A profit-maximizing economic lot scheduling problem with price optimization

The economic lot scheduling problem (ELSP) is a well known problem that focuses on scheduling the production of multiple items on a single machine such that inventory and setup costs are minimized. In this paper, we extend the ELSP to include price optimization with the objective to maximize profits. A solution approach based on column generation is provided and shown to produce very close to optimal results with short solution times on a set of test problems. The results are discussed and recommendations for further research are provided.

[1]  S. Yakowitz,et al.  An Introduction to Numerical Computations , 1986 .

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

[3]  M. J. Rosenblatt,et al.  Improving Profitability with Quantity Discounts under Fixed Demand , 1985 .

[4]  Ming-Jong Yao,et al.  Solving the economic lot scheduling problem with deteriorating items using genetic algorithms , 2005 .

[5]  Alan S. Manne,et al.  Programming of Economic Lot Sizes , 1958 .

[6]  R. W. Haessler.  An Improved Extended Basic Period Procedure for Solving the Economic Lot Scheduling Problem , 1979 .

[7]  William W. Trigeiro,et al.  Capacitated lot sizing with setup times , 1989 .

[8]  Robin O. Roundy,et al.  Rounding Off to Powers of Two in Continuous Relaxations of Capacitated Lot Sizing Problems , 1989 .

[9]  P. Kotler.  Marketing Decision Making: A Model-building Approach , 1971 .

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

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

[12]  J. G. Madigan,et al.  Scheduling a Multi-Product Single Machine System for an Infinite Planning Period , 1968 .

[13]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[14]  Timothy L. Urban.  Deterministic inventory models incorporating marketing decisions , 1992 .

[15]  Bret J. Wagner,et al.  A search heuristic for the sequence-dependent economic lot scheduling problem , 2002, Eur. J. Oper. Res..

[16]  Seyed Jafar Sadjadi,et al.  Optimal Production and Marketing Planning , 2005, Comput. Optim. Appl..

[17]  Earl E. Bomberger,et al.  A Dynamic Programming Approach to a Lot Size Scheduling Problem , 1966 .

[18]  Avijit Banerjee,et al.  Concurrent pricing and lot sizing for make-to-order contract production , 2005 .

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

[20]  James P. Monahan.  A Quantity Discount Pricing Model to Increase Vendor Profits , 1984 .

[21]  Jack D. Rogers.  A Computational Approach to the Economic Lot Scheduling Problem , 1958 .

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

[23]  Stephen A. Smith,et al.  Clearance Pricing and Inventory Policies for Retail Chains , 1998 .

[24]  Dong X. Shaw,et al.  Complexity of the ELSP with general cyclic schedules , 1997 .

[25]  Gary C. Lin,et al.  Determining a common production cycle time for an economic lot scheduling problem with deteriorating items , 2006, Eur. J. Oper. Res..

[26]  Bala Shetty,et al.  A Model for Resource Constrained Production and Inventory Management , 1994 .

[27]  J. Richard,et al.  Optimal pricing and inventory decisions for non-seasonal items , 1971 .

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

[29]  Ping-Teng Chang,et al.  A genetic algorithm for solving a fuzzy economic lot-size scheduling problem , 2006 .

[30]  Kjetil K. Haugen,et al.  The profit maximizing capacitated lot-size (PCLSP) problem , 2007, Eur. J. Oper. Res..

[31]  S. Ladany,et al.  The Interaction of Economic Ordering Quantities and Marketing Policies , 1974 .

[32]  Edward A. Silver,et al.  Finding effective schedules for the economic lot scheduling problem: A simple mixed integer programming approach , 2004 .

[33]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[34]  S. P. Ladany.  Optimal market segmentation of hotel rooms—the non-linear case , 1996 .

[35]  Won J. Lee.  Determining Order Quantity and Selling Price by Geometric Programming: Optimal Solution, Bounds, and Sensitivity* , 1993 .

[36]  S. Graves.  Note---On the Deterministic Demand Multi-Product Single-Machine Lot Scheduling Problem , 1979 .

[37]  T. M. Whitin.  Inventory Control and Price Theory , 1955 .

[38]  P. Abad.  Joint Price and Lot-Size Determination When Supplier Offers Incremental Quantity Discounts , 1988 .

[39]  Prakash L. Abad,et al.  Determining Optimal Selling Price and Lot Size When the Supplier Offers All‐Unit Quantity Discounts* , 1988 .

[40]  DaeSoo Kim,et al.  Optimal joint pricing and lot sizing with fixed and variable capacity , 1998, Eur. J. Oper. Res..