Capacity allocation and coordination issues for the timely processing of outsourced operations

Abstract

We consider dynamic capacity booking problems faced by multiple manufacturers each outsourcing certain operations to a common third-party firm. Each manufacturer, upon observing the current state of the third-party schedule, books capacity with the objective to jointly minimize holding costs that result from early deliveries, tardiness penalties due to late deliveries, and third-party capacity booking costs. When making a reservation, each manufacturer evaluates two alternative courses of action: (i) reserving capacity not yet utilized by other manufactures who booked earlier; or (ii) forming a coalition with a subset or all of other manufacturers to achieve a schedule minimizing coalition costs, i.e., a centralized schedule for that coalition. The latter practice surely benefits the coalition as a whole; however, some manufacturers may incur higher costs if their operations are either pushed back too much, or delivered too early. For this reason, a cost allocation scheme making each manufacturer no worse than they would be when acting differently (i.e., participating in a smaller coalition or acting on their own behalf,) must accompany centralized scheduling for the coalition. We model this relationship among the manufacturers as a cooperative game with transferable utility, and present optimal and/or heuristic algorithms to attain individually and coalitionally optimal schedules as well as a linear program formulation to find a core allocation of the manufacturers’ costs.

Keywords

Outsourcing / scheduling / capacity allocation / cooperative games

References

[1] Agnetis A, Hall N G, Pacciarelli D. Supply chain scheduling: sequence coordination. Discrete Applied Mathematics, 2006, 154(15): 2044-2063.

[2] Aydinliyim T, Vairaktarakis G L. Coordination of outsourced operations to minimize weighted flow time and booking costs. Manufacturing & Service Operations Management, 2010, 12(2): 236-255.

[3] Aydinliyim T, Vairaktarakis G L. Kempf K, Keskinocak P, Uzsoy R. Sequencing strategies and coordination yssues in outsourcing and subcontracting operations. planning production and Inventories in the extended enterprise, 2011, New York, NY: Int. Series in Operations Research and Management Science, Springer 269-319.

[4] Aydinliyim T, Vairaktarakis G L. A cooperative savings game approach to a time sensitive capacity allocation and scheduling problem. Decision Sciences, 2013, 44(2): 357-376.

[5] Bukchin Y, Hanany E. Decentralization cost in scheduling: a game-theoretic approach. Manufacturing & Service Operations Management, 2007, 9(3): 263-275.

[6] Cai X Q, Vairaktarakis G L. Coordination of outsourced operations at a third-party facility subject to booking, Overtime, and tardiness Costs. Operations Research, 2012, 60(6): 1436-1450.

[7] Calleja P, Estévez-Fernández M A, Borm P, Hamers H. Job scheduling, cooperation and control. OR Letters, 2006, 34(1): 22-28.

[8] Chen Z L, Hall N G. Supply chain scheduling: conflict and cooperation in assembly systems. Operations Research, 2007, 55(6): 1072-1089.

[9] Chen Z L, Li C L. Scheduling with subcontracting options. IIE Transactions, 2008, 40: 1171-1184.

[10] Curiel I, Pederzoli G, Tijs S. Sequencing games. European Journal of Operational Research, 1989, 40: 344-351.

[11] Curiel I, Potters J, Prasad V R, Tijs S, Veltman B. Sequencing and cooperation. Operations Research, 1994, 42: 566-568.

[12] Curiel I, Hamers H, Klijn F. Borm P, Peters H. Sequencing Games: A survey. Chapters in Game Theory: in honor of stef Tijs’, 2002, Boston: Kluwer Academic Publishers 27-50.

[13] Dawande M, Geismar H N, Hall N G, Sriskandarajah C. Supply chain scheduling: distribution systems. Production Operations Management, 2006, 15: 243-261.

[14] Hain R, Mitra M. Simple sequencing problems with interdependent costs. Games and Economic Behavior, 2004, 48(2): 271-291.

[15] Hall N G, Liu Z. Cooperative and noncooperative games for capacity Planning and Scheduling. Tutorials in Operations Research, 2008 108-129.

[16] Hall N G, Liu Z. Capacity allocation and scheduling in supply chains. Operations Research, 2010, 58(6): 1711-1725.

[17] Hall N G, Potts C N. Supply chain scheduling: batching and delivery. Operations Research, 2003, 51(4): 566-584.

[18] Manoj U V, Sriskandarajah C, Wagneur E. Coordination in a two-stage production system: complexity, conflict and cooperation. Computers and Operations Research, 2012, 39(6): 1245-1256.

[19] Manoj U V, Gupta J N D, Gupta S, Sriskandarajah C. Supply chain scheduling: Just-in-Time environment. Annals of Operations Research, 2008, 161: 53-86.

[20] Vairaktarakis G L. Noncooperative games for subcontracting operations. Manufacturing & Service Operations Management, 2013, 15(1): 148-158.

[21] Vairaktarakis G L, Aydinliyim T. Coordinating the scheduling of subcontracted operations: centralization, competition and FCFS processing, 2014