Optimal control of an assembly system with demand for the end-product and intermediate components

This article considers the production and admission control decisions for a two-stage manufacturing system where intermediate components are produced to stock in the first stage and an end-product is assembled from these components through a second-stage assembly operation. The firm faces two types of demand. The demand for the end-product is satisfied immediately if there are available products in inventory while the firm has the option to accept the order for later delivery or to reject it when no inventory is available. Demand for intermediate components may be accepted or rejected to keep components available for assembly purposes. The structure of demand admission, component production and product assembly decisions are characterized. The proposed model is extended to take into account multiple customer classes and a more general revenue collecting scheme where only an upfront partial payment is collected if a customer demand is accepted for future delivery with the remaining revenue received upon delivery. Since the optimal policy structure is rather complex and defined by switching surfaces in a multidimensional space, a simple heuristic policy is proposed for which the computational load grows linearly with the number of products and its performance is tested under a variety of example problems.

[1]  Kaj Rosling,et al.  Optimal Inventory Policies for Assembly Systems Under Random Demands , 1989, Oper. Res..

[2]  Jing-Sheng Song,et al.  Supply Chain Operations: Assemble-to-Order Systems , 2003, Supply Chain Management.

[3]  Yigal Gerchak,et al.  Component commonality in assemble-to-order systems: Models and properties , 1989 .

[4]  Roy Billinton,et al.  Reliability evaluation of engineering systems : concepts and techniques , 1992 .

[5]  Saif Benjaafar,et al.  Optimal Control of an Assembly System with Multiple Stages and Multiple Demand Classes , 2010 .

[6]  Jr. Shaler Stidham.  Optimal control of admission to a queueing system , 1985 .

[7]  Lawrence M. Wein,et al.  Optimal Control of a Two-Station Tandem Production/Inventory System , 1994, Oper. Res..

[8]  N. Agrawal,et al.  Winning in the aftermarket , 2006 .

[9]  U. Rieder,et al.  Markov Decision Processes , 2010 .

[10]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[11]  Erica L. Plambeck,et al.  A Separation Principle for Assemble-to-Order Systems with Expediting , 2003 .

[12]  Steven A. Lippman,et al.  Applying a New Device in the Optimization of Exponential Queuing Systems , 1975, Oper. Res..

[13]  Bin Liu,et al.  Order-Fulfillment Performance Measures in an Assemble-to-Order System with Stochastic Leadtimes , 1999, Oper. Res..

[14]  Albert Y. Ha.  Optimal Dynamic Scheduling Policy for a Make-To-Stock Production System , 1997, Oper. Res..

[15]  Izak Duenyas,et al.  Optimal Admission Control and Sequencing in a Make-to-Stock/Make-to-Order Production System , 2000, Oper. Res..

[16]  Albert Y. Ha.  Inventory rationing in a make-to-stock production system with several demand classes and lost sales , 1997 .

[17]  Chung-Yee Lee,et al.  Technical Note - Optimal Control of an Assembly System with Multiple Stages and Multiple Demand Classes , 2011, Oper. Res..

[18]  Cheng-Yuan Ku,et al.  Access control to two multiserver loss queues in series , 1997 .

[19]  Hau L. Lee,et al.  Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies , 1998, Eur. J. Oper. Res..

[20]  Jing-Sheng Song,et al.  Chapter 11 ∗ Supply Chain Operations: Assemble-to-Order Systems , 2003 .

[21]  Steven Nahmias,et al.  Optimal Policy for a Two-Stage Assembly System under Random Demand , 1985, Oper. Res..

[22]  Scott Jordan,et al.  Access control of parallel multiserver loss queues , 2002, Perform. Evaluation.

[23]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

[24]  Saif Benjaafar,et al.  Production and Inventory Control of a Single Product Assemble-to-Order Systems with Multiple Customer Classes , 2006, Manag. Sci..

[25]  Shaler Stidham,et al.  Control of arrivals to two queues in series , 1985 .

[26]  Ger Koole,et al.  Monotonicity in Markov Reward and Decision Chains: Theory and Applications , 2007, Found. Trends Stoch. Syst..

[27]  Susan H. Xu,et al.  Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System , 2004, Manag. Sci..