Order Assignment and Scheduling in a Supply Chain

We consider the supply chain of a manufacturer who produces time-sensitive products that have a large variety, a short life cycle, and are sold in a very short selling season. The supply chain consists of multiple overseas plants and a domestic distribution center (DC). Retail orders are first processed at the plants and then shipped from the plants to the DC for distribution to domestic retailers. Due to variations in productivity and labor costs at different plants, the processing time and cost of an order are dependent on the plant to which it is assigned. We study the following static and deterministic order assignment and scheduling problem faced by the manufacturer before every selling season: Given a set of orders, determine which orders are to be assigned to each plant, find a schedule for processing the assigned orders at each plant, and find a schedule for shipping the completed orders from each plant to the DC, such that a certain performance measure is optimized. We consider four different performance measures, all of which take into account both delivery lead time and the total production and distribution cost. A problem corresponding to each performance measure is studied separately. We analyze the computational complexity of various cases of the problems by either proving that a problem is intractable or providing an efficient exact algorithm for the problem. We propose several fast heuristics for the intractable problems. We analyze the worst-case and asymptotic performance of the heuristics and also computationally evaluate their performance using randomly generated test instances. Our results show that the heuristics are capable of generating near-optimal solutions quickly.

[1]  Hau L. Lee,et al.  Strategic Analysis of Integrated Production-Distribution Systems: Models and Methods , 1988, Oper. Res..

[2]  Zhi-Long Chen,et al.  Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs , 1996 .

[3]  Ricardo Ernst,et al.  Global Operations and Logistics: Text and Cases , 1998 .

[4]  Rakesh Nagi,et al.  A review of integrated analysis of production-distribution systems , 1999 .

[5]  Guoqing Wang,et al.  Parallel machine scheduling with batch delivery costs , 2000 .

[6]  T. C. Edwin Cheng,et al.  Single machine scheduling with batch deliveries , 1996 .

[7]  Gerhard J. Woeginger,et al.  A polynomial‐time approximation scheme for single‐machine sequencing with delivery times and sequence‐independent batch set‐up times , 1998 .

[8]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[9]  W. A. Horn.  Technical Note - Minimizing Average Flow Time with Parallel Machines , 1973, Oper. Res..

[10]  George L. Vairaktarakis,et al.  Integrated Scheduling of Production and Distribution Operations , 2005, Manag. Sci..

[11]  Francesca Fumero,et al.  Synchronized Development of Production, Inventory, and Distribution Schedules , 1999, Transp. Sci..

[12]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[13]  M. E. Johnson,et al.  Learning from Toys: Lessons in Managing Supply Chain Risk from the Toy Industry , 2001 .

[14]  Chung Yee Lee,et al.  On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date , 1993 .

[15]  C. N. Potts,et al.  Analysis of a linear programming heuristic for scheduling unrelated parallel machines , 1985, Discret. Appl. Math..

[16]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[17]  C. N. Potts,et al.  Technical Note - Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times , 1980, Oper. Res..

[18]  Chris N. Potts,et al.  Scheduling with Fixed Delivery Dates , 2001, Oper. Res..

[19]  Candace A. Yano,et al.  The Economic Lot and Delivery Scheduling Problem: Powers of Two Policies , 1995, Transp. Sci..

[20]  Zhi-Long Chen,et al.  Machine scheduling with transportation considerations , 2001 .

[21]  G. McCormick.  Nonlinear Programming: Theory, Algorithms and Applications , 1983 .

[22]  David Simchi-Levi,et al.  Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science) , 2004 .

[23]  J. Hammond,et al.  Sport Obermeyer Ltd. , 1994 .

[24]  David B. Shmoys,et al.  Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better , 1992, Math. Oper. Res..

[25]  Gerhard J. Woeginger,et al.  heuristics for parallel machine scheduling with delivery times , 1994, Acta Informatica.

[26]  Marshall L. Fisher,et al.  Coordination of production and distribution planning , 1994 .

[27]  Chris N. Potts,et al.  Supply chain scheduling: Batching and delivery , 2003, Oper. Res..