to volatile and uncertain volumes. This level is relevant since manufacturing costs are highly sensitive due to fixed cost components and main fixed costs are bound on this system level [START_REF] Wildemann | Fixkostenmanagement -Leitfaden zur Anpassung von Kostenstrukturen an volatile Märkte[END_REF]. Main fixed costs of a production plant consist of assets and personnel costs, in particular in indirect plant functions. It is at the strategic plant level where structures, (i.e., people and assets) are determined and planned upon. Measures to synchronize costs and capacity with demand can be implemented by taking a holistic perspective and has probably the highest leverage potential since plant management is not limited to managing production functions but also several supportive functions. Therefore, an approach should holistically address the strategic plant level and define the system boundaries accordingly. The manufacturing network, supply chain and company level are considered as supersystem, whereas the factory level (in the narrower, production-related sense) and further downward levels are defined as subsystem. The specific needs and obstacles of a plant's general managers to handle demand volatility and uncertainty should be addressed. In particular, their permitted and authorized scope for action should be appropriately taken into consideration since this scope might set significant limitations and restrictions to modifying and intervening in the plant and further cross-organizational processes, structures and patterns. Thus, this requirement mainly addresses obstacle O4 and additionally O3 and O5.

Interdisciplinary solution space. Basically, a multitude of approaches, measures and solutions for different partial problem aspects and occurring tasks within the broad concept of changeability exist [START_REF] Kampker | Analysis of sociotechnical structures in order to increase the changeability of producing companies[END_REF][START_REF] Nyhuis | Wandlungsfähige Produktion. Heute für morgen gestalten[END_REF]. Since VoC-relevant measures were developed from a multitude of different disciplines (e.g., finance and sourcing, engineering and factory planning, supply chain management, human resource), an integrated toolkit is barely available for holistic, strategic management level. The intentions and priorities of the various disciplinary streams differ and are sometimes contradictive to each other [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF]. For example, technical approaches to increase the changeability of production systems, which could be advantageous from an engineering perspective, might stand in contrast to measures proposed by asset management approaches. Therefore, a portfolio of solution options and alternatives from different disciplines should be comprehensively revealed and an overview of specific measures provided for practitioners in order to be able to compare dis-/advantages of measures and resulting target conflicts, to select plant-specific appropriate measures and to combine their impacts. Interdisciplinary solution space is beneficial in taking obstacles O3 and O4 into account.

Organization concept-oriented requirements

Based on the above mentioned system level, the organizational concept of the plant has to be considered according to management aspects and dimensions since system-dependent contradictions and restrictions originate here [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF]. Partly, they can be influenced by the plant management in the short-, middle-or long-term.

Socio-technical management aspects. A socio-technical system is a hybrid form of a social system and a technical system and consists of interrelated elements of both system types [START_REF] Zink | Soziotechnische Ansätze[END_REF]. Therefore, a production plant can be considered a socio-technical system since it consists of human beings and technical devices interacting with each other [START_REF] Schönsleben | Integral Logistics Management. Operations and supply chain management within and across companies[END_REF]. Socio-technical analysis of VoC means to consider not merely comprising human and technical system elements and their interactions but to extend the view beyond that and integrate in particular behavioral and activity-oriented aspects. In order to include this understanding, the system aspects "structure," "behavior" and "activities" should be addressed in an integrated manner [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF]. In regard to synchronizing capacities and costs with demand volumes, the following topics of these aspects can be considered as relevant: Structure consists of resources mainly in the form of personnel and assets as well as organizational structure and processes [START_REF] Gagsch | Wandlungsfähigkeit von Unternehmen Konzept für ein kontextgerechtes Management des Wandels[END_REF]. This structure is the object that is managed in relation to volatile and uncertain demand volumes. Here, preventive measures are to be applied in order to make the structure compliant with its environment. Behavior refers to the decision-making, underlying rationales and cognitive biases of management (as function) and managers (as individuals) in a production plant. Here, attitude towards risk, time preferences, degree of commitment and cohesiveness play an important role [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF]. When it comes to the described environment, decision-making regarding uncertainty in practice as well as established incentive, steering and performance measurement systems influencing the social practices are to be investigated. Activities on the strategic level comprise the strategy development and formulation process, here referred to as strategizing, in order to adjust structures and behavior, to implement measures and to conduct detailed studies and projects afterwards. Including the management aspects significantly influences the speed of action and the culture of decision making and addresses obstacles O1, O2 and O3.

Management dimensions. As defined above, the strategic plant management is the relevant system level to be considered. According to Bleicher [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF], the focus of strategic considerations are strategic programs as well as the design of fundamental structures, systems of management and of the problem solving behavior of the relevant individuals. However, this management dimension should not be considered independently since manifold interdependencies take place [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF]. Bleicher also argues that the task of strategic management is to influence the alignment of activities, which are established by the normative management and which focus on general targets, principles, norms and guidelines. The operational management focuses on the implementation of conceptual specifications of the normative and strategic level by means of operations according to capabilities and resources [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF]. However, unexpected events can occur as obstacles within operations, which require changing future expectations (visions of the normative level) and strategies (programs of the strategic level) [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF]. Ac-cordingly, the normative and the operational plant management level has to be considered in an integrative manner within strategizing VoC. However, the potential to influence might be limited since important aspects are largely given by corporate directives (e.g., role and functions of the plant within the manufacturing network and supply chain) and can just be "translated or completed" by local plant management. Furthermore, behavior aspects of the normative level (e.g., plant-specific characteristics of corporate culture) can be indirectly influenced in the long-term. The implementation on the operational level might require adaptations to local (cultural and legal) conditions (e.g., social practices, concerns and reservations due to events in the past, formal and informal leadership, statutory participation of employees) [START_REF] Gagsch | Wandlungsfähigkeit von Unternehmen Konzept für ein kontextgerechtes Management des Wandels[END_REF]. These could incorporate plant-specific restrictions if plant management cannot directly and fully influence them. Therefore, an approach should integrate management dimensions beyond the strategic level as a generic framework in order to enable adaptation to plant-specific conditions and restrictions within strategizing. Thereby, it focuses on obstacles O3, O4 and O5.

Contextual requirements

The contextual requirements address areas beyond the plant-or project-specific system boundaries, which should be investigated due to their relevance as input for strategizing VoC or due to the impact of VoC on them. They incorporate relevant relations to the hierarchical superior (supersystem) and subordinate systems (subsystem), which affect setting management priorities. Hence, the contextual prerequisites, the organizational and strategic embeddedness of the plant into the manufacturing network and the company as a whole and inter-organizational implications are to be regarded [START_REF] Schnetzler | Kohärente Strategien im Supply Chain Management-eine Methodik zur Entwicklung und Implementierung von Supply Chain-Strategien[END_REF]. Consistent strategic alignment. The above summarized obstacles [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF] highlight the complexity of the underlying problem. The obstacles O1 and O2 reveal existing and dynamic changing target conflicts for managers. The obstacles O3 and O4 worsen and cause further target conflicts due to various existing interfaces and interdependencies between different target dimensions, management aspects and interests of stakeholders across several organizational and hierarchical company levels [START_REF] Rippel | Profiling as a means of implementing volume-oriented changeability in the context of strategic production management[END_REF]. These kind of target conflicts often exist in management aspects of networked systems [START_REF] Bleicher | Das Konzept Integriertes Management[END_REF] and involve cross-hierarchical practices [START_REF] Rippel | Building Blocks for Volume-Oriented Changeability of Assets in Production Plants[END_REF]. An approach should make these target conflicts transparent to decision makers, probe the causes of them and provide options to balance them. Consistent strategic alignment should address the obstacles O3, O2 and O1.

Coherent strategic alignment. This requirement takes into account the subordinate production-related system level as well as the interfaces towards corporate management and network management. The subordinate levels include crucial elements in regard to cost structure (e.g., labor, material and machinery) and comprise technical and/or technological potentials or limitations. The superior levels set the rules and assignments for the plant management. Lastly, it is within each plant management's target scope to identify and sustain its strategic value within the company's manufacturing network (e.g., within performance measurement, which might focus on benchmarks of the plant in relation to internal and external competitors). Thus, it is necessary to closely look at the temporal preferences of the organization and individuals (i.e., incentive systems) regarding realizing benefits. The requirement focuses on obstacles O1, O2 and O3.

3.5

Approach-oriented requirements

Many theoretically founded management approaches are too complex or too generic to be directly applied in practice. Besides, various approaches are lacking clear guidance on how to be applied in practice. Kerr et al. point out seven key principles for developing industrially relevant strategic technology management toolkits [START_REF] Kerr | Key principles for developing industrially relevant strategic technology management toolkits[END_REF]: Since strategic problem solving is a social process, it should be developed under participation and social interaction of individuals, i.e. human-centric. The mode of this interaction and participation shall be workshop-based since it offers the opportunity to merge individual knowledge into collective knowledge which is crucial in face of the complexity of strategic problems. The process shall be neutrally-facilitated by an individual external to the system. The process shall remain lightly processed, i.e. flexible. It includes alternating steps of divergence and convergence as well as plenary and small group sessions. Different tools shall be integrated. Results shall be in a modular form. The tools should be scalable and applicable at different levels within the organization. It should be visualized both in the application and in the output. These should also serve as guiding principles for an applicable approach for strategizing VoC. In order to get solid results within a limited timeframe, existing approaches might need to be adapted.

Conclusion and Outlook

The target of volume-oriented changeability (VoC), synchronizing of capacities and costs with demand fluctuation, should ensure the plant's profitability and competitiveness. However, obstacles arise within the strategizing. Practitioners' on the plant level require methodical and conceptual support to realign their strategy regarding structure, activities and behavior in a socio-technical perspective. Within this paper requirements are presented in order to provide scientific researchers a guideline for developing an academically sound and practice-oriented approach that support plant managers in strategizing VoC. The requirements also function as criteria to evaluate existing scholarly approaches regarding their appropriateness for the given problem context.


Parinya Kaweegitbundit

Toru Eguchi
email: eguchi@hiroshima-u.ac.jp

Job Shop Scheduling with Alternative Machines Using a Genetic Algorithm Incorporating Heuristic Rules -Effectiveness of Due-date Related Information

Keywords: Job shop scheduling, alternative machines, tardiness, heuristic rule, genetic algorithm

This paper deals with an efficient scheduling method for job shop scheduling with alternative machines with the objective to minimize mean tardiness. The method uses a genetic algorithm incorporating heuristic rules for job sequencing and machine selection. Effective heuristic rules for this method have been proposed so far. However due-date related information has not been included in the heuristic rule for machine selection even though the objective is to minimize mean tardiness. This paper examines the effectiveness of due-date related information for machine selection in this method through numerical experiments.

Introduction

This paper deals with an efficient scheduling method for job shop scheduling with alternative machines. Some research papers related to this problem have been proposed in the literature [START_REF] Nasr | Job shop scheduling with alternative machines[END_REF] [START_REF] Moon | Genetic algorithm for job shop scheduling problems with alternative routing[END_REF]. In this problem, the machine for processing each operation is not fixed only one; there can be alternative machines. Not only the sequence of jobs on machine, but also the machine which process each operation must be selected for this scheduling. We have already proposed a scheduling method using a genetic algorithm incorporating heuristic rules [3][4]. In this method, heuristic rules for job sequencing and machine selection are embedded in the search of genetic algorithm. The performance of scheduling is improved using the knowledge of the rules. The rules for job sequencing are used when a machine became idle and there are multiple waiting jobs to be processed on the machine. The rules give priority values for the waiting jobs and the job with the highest priority value is selected as the next job to be processed on the machine. The rules for machines selection are used when a machine finishes processing an operation of a job. The rule gives values for candidate machines to process the next operation of the job. We have examined various heuristic rules for incorporation when the objective of scheduling is to minimize mean tardiness. As a result, (SL/RPN)+SPT rule [START_REF] Yoda | Job shop scheduling for meeting due dates and minimizing overtime using genetic algorithm incorporating new priority rules[END_REF] performed best for job sequencing. (WINQ+RPT+PT)×PT rule [START_REF] Eguchi | A Machine Selection Rule for Dynamic Job Shop having Alternative Machines with Processing Times[END_REF] performed best for machine selection. Although the objective of scheduling is to minimize mean tardiness, the machine selection rule does not include due-date related information. In this paper, we examine the effectiveness of considering due-date related information for machine selection rules. Numerical experiments are carried out to show the effectiveness of including the information.

Job shop scheduling with alternative machines

The scheduling problem considered in this paper is described as follows: Consider the job shop that consists of R work centers.

I d C T I i i i / ) , 0 max( 1     (1)
where C i and d i are the completion time and the due-date of job J i , respectively.

Scheduling optimization using a genetic algorithm

In this chapter, the genetic algorithm used in this paper is described. In the genetic algorithm, each operation has a gene for job selection and genes for machine selection.

The number of genes for machine selection is the same as the number of candidate machines which can process the operation. Each gene for machine selection is prepared for each candidate machine. Each gene for job selection and machine selection is coded as a real value between 0 and 1. The set of genes for all the operations of jobs corresponds to a chromosome. Decoding is carried out using a feed-forward scheduling simulation in which the genes are considered as priority values for job selection and machine selection. When machine finishes processing an operation of a job, the job goes to the input buffer of one of the candidate machine which can process the next operation of the job. The machine which has the largest value of gene is selected as the next machine to process the next operation. When a machine became idle and there are multiple waiting jobs to be processed in the input buffer of the machine, one of the waiting job is selected and is started to be processed on the machine. The job with the highest value of gene is selected as the next job. By this method, when all the operations of jobs are completed, a schedule is obtained. The mean tardiness of jobs in the schedule is used for calculating the fitness. The individual which has the smaller mean tardiness is defined to have the higher fitness in this method.

An elite strategy is adopted in this paper. The best 20% of individual is copied to the next generation. The other 80% individuals are generated using crossover by randomly selecting two individuals from the current generation. In crossover, 30% genes are randomly selected from one individual and the other 70% genes are randomly selected from another individual. The rate of mutation is 1%. For the detail construction of this genetic algorithm, refer to the literature [5][7].

4

Genetic algorithm incorporating heuristic rules

Incorporation of heuristic rules

Although the genetic algorithm alone described in chapter 3 can search the optimal schedule, the performance is not good. The performance of scheduling can be improved by incorporating problem specific knowledge. Eguchi et al. have proposed the job shop scheduling method using a genetic algorithm incorporating a priority rule for job selection [START_REF] Eguchi | Dynamic scheduling using the mixture of a genetic algorithm and a priority Rule[END_REF]. In this method, when decoding, a job is selected using not only the value of gene for job selection but also the value calculated by applying a priority rule. Specifically, the job with the highest value of the multiplication of the gene and the priority value calculated by the rule is selected as the next job to be processed. By this method, the knowledge of priority rule can be embedded in the search of genetic algorithm. As the same way, machine selection rules can be incorporated for machine selection. Specifically, the machine which has the highest value of the multiplication or division of the gene for machine selection and the value calculated using a machine selection rule is selected as the machine to process the next operation [3][4].

Job selection rules

From our previous research [START_REF] Kaweegitbundit | Job shop scheduling with alternative machines using genetic algorithm incorporating heuristic rules[END_REF], the best priority rule for job selection is (SL/RPN)+SPT rule [START_REF] Yoda | Job shop scheduling for meeting due dates and minimizing overtime using genetic algorithm incorporating new priority rules[END_REF] as follows:

1 1 0 , max 1                    i i i ijk ij rpn rpt t d p pri . ( 2
)
The value of rpt i represents the total processing time of remaining operations. If an operation has alternative machines, the mean processing time is used. The value of rpn i represents the number of remaining operations. When a machine became idle and there are multiple waiting jobs to be processed at time t, the job with the highest value of pri ij is selected as the next job. This paper used this rule for job selection.

Machine selection rules

Also from the previous research [START_REF] Kaweegitbundit | Job shop scheduling with alternative machines using genetic algorithm incorporating heuristic rules[END_REF], the best machine selection rule is (WINQ+RPT+PT)×PT rule [START_REF] Eguchi | A Machine Selection Rule for Dynamic Job Shop having Alternative Machines with Processing Times[END_REF]. This rule is the combination of WINQ, RPT and PT. These rules select the next machine as follows:

 PT:The rule selects the machine which has the shortest processing time to process the next operation of the job.



NINQ:The rule selects the machine which has the smallest number of waiting jobs.



WINQ:The rule selects the machine which has the smallest summation of the processing times of waiting jobs.



WINQ+RPT+PT:The rule selects the machine which has the smallest summation of (1) the processing times of waiting jobs, (2) the remaining processing time currently being processed on the machine and (3) the processing time of the next operation when the operation is processed on the machine.  (WINQ+RPT+PT)×PT:The rule selects the machine which has the smallest value of {((1)+( 2)+(3))×(3)}.

The rules described above are not using due-date related information. Because the objective of scheduling is related to due-dates, machine selection using due-date related information seems to be effective. In this paper we examine new machine selection rules using due-date related information as follows.



MAX MIN SLACK: The rule calculates slack value (= due-date -current timesum of remaining processing time) for each waiting job in the input buffer of machine. Then the minimum slack value is selected for each machine. Finally, the machine which has the largest value of the minimum slack value is selected as the machine to process the next operation. The objective of this rule is to select the machine which has larger slack in terms of minimum value.  MAX TOTAL SLACK: The rule calculates the sum of slack values for all the waiting jobs in the input buffer of machine. Then the machine which has the largest value of the sum of slack values is selected as the machine to process the next operation. The objective of this rule is to select the machine which has larger slack in terms of total value.  MIN MAX (SL/RPN)+SPT: The rule calculates the value of equation ( 2) for each waiting job in the input buffer of machine. Then the maximum value of it is selected for each machine. Finally, the machine which has the smallest value of the maximum value is selected as the machine to process the next operation. The smaller value of equation ( 2) corresponds to larger slack value. Therefore, the machine with smaller value of the maximum value of equation ( 2



MAX MIN EDD: This rule selects the earliest due-date in the input buffer of machine. Then the machine with the maximum value of it is selected as the next machine to process the next operation.  MAX TOTAL EDD: This rule calculates the sum of the due-date for all the waiting job in the input buffer of machine. Then the machine which has the largest value of it is selected as the machine to process the next operation.

Numerical Experiments

Numerical conditions

Numerical experiments are carried out to examine the effectiveness of the method in this paper. The number of job is 100. There are eight work centers (R=8) in the shop floor. Each work center has two machines (M r =2). Any operation assigned to work center can be processed on both machines in the work center. The number of operations n i for each job is randomly determined between 4 and 8. The order of work centers to process each operation of a job is determined randomly. It is assumed that one of the machines in a work center can process the operations faster than the other machine. The processing time of an operation on the most efficient machine is determined by the uniform distribution between 5 and 100. The processing time on the other machine in the same work center is determined by multiplying a speed factor by the processing time on the most efficient machine. The speed factor is randomly determined by the uniform distribution between 1 and 2. The due-dates of jobs are determined based on TWK method [START_REF] Conway | Priority dispatching and job lateness in a job shop[END_REF]. The problems with two different levels of due-date tightness are generated. When the due-dates of jobs are loose, the number of tardy jobs is set to about 10%-15% by tuning the due-date factor in TWK method. When the due-dates of jobs are tight, the number of tardy jobs is set to about 25%-30%. The thirty problems are randomly generated. The scheduling performance is evaluated by the mean value of equation [START_REF] Nasr | Job shop scheduling with alternative machines[END_REF] for the thirty problems and the standard deviation from the best rules. For all the conditions, (SL/RPN)+SPT rule is used for the job selection rule.

Experimental results

Table 1 and Table 2 show the experimental results when using heuristic rules alone. These are the results obtained not using the genetic algorithm. For both due-date tightness levels, (WINQ+RPT+PT)×PT rule for machine selection performed best. The best rule using due-date related information was MAX MIN SLACK. Table 3 and Table 4 show the experimental results when using the genetic algorithm incorporating heuristic rules. MAX MIN SLACK rule is used as a machine selection rule which includes due-date related information. When incorporating MAX MIN SLACK rule, the minimum slack value can be negative. Therefore, when the value of minimum slack is s, the value s + =exp(s) is calculated and the maximum value of the multiplication of s + and the value of gene is used for machine selection in the genetic algorithm. The results in Table 3 and Table 4 indicate that (WINQ+RPT+PT)×PT rule performed best for incorporation for both due-date tightness levels.

Conclusion

In this paper, a genetic algorithm incorporating heuristic rules is applied for job shop scheduling with alternative machines. There are two decision situations in this scheduling: job sequencing and machine selection. (SL/RPN)+SPT rule is used for job sequencing. Various machine selection rules are examined. Some rules such as WINQ, NINQ, (WINQ+RPT+PT)×PT are the ones which do not include due-date related information. Because the objective function for scheduling in this paper is mean tardiness, due-date related information seems to be important also for machine selection rules. However, the experimental results show that the best machine selection rule is (WINQ+RPT+PT)×PT rule both when using heuristic rules alone and when applying the genetic algorithm incorporating the heuristic rules. (WINQ+RPT+PT)×PT rule works for load balancing. Numerical results suggest that it is not necessary to include due-date related information in machine selection if the due-date related information is considered in job selection and load balancing is considered in machine selection appropriately.

  Each work center W r (r∈{1,2,…, R} ) has M r machines. The operation to be processed in a work center is performed on one of the machines in the work center. Each Job J i (i =1,2,…, I ) has n i operations {o ij (j=1,2,…, n Each machine can process only one job at a time; each job can be processed only on one machine at a time. The objective of scheduling is to minimize the mean tardiness defined as follows:

i )} that are processed by the increasing order of the operation number j. The operation o ij is processed on a work center Wz ij (z ij ∈{1,2,…,R}) and the routings of the operations through work centers are diverse. We assume that Wz ij ≠Wz i,j+1 for j=1,…, n i -1. The processing time of the operation o ij on machine k (k=1,2,…, Mz ij ) is p ijk . Operations cannot be interrupted (non-preemption).

  ) is selected.  MIN TOTAL (SL/RPN)+SPT: This rule calculates the sum of the values of equation (2) for all the waiting job in the input buffer of machine. Then the machine which has the smallest value of the sum of the values is selected as the machine to process the next operation.

		MIN MAX CR+SPT: This rule uses CR+SPT rule [8] instead of (SL/RPN)+SPT
		in MIN MAX (SL/RPN)+SPT.
		MIN TOTAL CR+SPT: This rule uses CR+SPT rule [8] instead of (SL/RPN)+SPT
		in MIN TOTAL (SL/RPN)+SPT.
		MIN MAX ATC: This rule uses ATC rule [9] instead of (SL/RPN)+SPT in MIN
		MAX (SL/RPN)+SPT.
		MIN TOTAL ATC: This rule uses ATC rule [9] instead of (SL/RPN)+SPT in MIN
		TOTAL (SL/RPN)+SPT.

Table 1 .

 1 Mean tardiness using heuristic rules alone in the loose due-date condition

	Machine selection rules	Mean tardiness	S.D. from the best
	PT	755.8	102.5
	NINQ	56.9	16.5
	WINQ	59.7	18.4
	WINQ+RPT+PT	34.9	11.8
	(WINQ+RPT+PT)×PT	24.0	0.0
	MAX MIN SLACK	60.3	19.9
	MAX TOTAL SLACK	70.6	23.2
	MIN MAX (SL/RPN)+SPT	68.1	21.9
	MIN TOTAL (SL/RPN)+SPT	66.0	20.2
	MIN MAX CR+SPT	85.8	27.8
	MIN TOTAL CR+SPT	72.7	21.9
	MIN MAX ATC	73.2	24.2
	MIN TOTAL ATC	66.1	19.8
	MAX MIN EDD	61.7	18.6
	MAX TOTAL EDD	82.0	29.6

Table 2 .

 2 Mean tardiness using heuristic rules alone in the tight due-date condition

	Machine selection rules	Mean tardiness	S.D. from the best
	PT	837.6	92.2
	NINQ	97.9	17.1
	WINQ	99.6	17.6
	WINQ+RPT+PT	65.5	9.1
	(WINQ+RPT+PT)×PT	45.2	0.0
	MAX MIN SLACK	96.4	19.4
	MAX TOTAL SLACK	103.2	18.6
	MIN MAX (SL/RPN)+SPT	107.8	25.1
	MIN TOTAL (SL/RPN)+SPT	101.2	21.5
	MIN MAX CR+SPT	126.1	23.4
	MIN TOTAL CR+SPT	110.2	22.1
	MIN MAX ATC	114.3	25.3
	MIN TOTAL ATC	108.5	22.5
	MAX MIN EDD	99.4	19.4
	MAX TOTAL EDD	123.2	28.5

Table 3 .

 3 Mean tardiness using the genetic algorithm incorporating heuristic rules in the loose due-date condition

	Machine selection rules	Mean tardiness	S.D. from the best
	GA+ PT	22.4	8.5
	GA+ NINQ	16.9	5.3
	GA+ WINQ	17.4	5.4
	GA+ WINQ+RPT+PT	12.0	2.4
	GA+ (WINQ+RPT+PT)×PT	9.9	0.0
	GA+ MAX MIN SLACK	20.4	8.0

Table 4 .

 4 Mean tardiness using the genetic algorithm incorporating heuristic rules in the tight due-date condition

	Machine selection rules	Mean tardiness	S.D. from the best
	GA+ PT	46.4	10.2
	GA+ NINQ	38.6	5.4
	GA+ WINQ	39.0	5.2
	GA+ WINQ+RPT+PT	31.1	3.0
	GA+ (WINQ+RPT+PT)×PT	26.7	0.0
	GA+ MAX MIN SLACK	45.5	9.8


Do Fábio

Jair Minoro Amaral
email: favamaral@gmail.com

Alexandre Sandor Abe

Cadim

Zaneti Caique

Carlos Kirilo

Arruda Baltazar

Luís Fábio

Hélio Pereira

De Araújo

Costa Henry

Lauro Ungaro

Castro De

Tomiatti
email: tomiatti1@hotmail.com

Machi Luiz

Lozano
email: luizlozano@icloud.com

Carlos Arruda Baltazar
email: carlosarrudabaltazar@gmail.com

Fábio Vieira Do Amaral

Jair Minoro

Alexandre Jacob

Sandor Cadim
email: cardimajs@gmail.com

Caique Zaneti Kirilo
email: caiquez.kirilo@hotmail.com

Fábio Luís Pereira

Hélio Côrrea De Araújo

Henry Costa Ungaro

Lauro Henrique De Castro Tomiatti

Luiz Carlos

Machi Lozano

Renan Dos

Santos Tampellini
email: renan.tampellini@hotmail.com

Renato Hildebrando Parreira

Uanderson Celestino
email: uandersoncelestino@hotmail.com

Paraconsistent Artificial Neural Network Applied in Breast Cancer Diagnosis Support

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experiments with calcifications show: Paraconsistent Classifier (Az = 0.986), MLP classifier (Az = 0.70), ART2LDA Classifier (Az = 0.696) and RBF Classifier -Simulated Annealing (Az = 0.94). For experiments with mammographic masses and tumors show: Set 1, Paraconsistent Classifier (Az = 0.939), MLP classifier (Az = 0.994), ART2LDA Classifier (Az = 0.901) and RBF Classifier -Simulated Annealing (Az = 0.912). Set 2, Paraconsistent Classifier (Az = 0.935), MLP classifier (Az = 0.994), ART2LDA Classifier (Az = 0.890) and RBF Classifier -Simulated Annealing (Az = 0.924). Set 3, Paraconsistent Classifier (Az = 0.875), MLP classifier (Az = 0.970), ART2LDA Classifier (Az = 0.850) and RBF Classifier -Simulated Annealing (Az = 0.996). Set 4, Paraconsistent Classifier (Az = 0.500), MLP classifier (Az = 0.887), ART2LDA Classifier (Az = 0.767) and RBF Classifier -Simulated Annealing (Az = 0.907). Set 5, Paraconsistent Classifier (Az = 0.929), MLP classifier (Az = 0.987), ART2LDA Classifier (Az = 0.884) and RBF Classifier -Simulated Annealing (Az = 0.998). Set 6, Paraconsistent Classifier (Az = 0.939), MLP classifier (Az = 0.982), ART2LDA Classifier (Az = 0.885) and RBF Classifier -Simulated Annealing (Az = 0.999). In the case of the Paraconsistent Classifier, the eighth experiment was composed of the total image attributes relating to mammographic masses and tumors (Az = 0.939). In the particular case of the RBF-Sort Simulated Annealing experiment with all the image attributes, it was proved its unfeasibility, due to the complexity of their algorithm, where the processing time tends to infinity for a larger number of elements. For the experiments, the Paraconsistent classifier used 20% of the samples for the neural network training, against the total number of samples available minus one for the other classifiers.

I. INTRODUCTION

Breast cancer fills second place in cancer occurrences in the world, with 22% of all the new cases each year. If diagnosis point and treatment occurs in start, healing prognosis is favorable. [START_REF] Gomes Da Silva | Coordenação Geral de Ações Estratégicas[END_REF] In world population, the average after life reach five years after diagnosis in 61% of the cases.

Brazil epidemiological illness profile subdued special attention in politic decisions of federal government. Breast cancer brings high mortality rate, because is only diagnosed in final stages. The Plan for Strengthening Prevention Actions and Qualification of the Diagnosis and Treatment of Cervical and Breast Cancers, released on March 2012, is an example of this premise. The incentive of X-ray exam realization in breast of caring population also belongs in this prevention politics.

[1] [START_REF] Espírito | Classification of Breast Masses in Mammograms Using Radial Basis Functions and Simulated Annealing[END_REF] Breast X-ray (mammography) is the most indicated for detect early the presence of nodes inside breasts. Clinical exam and others image and lab exams could also support the diagnosis.

The exam shows a variety of adipose tissue, parenchyma and normal and abnormal tissues. The radiologist should analyze abnormally, using attributes, dimension, form and texture. After analysis is possible to identify illness presence. Then analyze if the node is actually a bad one, besides the fact that most of them are not. [START_REF] Espírito-Santo | Discriminação de Classes Fundamentada em Técnicas de Otimização Não Linear e Combinatória Associadas a Funções de Base Radiais: Um estudo de Caso em Mamografia[END_REF] [START_REF] Espírito | Classification of Breast Masses in Mammograms Using Radial Basis Functions and Simulated Annealing[END_REF] The risk of a wrong diagnosis, false positive or false negative, is high. Clinical exams shows that some Brazilian cities has 50% of mammography tests with difficult in reading and diagnosis. The process realized during the exam is highly important for exams quality.

[1] [START_REF] Espírito | Classification of Breast Masses in Mammograms Using Radial Basis Functions and Simulated Annealing[END_REF] For reach acceptable trust level, is necessary to raise the prediction of positive values. The percentage of breast cancer cases identified in mammography and confirmed by biopsy that can reach 30%. Considering the traumatic aspect and costs for biopsy realization, it is relevant an alternate computational capable of raise distinguish between good and bad items found. This method could work well as decision-making tool. The radiologist would use this tool as part of the analysis protocol of mammography. With this, the wrong diagnosis would been minimized and the exam recommendations of biopsy reduced. [START_REF] Espírito-Santo | Discriminação de Classes Fundamentada em Técnicas de Otimização Não Linear e Combinatória Associadas a Funções de Base Radiais: Um estudo de Caso em Mamografia[END_REF] [START_REF] Espírito | Classification of Breast Masses in Mammograms Using Radial Basis Functions and Simulated Annealing[END_REF] This work treat to propose a tool capable of analyze and classify good and bad mammography attributes and a change in the process.

Attribute image classification will be supported by paraconsistent artificial neural network. This tool does not manipulate mammography. In this part of the work will be treated only aspects related to calcification. To practice this simulations will be used a database, obtained from segmentations treated in mammography acquired with Department of Radiological Sciences and Diagnosis Imaging Foothills Hospital, located in Calgary, Alberta, Canada, this database is built from 69 good cases and 79 bad ones, identified manually from a radiologist specialized in mammography. From this point, the identifications determine the factors in Momentum (m), Compaction factor (c) and Fourier description (f). [START_REF] Espírito-Santo | Discriminação de Classes Fundamentada em Técnicas de Otimização Não Linear e Combinatória Associadas a Funções de Base Radiais: Um estudo de Caso em Mamografia[END_REF] [START_REF] Espírito | Classification of Breast Masses in Mammograms Using Radial Basis Functions and Simulated Annealing[END_REF].

II. DIGITAL IMAGES ATTRIBUTES

The computed detection of good masses, bad tumors and calcification in mammography are not simply filled with Neural Networks specialized in ordinary recognition. In existing ordinary recognition (as mammography) built by neural networks, identify forms from borders and patterns (image segmentation), so, localizing frontiers between background and pattern. In this recognizing, the better image definition of frontier in patterns the better results of border detection. In mammography, most of the good masses, just like good calcifications, has well-defined aspects and frontier (borders) with high contrasted degree. Forms of good calcifications can be circular and oval shaped. Contour of the benign masses beyond the circular and oval form, could also present the macro lobular form, shown in picture 2. The border transition is clear from inside the dense tissue from outside, less dense. Malignant calcifications, although, seems to have cloudy contrast and frontier not so clear. Malignant calcification outlines shows lobular shape, and malignant tumors shows microlobulated shape. In this case, the transition of interne tissue (denser), from extern is not very clear or defined. However, some benign masses such as fiber adenoma could present erased borders in mammography.

About the convexity and concavity of masses shape, we could see that the most benign masses presents convex shapes. Some of them are concaved or speculated. However, malignant tumors could present both convex and concaved, and even predominant tentacles shape. And if compared, benign masses and malignant tumors, are both homogeneous in terms of density and distribution. Given these facts, if a neural network was trained for pattern recognizing of masses and benign and malign calcification, it would be, depending on network implementation, an efficient benign masses recognizer, but not so efficient detecting malign tumors, sometimes not recognizing fiber adenomas. Therefore, neural networks trained to recognize only patterns are not well suited and recommended to support cancer diagnosis, because it lacks where radiologists need it the most, identify cancer. The fact that the simply pattern recognizing has few or no application in mammography, shape factors, distinctness detection of masses outline and measures of texture are the answer CAD (Computer-Aided Diagnosis) for diagnosing attributes extraction in mammography.

Parameters that describe calcifications identified in mammography: Based on these criteria and foundations that enable the implementation of CNAP's necessary recognition system were established. [START_REF] Pereira | Reconhecimento de Caracteres Numéricos Manuscritos Utilizando Redes Neurais Artificiais Paraconsistentes[END_REF][8]

 Momentum (m)  Fourier (f)  Compaction factor (C)  Radial (r)  Distance (d)  Standard
• Analytical Connection • Simple Logic Connecton • Selective Logic Connection • Passageway • Complementation • Decision • Learning • Memorization A. Artificial Paraconsistent Learning Cell (CNAPa)
As part of this memory unit or as standards in primary sensor layers, in other words, all information learned or stored, must pass for such cell. This cell act as a node of decision in RNAP's. In your entry, applying two signals from another network area, resulting in only one exit that matches one conclusive analysis of these entries.

Picture 5 -Representation of CNAPd [START_REF] Pereira | Reconhecimento de Caracteres Numéricos Manuscritos Utilizando Redes Neurais Artificiais Paraconsistentes[END_REF] [START_REF] Silva | Fundamentos das Redes Neurais Artificiais Paraconsistentes[END_REF] The possible output values are:

 Output equals to 1 represents the pattern "True".  Output equals to 0 represents the pattern "Falsity".  Output equals to 0.5 represents the pattern "Uncertainty".

Establishes the logical connective OR (maximization) between degrees of belief applied to the input of the cell, telling you which of the two signals applied to the input of the cell has the highest value, setting the signal at the output. Picture 6 -Representação de uma CNAPCls [7][8] IV. PARACONSISTENT ANALYZER Considering traumatic aspects and the cost for realization of biopsy, and is relevant an alternative computational way capable of raise distinguish between benign and malign calcification. This method works like a decision support tool. The radiologist would use this tool as a protocol stage, helping mammography analysis. With this, wrong diagnosis would been lowered and biopsy exam recommendation.

This software will implement a RNAP for each image attribute (m, c and f), and in the process ending it will show the diagnosis.

In the image below, the process of paraconsistent classification. This process will be similar to calcification classifications.

A. Network composition

Main part of the network is built by a group of CNAPa that learn and spread for others parts of the network.

The second layer is composed by CNAPd, aiming stabilish the evidence degree between standard stored in CNAPa.

The third layer is built by CNAPCI, created for maximization, forming a competitive network, in which only one value is understood as winner.

V. FINAL CONCLUSIONS

The paraconsistent analyzer in its first version could reach 94% hits for calcification.

Considering the diagnosis errors could reach 50% in extreme cases, there was a significant reduction of diagnosis with false positives or false negatives.

RNAP characteristics also need to be quoted.  Low number of samples needing.  In this tool case, there was no detraining in network, so required less time training.  The algorithm complexity implemented also presents easy mastery.

  Keywords: Attributes of Images Classifier, Breast cancer, Computer-Aided Diagnosis, Paraconsistent Annotated Evidential Logic Et, Paraconsitent Artificial Neural Network Mammography

Fig. 1 -

 1 Fig. 1 -Morphology of calcification visualized in Mammography.

Fig. 2 -

 2 Fig. 2 -Shape examples, benign (a) and (b), malign (c) and (d).

Picture 4 -

 4 Representation of CNAPa B. Artificial Paraconsistent Decision Cell (CNAPd)

B

  . Database register used for RNAP training For network training it is not necessary a high number of values. C. RNAP training D. RNAP classification This module function can obtain a value resulting of network process, capable of determinate if a newer sample is benign or malign, and shows quality and reliability of classification through calculations of sensibility, specificity, predicted positive value, predicted negative value, likelihood positive reason, likelihood negative reason and accuracy. And how much true positive, false positive, true negative and false negative it has.