Quasi-fixed cyclic production schemes for multiple products with stochastic demand

In this paper we present an approach to generate cyclic production schemes for multiple products with stochastic demand to be produced on a single production unit. This scheme specifies a fixed and periodic production sequence, called a cycle, where each product may occur more than once in the sequence. In order to stabilize the cycle length alternative control strategies are introduced. These strategies keep the cycle length close to a target length by means of adding idle time to the cycle, cutting production short or overproduction. On basis of the selected control strategy as well as a base-stock policy target inventory levels are determined for each production run in the cycle. Demand can be backlogged but a certain service level is required. Setup times are sequence-dependent and the storage is capacitated. Employing the developed strategies we investigate the tradeoff between stability of cycle length and total cost induced by the production schedule in a computational study based on both, real world data and random test instances.

[1]  Tayfur Altiok,et al.  Pull-type manufacturing systems with multiple product types , 2000 .

[2]  G. Gallego.  Scheduling the production of several items with random demands in a single facility , 1990 .

[3]  Timothy S. Vaughan,et al.  The effect of correlated demand on the cyclical scheduling system , 2003 .

[4]  Paul H. Zipkin.  Computing Optimal Lot Sizes in the Economic Lot Scheduling Problem , 1991, Oper. Res..

[5]  Hanoch Levy,et al.  Efficient Visit Orders for Polling Systems , 1993, Perform. Evaluation.

[6]  W. Hsu.  On the General Feasibility Test of Scheduling Lot Sizes for Several Products on One Machine , 1983 .

[7]  Awi Federgruen,et al.  Determining Production Schedules Under Base-Stock Policies in Single Facility Multi-Item Production Systems , 1998, Oper. Res..

[8]  Timothy S. Vaughan,et al.  Cyclical schedules vs. dynamic sequencing: Replenishment dynamics and inventory efficiency , 2007 .

[9]  Gregory Dobson,et al.  The Economic Lot-Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes , 1987, Oper. Res..

[10]  Richard Loulou,et al.  Multiproduct production/inventory control under random demands , 1995, IEEE Trans. Autom. Control..

[11]  Stefan Minner,et al.  Simulation optimization for the stochastic economic lot scheduling problem with sequence-dependent setup times , 2014 .

[12]  Ivo J. B. F. Adan,et al.  The stochastic economic lot scheduling problem: A survey , 2011, Eur. J. Oper. Res..

[13]  Stefan Minner,et al.  Simulation optimization for the stochastic economic lot scheduling problem , 2013 .

[14]  M Michael Wagner,et al.  A local search algorithm for the optimization of the stochastic economic lot scheduling problem , 2004 .

[15]  Paul H. Zipkin,et al.  Models for Design and Control of Stochastic, Multi-Item Batch Production Systems , 1986, Oper. Res..

[16]  V. Sridharan,et al.  A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands , 1995 .

[17]  Yves Dallery,et al.  Analysis of order-up-to-level inventory systems with compound Poisson demand , 2010, Eur. J. Oper. Res..

[18]  A. Federgruen,et al.  The stochastic Economic Lot Scheduling Problem: cyclical base-stock policies with idle times , 1996 .

[19]  S. Elmaghraby.  The Economic Lot Scheduling Problem (ELSP): Review and Extensions , 1978 .

[20]  Robert W. Haessler,et al.  Note---A Note on the Single-Machine Multi-Product Lot Scheduling Problem , 1976 .

[21]  Alon Itai,et al.  A golden ratio control policy for a multiple-access channel , 1984 .

[22]  C. R. Sox,et al.  Optimization-based planning for the stochastic lot-scheduling problem , 1997 .

[23]  Peter Köchel,et al.  Simulation-based sequencing and lot size optimisation for a production-and-inventory system with multiple items , 2006 .

[24]  Ludo Gelders,et al.  Production planning: a review , 1981 .

[25]  C. Yano,et al.  The strategic use of capacity slack in the economic lot scheduling problem with random demand , 1994 .

[26]  James A. Rappold,et al.  Setting safety stocks for stable rotation cycle schedules , 2014 .

[27]  Robert W. Hall.  Cyclic scheduling for improvement , 1988 .

[28]  C L Doll,et al.  AN ITERATIVE PROCEDURE FOR THE SINGLE-MACHINE, MULTI-PRODUCT LOT SCHEDULING PROBLEM : A WORKING PAPER , 1973 .

[29]  Salah E. Elmaghraby,et al.  The economic lot scheduling problem under power-of-two policy , 2001 .

[30]  Pär Brander,et al.  Determination of safety stocks for cyclic schedules with stochastic demands , 2006 .

[31]  Timothy S. Vaughan.  Alternative control mechanisms for cyclical scheduling systems , 2009 .