A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements

In a supply chain, it is an important issue for logistic managers to offset the replenishment cycles of multiple products sharing a warehouse so as to minimize the maximum warehouse space requirement (MWSR). Most of the studies in the literature assume that warehouses replenish at the beginning of some basic planning period. In this paper, we relax this assumption by allowing the warehouse to replenish at any time. In order to solve this problem, we conduct theoretical analysis based on Fourier series and Fourier transforms and propose a procedure that is used to calculate MWSR efficiently for any given replenishment schedule. Then, we employ this procedure in a genetic algorithm (GA) to search for the optimal replenishment schedule. Using randomly generated instances, we show that the proposed GA significantly outperforms a previously published heuristic.

[1]  Kyung S. Park,et al.  Optimal Scheduling of Periodic Activities , 1985 .

[2]  Sungjune Park,et al.  Optimal lot sizing under continuous price decrease , 2003 .

[3]  Salah E. Elmaghraby,et al.  ON THE FEASIBILITY TESTING OF THE ECONOMIC LOT SCHEDULING PROBLEM USING THE EXTENDED BASIC PERIOD APPROACH , 2003 .

[4]  R. Paul,et al.  Multi-Product Inventory Situations with One Restriction , 1976 .

[5]  K. Zoller.  Deterministic Multi-Item Inventory Systems with Limited Capacity , 1977 .

[6]  Weng-Ming Chu,et al.  Determination of replenishment dates for restricted-storage, static demand, cyclic replenishment schedule , 2008, Comput. Oper. Res..

[7]  Kyung S. Park,et al.  Technical Note - Optimal Scheduling of Periodic Activities , 1985, Oper. Res..

[8]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[9]  Barry L. Nelson,et al.  A framework for simulation-optimization software , 2003 .

[10]  Ming-Jong Yao,et al.  The peak load minimization problem in cyclic production , 2001, Comput. Oper. Res..

[11]  Ruud H. Teunter.  A note on “Khouja and Park, optimal lot sizing under continuous price decrease, Omega 31 (2003)” , 2005 .

[12]  Jonas C. P. Yu,et al.  Optimal inventory model for items with imperfect quality and shortage backordering , 2007 .

[13]  Raymond G. Vickson,et al.  WRLSP: A Single-Machine, Warehouse Restricted Lot Scheduling Problem , 1988 .

[14]  R. K. Wangsness.  Electromagnetic fields , 1979 .

[15]  W. C. Benton,et al.  Offsetting inventory cycles of items sharing storage , 2003, Eur. J. Oper. Res..

[16]  Nicholas G. Hall.  A multi-item EOQ model with inventory cycle balancing , 1988 .

[17]  F. W. Kellaway,et al.  Advanced Engineering Mathematics , 1969, The Mathematical Gazette.

[18]  Roger Hartley,et al.  An Algorithm for Limited Capacity Inventory Problem with Staggering , 1983 .