Operational Research Models and Methods in CIM1
Abstract : Many models and methods of Operational Research can be adapted for industrial applications. In this chapter, we show on one hand the main problems of a manufacturing system and, on the other hand, how they can be ranged in a hierarchical order, derived from a CIM architecture (from the strategic decisions to the production constraints). Then, we present an Operational Research tool for solving each of these problems.

1 Introduction
Flexible Manufacturing Systems (FMS) are nowadays installed in the mechanical industry, especially in car factories. However, the market constraints impose to always improve the production system and the whole production organization. The concepts developed by Taylor and applied at the beginning by Ford are progressively abandoned and replaced by the Just-In-Time concept and the Computer Integrated Manufacturing philosophy (CIM). One of the aims of the CIM philosophy is to provide an integrated information system which avoids the rigid separations between the different functionalities of a complete production system. With such integrated information systems, the loss of time on one hand between the customer order and the part delivery, on the other hand between the product design and its manufacture will be drastically reduced. To understand the complete production system, it is relatively easy to find in the scientific literature excellent general books explaining the different aspects of the Production and Operations Management (POM) ([1], [2], [3], [4], [5]). It is more difficult to discover a writing dedicated to use of Operational Research (OR) models and methods in the industrial context [6]. And it is quite impossible to find a book which offers a good balance between POM and OR … In this chapter, we will show how a CIM architecture can be partially decomposed along two main axes : the production management aspect (from the customer order to the bill) and the logistics aspect (from the supply to the distribution). Then, we will show how to integrate Operations Research models and methods in this CIM architecture. A basic CIM architecture defined by Scheer [7] is presented in Section 2 and its limits are highlighted. In Section 3, a production planning decision hierarchy is proposed, containing five main phases. The two last phases are then developed in the different components, describing a two-axes structure, the vertical axe representing the production control and the horizontal one dealing with the logistics. Section 4 is dedicated to the application of different OR models and methods in the CIM context. These are mainly useful in the solution of the following problems : plant sizing and location, equipment type and amount, production allocation among plants, order management, product design, planning, scheduling, shop floor control, supplying logistics and inventory management, and distribution logistics. Finally, Section 5 concludes this chapter suggesting new research topics for Operational Research in CIM context.

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Paper published in : H.H. Adelsberger, J. Lazansky and V. Marik (Eds), Information Management in Computer Integrated Manufacturing, Lecture Notes in Computer Science No.973 (1995), Springer-Verlag Berlin Heidelberg, pp 179-194.

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2 A CIM architecture
Chase and Aquilano give in their book an interesting description of different aspects of the Production and Operations Management, based on a life cycle approach [1]. To define a good CIM-architecture, Scheer takes a step which is quite similar [7]. He considers on the one hand the organizational planning functions and on the other hand the technical functions (fig. 1). Of course, these two sets of functions are tightly linked in the implementation phase, which corresponds to the real time control of the manufacturing system.

Organizational planning functions Order control Cost estimating Master production planning Material manag. Cap. Req. Plan. Cap. adjustment Order release Production control Operational data collection Control (qualities, times, costs) Shipping lan od Pr

Technical functions

Product outline

NC-Programming Control of resources Conveyance control Inventory control Assembly control Maintenance Quality control

CA P

CAQ

Fig. 1. Information systems in production : the "Y" of Scheer [7]

The Scheer's architecture gives a relatively complete description of an existing manufacturing system, where the production resources are globally known and where the production strategies have been defined. But if the manufacturing system has to be created, some important decision steps do not appear in the "Y". We propose in next Section a multiple phase approach which includes strategic decisions.

3 The Integrated Production Management
3.1 The production planning decision hierarchy

When an industrial company decides to built news factories, it has to solve a set of problems, which are ordered according to a production planning decision hierarchy (fig. 2). It is important to solve each problem, one after the other, to avoid an economical disaster ! The first step consists in selecting the optimal locations for the new plants, taking into account constraints such as economical factors (taxes, wages) and management facilities (proximity of suppliers and customers). The equipment type and their amounts are defined for each plant in the second phase. When the shop floor descriptions are complete for the different resources (human and material), the next step consists in defining the production allocation among the plants.

2

Implementation

CAM

Pl

Process planning

an

ni

ng

Design

CA D

CA E

P la

tio uc np

nn in

g
Implementation

nin g and control

At this point, all the conditions to use the CIM architecture of Scheer are satisfied. However, we prefer to describe a concept of integrated production management, where it is possible to highlight easily some basic problems which can be solved thanks to Operational Research tools.

Plant sizing and location

constraints

Equipment type and amount

constraints
Production allocation among plants

constraints

performance characteristics and operation results

Plant capacity planning

constraints

Item production schedules

Fig. 2. The production planning decision hierarchy [1]

3.2

The integrated production management

To define the integrated production management, we will describe the different modular notions which appear in every production system, independently of the size or of the functionality of the factory (fig. 3). To depict the production control, the process between the customer's order and its delivery is first studied. When a customer gives an order to the factory, this order belongs to one of the two following categories : • the ordered product is described in a catalogue (like a car with its several options). That means that the manufacturing process is known. In such a case, the customer's order is recorded in a module of order management ; • the ordered product is new (the manufacturing process is unknown). Before being able to insert the customer's order in the module of order management, it is necessa-ry to design the product : this work is done in a module called product design. The order management module, eventually associated with a forecasting module (depending of the chosen production type), is in constant dialogue with the module of inventory management to define the quantities to produce and the delivery delay for the customer. Naturally, to determine the delays, a planning module has to be used, taking into account the work in process or the foregone manufacture. This module answers the question : when should we produce ? These delays are also important to determine the moments when orders have to be given to the suppliers : it means that there is a dialogue between the planning module and a supplying management module. When the quantities of different products to manufacture during the next planning period are known (we dispose of the list of parts to be processed during a production period), we have to determine the scheduling of the products which should be manufactured respecting some criteria (to avoid too many set ups of the machines, to minimize the transfers, to minimize the waiting times,…), to avoid a non-optimal

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utilization of the resources. So, this module answers the question : how should we produce ? Then, when the production is released, we have to respect as faithfully as possible the sequence established by the scheduling. This is the task of the shop floor control module : it takes care of the production reporting and of the production resource management in real time (machines, conveyors,…). A module of quality control could be associated with it, as well as a module of maintenance management. If the firm does not work in just-in-time, the shop floor control module has to dialogue with the forecasting module.

order management

product design

planning

scheduling release

production reporting shop floor control

supplying logistics

manufacturing system distribution logistics inventory LOGISTICS

invoicing PRODUCTION CONTROL

Fig. 3. The Integrated Production Management [8]

After this phase of real time control, the parts are finished products (or considered as finished products by the factory which manufacture them). The last operations consist in sending the goods to the customer and to submit the bill (distribution logistics module and invoicing module). This concludes the main description of the production control. Let us now explain the components of the logistics aspect, which define the product in term of material, from the raw material to the finished product. Before the arrival in the shop floor, the raw material has to be ordered : this task is devolved upon a module of supplying logistics. To apply successfully the just-intime concept, the suppliers as well as the firm have to work in just-in-time. Then, when we decide to manufacture the products, we have to manage the inventory. This could be an inventory of raw material, in-process parts, semi-finished or finished products. Even if the just-in-time concept recommends the notion of zeroinventory, a minimum inventory is always necessary (as a stabilization stock).

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Finally, when the products are finished, they have to be delivered to the customers. This last step is done by the distribution logistics. Thus, the ordered product arrives to the customer and this completes the logistics aspect. To conclude with this two-axes structure, we highlight the fact that some modules have an evolutive aspect. For example, the planning module loses the main part of its importance when the firm works in just-in-time. If we add to this aspect the fact that the life cycle of products is shorter and shorter, it is easy to understand the non negligible consequences on the inventory management module. Notice that we have deliberately omitted to talk about a marketing module, which is marginal in the production process. However, this marketing aspect has not to be neglected, as it has an influence on the forecasted order management and on new products, which are susceptible to be of interest to some potential customers. 3.3 A hierarchico-cyclical structure

In the integrated production management, the aspects of planning, scheduling and shop floor control could be joined in a global decision approach : the hierarchicocyclical structure ([9], [10]). To describe the last one, it is useful to consider the life cycle of a product (fig. 4). To produce parts, it is necessary to know the kind of available resources. The shop floor description defines the physical structure of the shop floor, i.e. the number of components of each type (machines, conveyors), the material handling system, the pallet quantity and eventually the fixture quantity. The resources described here are permanent elements of the system. The part description gives informations on the process plan of the different parts (sequence of operations, processing time, set of machines on which each operation can be executed). The planning takes into account the list of customer orders, the inventory level (if the just-in-time concept is not applied) and the work in process. This production planning helps the seller when he negotiates the delivery lead times.

4

shop floor description

3 2

part description

planning

1

scheduling

yes

perturbation ? no real time control

no

changes in production? yes Fig. 4. The hierarchico-cyclical structure [10]

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When the quantities of parts (to produce during the planning period) are known, the part scheduling has to be determined. It must respect some criteria to avoid an underoptimal utilization of the resources (minimize the transfer times, minimize the number of set ups on the machines, …). Then, when the manufacturing is released, it is necessary to respect as strictly as possible the defined scheduling. This task is dedicated to the system control and to realize that, one has to take into account the machine occupation, the pallet and fixture availability and the tools loaded on each machine. These two levels (scheduling and control) make up the real time control of the shop floor. When the production system is working, breakdowns and maintenance operations disturb the smooth working of the factory. If the maintenance operations can be kept down (they can be considered as fictitious parts), the breakdowns can generate complex problems. According to the importance of the perturbation, the reactions are fundamentally different. In the case of a momentary interruption, a new allocation of the workload among the remaining resources can be done thanks to a rescheduling (1). This means that the perturbation is absorbed by the real time control system. When the perturbations are more serious (2), it is necessary to establish a new planning. If there are no changes in the set of the products, the planning process restarts at the beginning of the next production period (3). Else, when new parts have to be produced, for which the process plans are not defined, it is necessary to introduce this information in the part description (4). Let us now explain how the technical evolution can be taken into account : if a product is modified in its process plan, one has to record it as a new part, whose production increases progressively in comparison with the old version of the product. When the old process plan is no more used, the associate product disappears from the part description.

Current state

data base

PLANNING
IP model Simulation Queueing

MODULE

Expert System

Production requests

Breakdowns
Updated state data base

Basic horizon

DYNAMIC CONTROL MODULE

SCHEDULING
Scheduling horizon Optimization criteria

MODULE
Expert System

O.R. Problem solving algorithms

Fig. 5. The model proposed by Solot [11]

This hierarchical and cyclical structure has huge advantages. It allows above all a global view on the whole control of the shop floor. It offers the advantage to be

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general enough to suit different types of shop floor, classical or flexible. Naturally, it must be adapted to be efficient for a determined factory : for example, it would be useful to couple an inventory management module to the planning module in some cases. In the conditions of the real time control, when some events occur, it is easy to see at which level one has to intervene. Thus, this structure helps the managers to take optimal decisions. Finally, notice that Solot has proposed a quite similar basic hierarchico-cyclical structure, including some elements of Artificial Intelligence like expert systems [11] (fig. 5).

4 OR models and methods in CIM context
In the previous Section, we have decomposed the CIM architecture into a set of problems. Each one should find a solution thanks to Operational Research tools. We present in this Section a few models and methods, mainly based on linear programming. Of course, they are basic answers for general problems : when solving real-life problems, the models have to include more accurate information in order to reflect reality. 4.1 Plant sizing and location

The selection's process of optimal locations for new plants has to take into account constraints such as establishment costs, proximity of suppliers and customers, production costs, etc. We present here a simplified formulation of this problem. min subject to : - demand constraints :

Σ i fi . yi + Σ Σ cij . xij i j

Σ i xij ≤ bj

∀j ∀i

- production constraints :

Σ j xij ≤ ai

- location and capacity constraints : xij ≤ ai.yi ∀ i, ∀ j - the number of new plants is fixed to N :

Σ i yi = N

- yi are Boolean variables : yi ∈ {0,1} - xij are non negative variables : xij ≥ 0

∀i

where : - fi is the establishment cost of a new factory in i - cij is the unit transportation cost from the factory i to the region j - bj is the demand in region j - ai is the capacity of factory in i

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- xij is the volume produced in factory i for the region j - yi is the decision variable if a factory is located in i or not 4.2 Equipment type and amount

Simulation is here an efficient tool. If we consider the discrete event simulation, some performant software could help the decision maker to select the suitable quantity of each resource type. But he should waste plenty of time before he arrives to the adequate solution ! Hopefully the analytical simulation avoids this tedious research. The queueing network theory gives all the elements to model the resources of the manufacturing system as well as the behaviour of the parts (fig. 6). Dallery and Frein have proposed an efficient method to determine the optimal configuration of a FMS [12]. Knowing the costs of the machines and the pallets, their algorithm finds the optimal quantity of resources allowing to reach a given production rate. Solot has developed some interesting models also based on queueing network theory dealing with pallet changes and resource reliability ([13], [14], [15],[16]). new part MT=MG 1

MODEL

MG 2

MG 3

MG M same part

Fig. 6. Queueing networks for shop floor description

4.3

Production allocation among plants

This problem is quite similar to the plant location. As the two previous steps have defined the geographical location of the plants and their resources, we know : • the ability of each factory to manufacture the parts ; • the production capacity of each factory. In these conditions, it is easy to adapt the formulation presented in 4.1 to take into account the production costs and the transportation ones. 4.4 Order management

For a long time, when the demand was greater than the offer, it was primordial to forecast the demand, in order to release the production of the parts before receiving the customer's order ! Such an anticipation was possible thanks to forecasting

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methods, as those presented by Chatfield ([17], [18]) : exponential smoothing, regression analysis, Box-Jenkins technique, … However, in the today's situation, the forecast is not so important, carrying away the order management with it : indeed, if it is necessary to know the quantity of basic parts which will be useful in the next production period, the specific components of the product are done only when the customer order is real. 4.5 Product design

The product design is one of the topics neglected by the OR tools. Some Traveling Salesman Problems (TSP) have to be solved. Indeed when several holes are made with the same tool on a face of a product, the path of the tool could be minimized solving a TSP [19]. But it would be interesting to study more deeply the problems linked to the product design, because they are probably many others cases which could be solved with OR methods. 4.6 Planning

Concerning the planning, it is necessary to distinguish two cases : • if the part is a prototype or if the part is unique, the most efficient method is to use a PERT model (Program Evaluation Research Task) ; • else, the planning of the production of several parts in different quantities could be solved thanks to famous Gantt charts (fig. 7). As explained before, some new concepts have appeared in the last twenty years, such as Just-in-time (JIT) or Optimized Production Technology (OPT), which give less importance to the planning module [20]. Notice that it exists some interesting models combining planning and scheduling problems, which could be applied in mechanical industry [11] or in chemical industry [21]. Let us present an integer programming model to plan the production of different parts over several time periods, in a manufacturing system where an unique critical resource exists. min

Σ Σ (cit . xit + fit . yit) i t

+

Σ (gt . ut + ht . vt) t subject to : - the satisfaction of the demands: xit + yi,t-1 - yit = dit - capacity constraints :

∀ i, ∀ t ∀t ∀t ∀t ∀i

Σ j ki . xit = ut + vt
-

- time constraints : 0≤ ut ≤ ut 0≤ vt ≤ vt - yi are Boolean variables : yi ∈ {0,1}

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- xit and yit are non negative variables : xit , yit ≥ 0 ∀ i, ∀ t where : - xit is the quantity of products i manufactured during period t - yit is the quantity of products i in inventory at the end of period t - ut is the quantity of normal working hours during period t - vt is the quantity of extra working hours during period t - cit is the production cost of one product i during period t - fit is the inventory cost of one product i during period t - gt is the cost of one normal working hour during period t - ht is the cost of one extra working hour during period t - dit is the demand of product i in period t - ki is the processing time to manufacture product i - ut is the quantity of normal working hours dedicated to period t - vt is the maximal quantity of extra working hours allowed during period t 4.7 Scheduling
-

The scheduling problems have held the attention of an huge amount of researchers during the last forty years, since Johnson has proposed optimal two and three-stage production schedules. Many heuristics have been developed to solve the problems of flow shop, job shop and open shop. Unfortunately, none of these heuristics are general models : they deal with some special cases, each one with specific constraints. A good review of some of these models is described in Blazewicz's books ([22], [23]).

m4 m3 m2 m1 23

Fig. 7. A scheduling solution taking into account tool switches (the black boxes represent the tool switches)

New developments are given in the topic of the scheduling considering compact cylindrical scheduling (repetitive production) [24] or dealing with the tool switches on one machine [25] or on several machines [26] (fig. 7). Let us present an integer programming model to minimize the number of tool changes in a flexible manufacturing system containing m machines and n monooperation products [27].

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p m min k=0 j=1 z

Σ ΣΣ

uzjk

subject to : - the number of tools allocated to machine j is less than or equal to the capacity Cj of the tool magazine of machine j :

Σ z yzjk ≤ Cj

∀ j, ∀ k

- the number of tools of type z allocated to all the machines is less than or equal to the limited number nb z of tools of type z : m j=1

Σ

yzjk ≤ nbz

∀ z, ∀ k

- ai parts of type i have to be produced : p m k=1 j=1

Σ Σ

xijk = ai

∀i

- the right tools have to be in the right place at the right moment : xijk ≤ ai . yzjk ∀ z ∈ Zi , ∀ i , ∀ j , ∀ k - sk is positive if at least one type of part is produced in time-shift k : n m i=1 j=1

n

ΣΣ

xijk ≤ sk .

i=1

Σ

ai

∀k ∀ k ∈ {1,..,p-1}

- sk is a non increasing variable : sk ≥ sk +1

- yzjk and sk are Boolean variables : yzjk ∈ {0,1} ∀ z, ∀ j, ∀ k sk ∈ {0,1} ∀k - xijk is a non negative integer variable : xijk ∈ N = {0, 1, 2, … } - no tools are loaded if no parts are processed in time-shift k : yzjk ≤ sk and yzj0 = 0 ∀ z, ∀ j, ∀ k ∈ {1,..,p} - and finally : - uzjk ≤ yzjk - yzj,k+1 ≤ uzjk

∀ z, ∀ j, ∀ k ∈ {1,..,p}

where : - xijk is the number of parts of type i produced on machine j in time-shift k - yzjk is 1 if a tool of type z is allocated to machine j in time-shift k , 0 otherwise - sk is 1 if at least one type of part is produced in time-shift k , 0 otherwise - uzjk is 1 if a tool of type z is added to or removed from machine j at the end of time-shift k, 0 otherwise - ai is the quantity of parts i which have to be manufactured - Cj is the capacity of the tool magazine of machine j - nbz is the limited number of tools of type z As the reader can realize, even "simple" scheduling problems have a complex formulation !

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4.8

Shop floor control

This is probably the topic where Operational Research models and methods have to be progressively developed. The shop floor control is a really complex problem : this fact explains partially the lack of efficient OR tools. However, it seems to be possible to introduce some algorithms or some heuristics methods in this context [28], but the search is at the starting point in this topic. 4.9 Supplying logistics and inventory management

These logistics aspects are two of the basic elements in a firm and they have focused the attention of several researchers. A good synthesis dealing with supplying logistics models and inventory management methods is presented by Peterson and Silver [29] and by Giard [30]. We do not give here more detailed explanations, as this topic is one of the most prevalent in the scientific literature. But as we have mentioned it previously, the just-in-time concept is now implemented in many factories and it recommends the notion of zero-inventory. That means this topic is less important nowadays, even if a minimal inventory is always necessary. 4.10 Distribution logistics

If we refer to Semet [31], the distribution logistics becomes a new topic of research. Indeed due to the reduction of production costs observed during the recent years, distribution costs have increased significantly as a percentage of the cost price of a product. Therefore the minimization of these costs is a new challenge for many companies which can addressed through solving numerous combinatorial problems, e.g., location problems or vehicle routing problems. Semet considers problems dealing with the vehicle routing problem when different means of transport are used (trains and trucks) and defines the accessibility constraints. He proposes a new feature of traveling salesman problem when these constraints have to be taken into account and can define a model using an integer programming formulation. Then he tackles the vehicle routing problem under accessibility constraints, modelled also thanks to an integer programming formulation. Notice that this type of problems is not easy to solve, because of the variety of reallife situations (time-windows for the delivery, accessibility constraints, rest time, capacity of the truck (weight and volume), …) [32].

5 Conclusion
We have shown how the complete production process can be defined as a production planning decision hierarchy, including an integrated production management, which can be decomposed into several modules. Then we have shown that some OR models and methods can be applied to each module. A good survey of the applications of Operational Research models and techniques in flexible manufacturing systems is presented by Kusiak [33], in a special issue of the European Journal of Operational Research dedicated to the FMSs. To conclude this chapter, we think that two topics could provide some interesting research fields : • the product design • the shop floor control.

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For this last point, it will be important to develop several dynamic algorithms, to react quickly to the behaviour of the manufacturing system.

6 Bibliography
[1] [2] [3] [4] [5] [6] [7] [8] [9] R. Chase, N. Aquilano : Production and Operations Management : A Life Cycle Approach. Irwin 1989 J. Dilworth : Operations Management : Design, Planning, and Control for Manufacturing and Services. McGraw-Hill 1992 N. Gaither : Production and Operation Management. The Dryden Press 1992 J .Heizer, B. Render : Production and Operation Management. Allyn and Bacon 1993. W. Stevenson : Production / Operations Management. Irwin 1993 E. Turban, J. Meredith : Fundamentals of Management Science. Irwin 1991 A.-W. Scheer : CIM Computer Integrated Manufacturing : Towards the Factory of the Future. Springer Verlag 1988. J.P. Wermeille, M. Widmer : Les composantes de l'intégration. Marché Suisse de Machines 21, 46-49 (1991) K.E. Stecke : Design, planning, scheduling, and control problems of flexible manufacturing systems. Annals of Operations Research 3, 3-12 (1985)

[10] M. Widmer : Modèles mathématiques pour une gestion efficace des ateliers flexibles. Presses Polytechniques et Universitaires Romandes 1991 [11] P. Solot : A Concept for Planning and Scheduling in an FMS. European Journal of Operational Research 45, 85-95 (1990) [12] Y. Dallery, Y. Frein : An Efficient method to Determine the Optimal Configuration of a Flexible Manufacturing System. Annals of Operations Research 15, 207-225 (1988) [13] P. Solot, J. Bastos : MULTIQ : A Queueing Model for FMSs with Several Pallet Types. JORS 39, 811-821 (1988) [14] P. Solot : A Heuristic Method to Determine the Number of Pallets in a Flexible Manufacturing System with Several Pallet Types. IJPR 2, 191-216 (1990) [15] P. Solot : Nouvelles approches mathématiques des problèmes de conception et de pilotage des ateliers flexibles. Thèse de l'Ecole Polytechnique Fédérale de Lausanne no 975, 1991 [16] M. Widmer, P. Solot : Do not forget the breakdowns and the maintenance operations in FMS design problems ! IJPR 28, 421-430 (1990) [17] C. Chatfield : The analysis of times series : theory and practice. Chapman and Hall 1975 [18] C. Chatfield : What is 'Best' Method of Forecasting ? Statistics 15 (1988) Journal of Applied

[19] V. Schaller : Ordonnancement d'opérations sur une machine à commande numérique (industrie mécanique). Projet de semestre EPFL-DMA, Lausanne 1986 [20] J. Browne, J. Harhen, J. Shivnan : Production Management Systems : a CIM perspective. Addison-Wesley 1988 [21] H. Groeflin, H. Schiltknecht : PEPI : Ein innovatives Produktionsplanungs instrument in der chemischen Industrie. Output 12, 59-64 (1989)

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[22] J. Blazewicz, W. Cellary, R. Slowinski, J. Weglarz : Scheduling under resource constraints : deterministic models. Annals of Operations Research 7 (1986) [23] J. Blazewicz, K. Ecker, G. Schmidt, J. Weglarz : Scheduling in Computer and Manufacturing Systems. Springer-Verlag 1993 [24] D. de Werra, P. Solot : Compact Cylindrical Chromatic Scheduling. SIAM Journal on Discrete Mathematics 4 (1991) [25] Y. Crama, A.W.J. Kolen, A.G. Oerlemans, F.C.R. Spiekma : Minimizing the number of tool switches on a flexible machine. IJFMS 6 (1994) [26] A. Hertz, M. Widmer : A new approach for solving the job shop scheduling problem with tooling constraints. Submitted for publication [27] D. de Werra, M. Widmer : Loading problems with tool management in flexible manufacturing systems : a few integer programming models. IJPR 3, 71-82 (1990) [28] Y. Mottet, M. Widmer : Dynamic Scheduling and Tool Loading. In : V.C. Venkatesh and J.A. McGeough (Eds.) : Proceedings of the 7th International Conference on Computer-Aided Production Engineering. Cookeville USA : Elsevier (1991), pp. 325-332 [29] R. Peterson, E.A. Silver : Decision Systems for Inventory Management and Production Planning. John Wiley and Sons 1985 [30] V. Giard : La gestion de la production. Economica 1988 [31] F. Semet : Elaboration de tournées de véhicules sous contraintes d'accessibilité. Thèse de l'Ecole Polytechnique Fédérale de Lausanne no 1163, 1993. [32] D. de Werra, F. Semet, P. Solot : La distributique. Output 9, 10, 11, 1990. [33] A. Kusiak : Application of operational research models and techniques in flexible manufacturing systems. EJOR 24, 336-345 (1986)

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