- Email: [email protected]
An extended enterprise planning methodology for the discrete manufacturing industry
European Journal of Operational Research 129 (2001) 317±325
www.elsevier.com/locate/dsw
Theory and Methodology
An extended enterprise planning methodology for the discrete manufacturing industry Florent Frederix a
a,b
Alcatel Microelectronics, Excelsiorlaan 44, B-1930 Zaventem, Belgium b Limburg University Centre, B-3590 Diepenbeek, Belgium Received 29 February 2000; accepted 30 May 2000
Abstract Extended factories consisting of geographically dispersed independent production facilities are already a reality in the global economy. Production facilities concentrate on core technologies and create partner networks for the manufacturing of their products, a trend initially visible in semiconductor manufacturing but quickly spreading to other industries. A methodology, more ¯exible and ecient than the traditional time-bucket-based techniques and dynamic dispatching heuristics, to plan the Extended Semiconductor Enterprise and schedule work at the dierent production entities is presented in this paper. The generic approach also opens opportunities for applications in other discrete manufacturing industries. The methodology uses stepwise search procedures to improve plans and make-or-buy decision processes to solve resource constraints. Focus of the paper is principally on resource scheduling and less on logistics and distribution topics. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Supply chain management; Scheduling; Simulated annealing; Manufacturing; Heuristics
1. Introduction This paper proposes a methodology to provide customers with realistic due dates and manufacturing entities, which are either part of the core enterprise or subcontractors, with realistic production plans. Customer orders should be met on time with low inventory, short lead times and at
E-mail address: ¯[email protected] (F. Frederix).
the lowest production cost. Unfortunately these goals are con¯icting. Customer orders can be met if inventory levels are large enough; short lead times require a large number of machines with low utilisation rates. It is important to identify tradeos among these objectives to ensure company pro®tability whether using its own or subcontracted facilities. This extended production enterprise concept creates more agility and increases eciency (see Fig. 1). It has already produced tremendous changes in the semiconductor industry as large conglomerates split into independent units and
0377-2217/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 0 0 ) 0 0 2 2 9 - 0
318
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
Fig. 1. The drive for an agile extended production enterprise.
new globally competing groups are formed in a short period of time. Changes that result from market, customer or material ¯ow dynamics require speedy recon®gurations of an extended enterprise as well as renegotiation among partners (including subcontractors). A decision support system can select optimum subcontracting scenarios, given existing production schedules at the enterprise's own facilities with its own set of con®rmed orders and frozen subcontracting schedules. An order or job can be `frozen' on a ®xed schedule for one of two reasons. The order has become critical with no rescheduling ¯exibility, for instance because a production schedule has been imposed by the extended enterprise. Alternatively, the production order may have been subcontracted with contractually de®ned starting and ending dates. In this case, the capacity required for frozen production orders will not be reallocated during rescheduling exercises.
2. Literature review The ®rst topic of interest in production planning and scheduling is probably MRP techniques, one of the most popular time-bucket techniques. Tardif [18] has recently published an advanced MRP-C technique for this type of application. Another option is to use continuous time techniques. These models incorporate scheduling events and obtain a more precise schedule. This option is computer-intensive and models are often more complex. Carmon [5] and Hung and Leachman [15] apply such a technique for semiconductor test facilities and semiconductor front-end manufacturing. The third modelling approach for extended enterprises and supply chains in the literature is statistical or stochastic [7]. These are fast computational techniques that can be used in steady-state mass production environments. Kaihara [10] introduced an extension to the Cobb± Douglas production function to de®ne equilibrium
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
319
Table 1 Candidate optimisation techniques for the extended enterprise Technique
Method proposed
Recent literature
Some characteristics
Time bucket-based
MRP and MRP II, MRP-C (capacitated MRP model) Linear programming, simulation
Ref. [18]
The `time bucket based' model is dierent from a task scheduler Resource dependency rules are not possible Simpli®cations are required due to model in¯exibility and computational requirements Model is applicable to steady-state markets (excluding agile and virtual manufacturing environments). Stochastic models are useful to optimise continuous `just in time' manufacturing processes Dispatching rules are ecient in speci®c environments. Locking and other issues depend on scheduling exercise. Local optimisation technique By sampling the solution space it is possible to approach a (local) optimum quickly. Global optimality not guaranteed Decomposition techniques to decrease complexity and increase the number of constraints on the movement of tasks
Continuous time techniques
Carmon [5] decision trees
Stochastic models
Service level and safety stocks
Refs. [13,10]
Heuristics
Resource dispatching rules
Dynamic and static scheduling and genetic algorithms. See Ref. [21]
Continuous time approximation techniques
Decision tree sampling, Monte-Carlo, Tabu search etc.
Hierarchical decomposition techniques
Functional split: rough planning between entities, detailed in the entity
Two-level approximation techniques, backtracking, `design of experiments' techniques Static scheduling, work cell- and time window-based decomposition. Holons combining hierarchical and local planning
in resource loading and order distribution in the extended enterprise. Hierarchical approaches for dealing with planning issues and the supply chain are given here, as in [9,12]. Recently, a dynamic hierarchical decomposition technique for the semiconductor industry has been proposed by Makatsoris [14]. Beamon [3] provides a more traditional view on supply chain modelling. Table 1 summarises these techniques which did not receive broad acceptance in the industry with the exception of MRP, and none of which integrate the make-orbuy process. 3. A stepwise optimisation methodology The methodology proposed in this paper is illustrated in Fig. 2. First of all, an early rough feasible plan is created using MRP or dynamic scheduling heuristics. It can be quickly generated and consists of a set of ®rst-order routings in the extended enterprise with order due dates and total
cost. This rough feasible plan can be used to answer questions about the feasibility of customer delivery due date. Many rough feasible plans can be generated using rules de®ned by the planner and/or other heuristic procedures. The next step is to search for a local optimum in the neighbourhood of this `rough' solution using the ®ne optimiser. The ®ne optimiser works on the whole extended enterprise and looks for slack in the orders to improve the rough schedule. The rough planner can also insert new orders into the existing schedule. If this is not possible, jobs for rescheduling are accumulated. The optimiser memorises a trail of intermediate solutions and the ®ne plan is run at regular intervals. Fig. 3 illustrates this process of incremental rescheduling: ®rst, new orders are scheduled and inserted into the existing plan, and whenever required, orders that still have enough slack and `non-frozen' orders are rescheduled. The next step reschedules all orders. In real life it is probably dicult to execute this last (re-)planning step due to order subcontracting limitations.
320
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
Fig. 2. Concept design of proposed solution.
When a `®ne plan' that includes all orders uses subcontracting, the method will search for a solution with less subcontracting without violating order due dates. Finally, an intelligent branchand-bound algorithm captures the speci®cs of the `make-or-buy' decision process in the semiconductor industry. A supply chain construct is then de®ned for the plan accepted.
3.1. The rough optimiser Most of the techniques discussed in Table 1 deliver more than one solution. A dierent rough solution can result from dierent job sequences de®ned at the beginning (as in the case of dynamic dispatching heuristics), dierent partitioning of entities (using hierarchical decomposition and
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
321
Fig. 3. Incremental rescheduling with `frozen' orders.
static scheduling) or addition of randomness to a set of dynamic dispatching decisions. The methodology described in this paper uses simulated annealing to execute a random walk for large solution spaces, and obtains rough feasible plans in much shorter periods of time than the steepest descent and tabu search algorithms.
3.2. The ®ne optimiser The ®ne optimiser starts with solutions provided by the rough optimiser and searches in the local neighbourhood for improved solutions. Several local neighbourhood algorithms have been considered in the extended enterprise environment, using for benchmarking the `total ¯oat algorithm'. Total ¯oat is calculated as follows: f totali s lsti ÿ s esti s lstfi ÿ s estfI ;
where si is the operation processing time for operation i, s esti the earliest starting time for operation i, slsti the latest starting time for operation i and/or the latest ®nishing time for preceding jobs, i.e., s lsti max i;j2V fs lstj sj g, s estfi the earliest ®nishing time: s estfi s esti si and s lstfi is the latest ®nishing time: s lstfi s lsti si : Minimising makespan implies that total ¯oats are minimised. The aim of this transition mechanism is to identify pairs of critical operations processed using the same resource to prioritise operations with the least total ¯oat. The net result is reduced idle resource times, a new critical path and a new solution.
4. The algorithm The steps in the algorithm proposed can be summarised as follows:
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F. Frederix / European Journal of Operational Research 129 (2001) 317±325
1. Consider critical operations i and j with total positive ¯oats fi and fj : If operation i precedes operation j in the current solution and fi > fj then operation j should precede operation i. 2. If there are many i; j pairs, the algorithm computes the dierence (fi ÿ fj ) and sorts the pairs in descending order. 3. If the sorted list is not empty, the algorithm swaps processing orders for pairs' operations with the highest free ¯oats. Steps 1±3 are repeated until the list is empty. If a non-feasible schedule is obtained, the swap is undone and the next operation set in the list is selected. 4. The swap of two critical consecutive operations provides a new starting sequence. In the initial iterations of the ®ne optimiser algorithm, it is possible that the intermediate schedule of an order does not meet the due date resulting in negative ¯oats. The total ¯oat transition algorithm is robust and will shift the operations back, where operations with a negative ¯oat receive a higher swap priority until the due date is met. No feasible schedule for the extended enterprise orders can be generated if there is not enough material to satisfy the demand, a condition de®ned as `work in progress in-feasibility' [18]. The `extended enterprise planner' will receive a signal informing that the whole order load cannot be satis®ed in the requested due time. Capacity infeasible schedules [18] can be eliminated by using more subcontracting.
5. Integrating the make-or-buy decision process The process of starting from feasible (trial) schedules and searching for less expensive subcontracting options corresponds to current practice in the semiconductor and other industries. See, for example, Chamard and Fischler [6] for applications to the aviation and automotive industries. A branch-and-bound algorithm is proposed here to select solutions that minimise the cost of subcontracting, assuming that available core capacity is fully utilised before any subcontracting is considered and that it represents a ®xed cost.
A Benders [4] decomposition algorithm is used to speed up the solution process. Two types of cuts in the branch-and-bound decision tree reduce the number of subcontracting scenarios to be evaluated. The ®rst identi®es infeasible (sub) sets of solutions and removes them from the decision tree while the second removes feasible but more costly (sub) sets from the tree. These de®nitions of feasibility and optimality cuts are not dicult to make because of the rather simple subcontracting scenario in the semiconductor manufacturing industry. First, it tries to produce the component using core enterprise manufacturing facilities. If this is not feasible, it replaces one or more core manufacturing by subcontracted facilities. To de®ne these terms mathematically, consider that if k is a member of the set of optional routes for order j and route k 1 contains more process steps in subcontracting than route k then Cjk < Cj k1 , where Cjk is the cost of producing order j using a route k. Feasibility and optimality cuts can be de®ned as follows: 1. Feasibility cuts. Given a subcontracting scenario consisting of selected routes rk1 ; rk2 ; rk3 ; . . ., where ki represents the route index for the ith job that has a subcontracting option, any subcontracting scenario for which i 6 k is infeasible. As stated in the previous paragraph, less subcontracting always increases the need for capacity at the core enterprise manufacturing facilities. 2. Optimality cuts. The cost of aP feasible subconL traction scenario is given by j1 Cjk where k represents the selected route for product-order j and L is the total product-order loading for the extended enterprise. Any subcontracting scenario with higher cost is not optimal and needs no feasibility check. Note that subcontracting combinations can be easily excluded from further evaluation using only objective function recalculations. 5.1. The algorithm for subcontracting The algorithm incorporating subcontracting can be summarised as follows:
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
1. Start with a feasible trial schedule. 2. Set the bounds for `optimality cut' as the cost of the trial schedule. 3. Store the schedule as the currently optimal schedule. 4. Select a new schedule with another set of subcontracting options. If done, go to 10. 5. Calculate the schedule cost (value of the objective function). 6. If schedule cost 6 bound for optimality cut go to step 4. 7. Check schedule against `feasibility cut' subcontracting scenarios. If schedule not feasible, go to step 4. 8. Check feasibility (due dates) of schedule. If schedule is feasible and cost < optimality cut, then go to step 2. If schedule is feasible but cost > optimality cut, then go to step 4. 9. If schedule is not feasible, add schedule to the set feasibility cut scenarios. Go to step 4. 10. Exit. Optimality cut is the cost of best solution. A set of subcontracting options can be generated through simple enumeration or other search methods. Heuristics can be used to select a set of subcontracting options. In real cases however, the number of subcontracting options is limited to some products and processes allocated to a few quali®ed subcontractors, thus making the decision tree approach highly advantageous as a solution method.
323
6. Results with experimental data sets Sixty-four experimental data sets were selected from [1,2,8,11,14,17,20] and used to benchmark the proposed methodology as well as ®ne tune the optimiser algorithm, as documented in Table 1. Dynamic dispatching rules are referenced in the recent literature [16,19] from which the following seven rules were selected for the benchmarking exercise: ®rst in ®rst out (FIFO); last in ®rst out (LIFO); shortest operation processing time ®rst (SOPT); select job with most remaining work ®rst (MRW); select job with least remaining work ®rst (LRW); select operation with smallest ratio of the operation processing time to the total remaining processing time (ODT); and select the operation with the smallest ratio obtained by multiplying the operation processing time by the total processing time (OMT). The results were compared with schedules generated by the ®ne optimiser starting from a randomly generated starting job sequence. Fig. 4 shows the global rankings based on the makespan values for every dispatching method applied to the set of exercises. The ®ne optimiser starting from randomly generated start sequences (RANDOM) outperforms the best performing rule (ODT). In the case of dynamic dispatching rules, performance strongly depends on the exercises although ®ne optimiser seems to be much less sensitive as it uses a global optimisation routine based on free slack and free ¯oat calculations.
Fig. 4. Ranking of dynamic dispatching rules.
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F. Frederix / European Journal of Operational Research 129 (2001) 317±325
Fig. 5. Relative makespan results, compared with MRP-C.
The MRP-C algorithm [18], which is one of the most recent developments in the area of capacitated discrete time-based techniques, was used in the second benchmark exercise. This algorithm uses total processing time and `normal' queuing time for every task as the time to complete the task. Normal queuing times and their standard deviation were calculated for 100 randomly generated best-®t solutions as well as total processing + queuing time and their standard deviation for every job. The largest routing determines the `makespan' recorded with a single-sided 95% con®dence interval. The MRP-C methodology is more ecient for problems with a large number of tasks where the number of tasks is de®ned as the product of the number of orders by the number of resources. Fig. 5 plots the results using curves which are appropriately labelled: dynamic for dynamic dispatching, random, etc. It also shows 95% MRP-C
curve plots. All makespans are drawn against the best solution obtained which is shown on the xaxis.
7. Summary The methodology described in this paper combines the ¯exibility requested by the industry with an optimisation approach that can work with replaceable constraint sets associated with supply chain constructs. It is able to do several things: (1) create ®nite capacity planning; (2) integrate human guidance rules into the optimisation process; (3) use the same model for the rough and ®ne planning cycle in a consistent and synchronised manner; (4) respect commitments made to subcontractors, limit rescheduling to non-frozen jobs and start from real work in progress; and (5) obtain
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
good solutions for typical semiconductor scheduling problems. Benchmark results show that the methodology obtains better results than dynamic dispatching heuristics and the MRP-C methodology and that it does not have the typical problems associated with these techniques. For example, dynamic dispatching heuristic performances depend on the speci®c exercise and MRP-C algorithms are unable to guarantee the feasibility of the proposed plan. The proposed methodology does not suer from either problem. References [1] J. Adams, E. Balas, D. Zawack, The shifting bottleneck procedure for job shop scheduling, Management Science 34 (1988) 391±401. [2] D. Applegate, W. Cook, A computational study of the jobshop scheduling instance, ORSA Journal on Computing 3 (1991) 149±156. [3] B.M. Beamon, Supply chain design and analysis: Models and methods, International Journal of Production Economics 55 (1998) 281±294. [4] J.F. Benders, Partitioning procedures for solving mixedvariable programming problems, Numerische Mathematik 4 (1962) 238±252. [5] T.F. Carmon, Production planning and scheduling for semiconductor device testing, Ph.D. Dissertation, University of California, 1995. [6] A. Chamard, A. Fischler, CHIC Lessons on CLP Methodology, Arti®cial Intelligence Software, Deliverable D6.5.3, Dassault Aviation, France, 1995. [7] M.A. Cohen, J. Eliashberg, T.-H. Ho, New product development: The performance and time-to-market tradeo, Management Science 42 (2), February 1996. [8] H. Fisher, G.L. Thompson, Probabilistic learning combinations of local job-shop scheduling rules, in: J.F. Muth, G.L. Thompson (Eds.), Industrial Scheduling, PrenticeHall, Englewood Clis, NJ, 1963, pp. 225±251. [9] K. Hadavi, K. Voigt, An integrated planning and scheduling environment, in: Proceedings of the Simulation and Arti®cial Intelligence in Manufacturing Conference, Society of Manufacturing Engineers, Long Beach, CA, 1987.
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[10] T. Kaihara, Supply chain management with multi-agent paradigm, in: Proceedings of the Eighth International ROMAN Conference, Pisa, Italy, 27±29 September 1999, pp. 394±399. [11] S. Lawrence, Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA, 1984. [12] R.C. Leachman, T.A. Ciriani, Modeling Techniques for Automated Production Planning in the Semiconductor Industry, Optimization in Industry, Wiley, New York, 1993. [13] H.L. Lee, C. Billington, The Evolution of Supply-ChainManagement Models and Practice at Hewlett-Packard, Interfaces 25 (5) (1995) 42±63. [14] C. Makatsoris, Planning, scheduling and control for distributed manufacturing systems, Imperial College of Science Technology and Medicine, London, Ph.D. Dissertation, 1997. [15] Y.-F. Hung, R.C. Leachman, A production planning methodology for semiconductor manufacturing based on iterative simulation and linear programming calculations, IEEE Transactions on Semiconductor Manufacturing 9 (2), May 1996. [16] I. Sabuncuoglu, A study of scheduling rules of ¯exible manufacturing systems: A simulation approach, International Journal of Production Research 36 (2) (1998) 527±546. [17] R.H. Storer, S.D. Wu, R. Vaccari, New search spaces for sequencing instances with application to job shop scheduling, Management Science 38 (1992) 1495±1509. [18] V. Tardif, Detecting scheduling infeasibilities in multistage, ®nite capacity, production environments, Ph.D. Dissertation, Northwestern University, Evanston, IL, 1995. [19] N.S. Tipi, S. Bennett, Dispatching rules for scheduling and feedback control in a virtual enterprise ± a simulation approach, in: Proceedings of the FAIM'99 Conference on CD, 1999. [20] T. Yamada, R. Nakano, A genetic algorithm applicable to large-scale job-shop instances, in: R. Manner, B. Manderick, Parallel Instance Solving from Nature, North-Holland, Amsterdam, vol. 2, 1992, pp. 281±290. [21] D.S. Wu, E. Byeon, R.H. Storer, A graph-theoretic decomposition of the job shop scheduling problem to achieve scheduling robustness, Management Science 47 (1) (1999).
www.elsevier.com/locate/dsw
Theory and Methodology
An extended enterprise planning methodology for the discrete manufacturing industry Florent Frederix a
a,b
Alcatel Microelectronics, Excelsiorlaan 44, B-1930 Zaventem, Belgium b Limburg University Centre, B-3590 Diepenbeek, Belgium Received 29 February 2000; accepted 30 May 2000
Abstract Extended factories consisting of geographically dispersed independent production facilities are already a reality in the global economy. Production facilities concentrate on core technologies and create partner networks for the manufacturing of their products, a trend initially visible in semiconductor manufacturing but quickly spreading to other industries. A methodology, more ¯exible and ecient than the traditional time-bucket-based techniques and dynamic dispatching heuristics, to plan the Extended Semiconductor Enterprise and schedule work at the dierent production entities is presented in this paper. The generic approach also opens opportunities for applications in other discrete manufacturing industries. The methodology uses stepwise search procedures to improve plans and make-or-buy decision processes to solve resource constraints. Focus of the paper is principally on resource scheduling and less on logistics and distribution topics. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Supply chain management; Scheduling; Simulated annealing; Manufacturing; Heuristics
1. Introduction This paper proposes a methodology to provide customers with realistic due dates and manufacturing entities, which are either part of the core enterprise or subcontractors, with realistic production plans. Customer orders should be met on time with low inventory, short lead times and at
E-mail address: ¯[email protected] (F. Frederix).
the lowest production cost. Unfortunately these goals are con¯icting. Customer orders can be met if inventory levels are large enough; short lead times require a large number of machines with low utilisation rates. It is important to identify tradeos among these objectives to ensure company pro®tability whether using its own or subcontracted facilities. This extended production enterprise concept creates more agility and increases eciency (see Fig. 1). It has already produced tremendous changes in the semiconductor industry as large conglomerates split into independent units and
0377-2217/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 0 0 ) 0 0 2 2 9 - 0
318
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
Fig. 1. The drive for an agile extended production enterprise.
new globally competing groups are formed in a short period of time. Changes that result from market, customer or material ¯ow dynamics require speedy recon®gurations of an extended enterprise as well as renegotiation among partners (including subcontractors). A decision support system can select optimum subcontracting scenarios, given existing production schedules at the enterprise's own facilities with its own set of con®rmed orders and frozen subcontracting schedules. An order or job can be `frozen' on a ®xed schedule for one of two reasons. The order has become critical with no rescheduling ¯exibility, for instance because a production schedule has been imposed by the extended enterprise. Alternatively, the production order may have been subcontracted with contractually de®ned starting and ending dates. In this case, the capacity required for frozen production orders will not be reallocated during rescheduling exercises.
2. Literature review The ®rst topic of interest in production planning and scheduling is probably MRP techniques, one of the most popular time-bucket techniques. Tardif [18] has recently published an advanced MRP-C technique for this type of application. Another option is to use continuous time techniques. These models incorporate scheduling events and obtain a more precise schedule. This option is computer-intensive and models are often more complex. Carmon [5] and Hung and Leachman [15] apply such a technique for semiconductor test facilities and semiconductor front-end manufacturing. The third modelling approach for extended enterprises and supply chains in the literature is statistical or stochastic [7]. These are fast computational techniques that can be used in steady-state mass production environments. Kaihara [10] introduced an extension to the Cobb± Douglas production function to de®ne equilibrium
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
319
Table 1 Candidate optimisation techniques for the extended enterprise Technique
Method proposed
Recent literature
Some characteristics
Time bucket-based
MRP and MRP II, MRP-C (capacitated MRP model) Linear programming, simulation
Ref. [18]
The `time bucket based' model is dierent from a task scheduler Resource dependency rules are not possible Simpli®cations are required due to model in¯exibility and computational requirements Model is applicable to steady-state markets (excluding agile and virtual manufacturing environments). Stochastic models are useful to optimise continuous `just in time' manufacturing processes Dispatching rules are ecient in speci®c environments. Locking and other issues depend on scheduling exercise. Local optimisation technique By sampling the solution space it is possible to approach a (local) optimum quickly. Global optimality not guaranteed Decomposition techniques to decrease complexity and increase the number of constraints on the movement of tasks
Continuous time techniques
Carmon [5] decision trees
Stochastic models
Service level and safety stocks
Refs. [13,10]
Heuristics
Resource dispatching rules
Dynamic and static scheduling and genetic algorithms. See Ref. [21]
Continuous time approximation techniques
Decision tree sampling, Monte-Carlo, Tabu search etc.
Hierarchical decomposition techniques
Functional split: rough planning between entities, detailed in the entity
Two-level approximation techniques, backtracking, `design of experiments' techniques Static scheduling, work cell- and time window-based decomposition. Holons combining hierarchical and local planning
in resource loading and order distribution in the extended enterprise. Hierarchical approaches for dealing with planning issues and the supply chain are given here, as in [9,12]. Recently, a dynamic hierarchical decomposition technique for the semiconductor industry has been proposed by Makatsoris [14]. Beamon [3] provides a more traditional view on supply chain modelling. Table 1 summarises these techniques which did not receive broad acceptance in the industry with the exception of MRP, and none of which integrate the make-orbuy process. 3. A stepwise optimisation methodology The methodology proposed in this paper is illustrated in Fig. 2. First of all, an early rough feasible plan is created using MRP or dynamic scheduling heuristics. It can be quickly generated and consists of a set of ®rst-order routings in the extended enterprise with order due dates and total
cost. This rough feasible plan can be used to answer questions about the feasibility of customer delivery due date. Many rough feasible plans can be generated using rules de®ned by the planner and/or other heuristic procedures. The next step is to search for a local optimum in the neighbourhood of this `rough' solution using the ®ne optimiser. The ®ne optimiser works on the whole extended enterprise and looks for slack in the orders to improve the rough schedule. The rough planner can also insert new orders into the existing schedule. If this is not possible, jobs for rescheduling are accumulated. The optimiser memorises a trail of intermediate solutions and the ®ne plan is run at regular intervals. Fig. 3 illustrates this process of incremental rescheduling: ®rst, new orders are scheduled and inserted into the existing plan, and whenever required, orders that still have enough slack and `non-frozen' orders are rescheduled. The next step reschedules all orders. In real life it is probably dicult to execute this last (re-)planning step due to order subcontracting limitations.
320
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
Fig. 2. Concept design of proposed solution.
When a `®ne plan' that includes all orders uses subcontracting, the method will search for a solution with less subcontracting without violating order due dates. Finally, an intelligent branchand-bound algorithm captures the speci®cs of the `make-or-buy' decision process in the semiconductor industry. A supply chain construct is then de®ned for the plan accepted.
3.1. The rough optimiser Most of the techniques discussed in Table 1 deliver more than one solution. A dierent rough solution can result from dierent job sequences de®ned at the beginning (as in the case of dynamic dispatching heuristics), dierent partitioning of entities (using hierarchical decomposition and
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
321
Fig. 3. Incremental rescheduling with `frozen' orders.
static scheduling) or addition of randomness to a set of dynamic dispatching decisions. The methodology described in this paper uses simulated annealing to execute a random walk for large solution spaces, and obtains rough feasible plans in much shorter periods of time than the steepest descent and tabu search algorithms.
3.2. The ®ne optimiser The ®ne optimiser starts with solutions provided by the rough optimiser and searches in the local neighbourhood for improved solutions. Several local neighbourhood algorithms have been considered in the extended enterprise environment, using for benchmarking the `total ¯oat algorithm'. Total ¯oat is calculated as follows: f totali s lsti ÿ s esti s lstfi ÿ s estfI ;
where si is the operation processing time for operation i, s esti the earliest starting time for operation i, slsti the latest starting time for operation i and/or the latest ®nishing time for preceding jobs, i.e., s lsti max i;j2V fs lstj sj g, s estfi the earliest ®nishing time: s estfi s esti si and s lstfi is the latest ®nishing time: s lstfi s lsti si : Minimising makespan implies that total ¯oats are minimised. The aim of this transition mechanism is to identify pairs of critical operations processed using the same resource to prioritise operations with the least total ¯oat. The net result is reduced idle resource times, a new critical path and a new solution.
4. The algorithm The steps in the algorithm proposed can be summarised as follows:
322
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
1. Consider critical operations i and j with total positive ¯oats fi and fj : If operation i precedes operation j in the current solution and fi > fj then operation j should precede operation i. 2. If there are many i; j pairs, the algorithm computes the dierence (fi ÿ fj ) and sorts the pairs in descending order. 3. If the sorted list is not empty, the algorithm swaps processing orders for pairs' operations with the highest free ¯oats. Steps 1±3 are repeated until the list is empty. If a non-feasible schedule is obtained, the swap is undone and the next operation set in the list is selected. 4. The swap of two critical consecutive operations provides a new starting sequence. In the initial iterations of the ®ne optimiser algorithm, it is possible that the intermediate schedule of an order does not meet the due date resulting in negative ¯oats. The total ¯oat transition algorithm is robust and will shift the operations back, where operations with a negative ¯oat receive a higher swap priority until the due date is met. No feasible schedule for the extended enterprise orders can be generated if there is not enough material to satisfy the demand, a condition de®ned as `work in progress in-feasibility' [18]. The `extended enterprise planner' will receive a signal informing that the whole order load cannot be satis®ed in the requested due time. Capacity infeasible schedules [18] can be eliminated by using more subcontracting.
5. Integrating the make-or-buy decision process The process of starting from feasible (trial) schedules and searching for less expensive subcontracting options corresponds to current practice in the semiconductor and other industries. See, for example, Chamard and Fischler [6] for applications to the aviation and automotive industries. A branch-and-bound algorithm is proposed here to select solutions that minimise the cost of subcontracting, assuming that available core capacity is fully utilised before any subcontracting is considered and that it represents a ®xed cost.
A Benders [4] decomposition algorithm is used to speed up the solution process. Two types of cuts in the branch-and-bound decision tree reduce the number of subcontracting scenarios to be evaluated. The ®rst identi®es infeasible (sub) sets of solutions and removes them from the decision tree while the second removes feasible but more costly (sub) sets from the tree. These de®nitions of feasibility and optimality cuts are not dicult to make because of the rather simple subcontracting scenario in the semiconductor manufacturing industry. First, it tries to produce the component using core enterprise manufacturing facilities. If this is not feasible, it replaces one or more core manufacturing by subcontracted facilities. To de®ne these terms mathematically, consider that if k is a member of the set of optional routes for order j and route k 1 contains more process steps in subcontracting than route k then Cjk < Cj k1 , where Cjk is the cost of producing order j using a route k. Feasibility and optimality cuts can be de®ned as follows: 1. Feasibility cuts. Given a subcontracting scenario consisting of selected routes rk1 ; rk2 ; rk3 ; . . ., where ki represents the route index for the ith job that has a subcontracting option, any subcontracting scenario for which i 6 k is infeasible. As stated in the previous paragraph, less subcontracting always increases the need for capacity at the core enterprise manufacturing facilities. 2. Optimality cuts. The cost of aP feasible subconL traction scenario is given by j1 Cjk where k represents the selected route for product-order j and L is the total product-order loading for the extended enterprise. Any subcontracting scenario with higher cost is not optimal and needs no feasibility check. Note that subcontracting combinations can be easily excluded from further evaluation using only objective function recalculations. 5.1. The algorithm for subcontracting The algorithm incorporating subcontracting can be summarised as follows:
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1. Start with a feasible trial schedule. 2. Set the bounds for `optimality cut' as the cost of the trial schedule. 3. Store the schedule as the currently optimal schedule. 4. Select a new schedule with another set of subcontracting options. If done, go to 10. 5. Calculate the schedule cost (value of the objective function). 6. If schedule cost 6 bound for optimality cut go to step 4. 7. Check schedule against `feasibility cut' subcontracting scenarios. If schedule not feasible, go to step 4. 8. Check feasibility (due dates) of schedule. If schedule is feasible and cost < optimality cut, then go to step 2. If schedule is feasible but cost > optimality cut, then go to step 4. 9. If schedule is not feasible, add schedule to the set feasibility cut scenarios. Go to step 4. 10. Exit. Optimality cut is the cost of best solution. A set of subcontracting options can be generated through simple enumeration or other search methods. Heuristics can be used to select a set of subcontracting options. In real cases however, the number of subcontracting options is limited to some products and processes allocated to a few quali®ed subcontractors, thus making the decision tree approach highly advantageous as a solution method.
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6. Results with experimental data sets Sixty-four experimental data sets were selected from [1,2,8,11,14,17,20] and used to benchmark the proposed methodology as well as ®ne tune the optimiser algorithm, as documented in Table 1. Dynamic dispatching rules are referenced in the recent literature [16,19] from which the following seven rules were selected for the benchmarking exercise: ®rst in ®rst out (FIFO); last in ®rst out (LIFO); shortest operation processing time ®rst (SOPT); select job with most remaining work ®rst (MRW); select job with least remaining work ®rst (LRW); select operation with smallest ratio of the operation processing time to the total remaining processing time (ODT); and select the operation with the smallest ratio obtained by multiplying the operation processing time by the total processing time (OMT). The results were compared with schedules generated by the ®ne optimiser starting from a randomly generated starting job sequence. Fig. 4 shows the global rankings based on the makespan values for every dispatching method applied to the set of exercises. The ®ne optimiser starting from randomly generated start sequences (RANDOM) outperforms the best performing rule (ODT). In the case of dynamic dispatching rules, performance strongly depends on the exercises although ®ne optimiser seems to be much less sensitive as it uses a global optimisation routine based on free slack and free ¯oat calculations.
Fig. 4. Ranking of dynamic dispatching rules.
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Fig. 5. Relative makespan results, compared with MRP-C.
The MRP-C algorithm [18], which is one of the most recent developments in the area of capacitated discrete time-based techniques, was used in the second benchmark exercise. This algorithm uses total processing time and `normal' queuing time for every task as the time to complete the task. Normal queuing times and their standard deviation were calculated for 100 randomly generated best-®t solutions as well as total processing + queuing time and their standard deviation for every job. The largest routing determines the `makespan' recorded with a single-sided 95% con®dence interval. The MRP-C methodology is more ecient for problems with a large number of tasks where the number of tasks is de®ned as the product of the number of orders by the number of resources. Fig. 5 plots the results using curves which are appropriately labelled: dynamic for dynamic dispatching, random, etc. It also shows 95% MRP-C
curve plots. All makespans are drawn against the best solution obtained which is shown on the xaxis.
7. Summary The methodology described in this paper combines the ¯exibility requested by the industry with an optimisation approach that can work with replaceable constraint sets associated with supply chain constructs. It is able to do several things: (1) create ®nite capacity planning; (2) integrate human guidance rules into the optimisation process; (3) use the same model for the rough and ®ne planning cycle in a consistent and synchronised manner; (4) respect commitments made to subcontractors, limit rescheduling to non-frozen jobs and start from real work in progress; and (5) obtain
F. Frederix / European Journal of Operational Research 129 (2001) 317±325
good solutions for typical semiconductor scheduling problems. Benchmark results show that the methodology obtains better results than dynamic dispatching heuristics and the MRP-C methodology and that it does not have the typical problems associated with these techniques. For example, dynamic dispatching heuristic performances depend on the speci®c exercise and MRP-C algorithms are unable to guarantee the feasibility of the proposed plan. The proposed methodology does not suer from either problem. References [1] J. Adams, E. Balas, D. Zawack, The shifting bottleneck procedure for job shop scheduling, Management Science 34 (1988) 391±401. [2] D. Applegate, W. Cook, A computational study of the jobshop scheduling instance, ORSA Journal on Computing 3 (1991) 149±156. [3] B.M. Beamon, Supply chain design and analysis: Models and methods, International Journal of Production Economics 55 (1998) 281±294. [4] J.F. Benders, Partitioning procedures for solving mixedvariable programming problems, Numerische Mathematik 4 (1962) 238±252. [5] T.F. Carmon, Production planning and scheduling for semiconductor device testing, Ph.D. Dissertation, University of California, 1995. [6] A. Chamard, A. Fischler, CHIC Lessons on CLP Methodology, Arti®cial Intelligence Software, Deliverable D6.5.3, Dassault Aviation, France, 1995. [7] M.A. Cohen, J. Eliashberg, T.-H. Ho, New product development: The performance and time-to-market tradeo, Management Science 42 (2), February 1996. [8] H. Fisher, G.L. Thompson, Probabilistic learning combinations of local job-shop scheduling rules, in: J.F. Muth, G.L. Thompson (Eds.), Industrial Scheduling, PrenticeHall, Englewood Clis, NJ, 1963, pp. 225±251. [9] K. Hadavi, K. Voigt, An integrated planning and scheduling environment, in: Proceedings of the Simulation and Arti®cial Intelligence in Manufacturing Conference, Society of Manufacturing Engineers, Long Beach, CA, 1987.
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