The Economic Lot Scheduling Problem (ELSP): Review and Extensions

The ELSP is a time-honored problem that "has been around" since 1915. It is the problem of accommodating cyclical production patterns when several products are made on a single facility. Recent contributions to its resolution resulted in either analytical approaches to a restricted problem, or heuristic approaches to the entire problem. This paper reviews critically the various contributions to the problem, and extends the analysis in the following four directions: (a) An improved analytical approach, (b) A test for feasibility, (c) A systematic means for escape from infeasibility, and (d) A procedure for the determination of a basic period for a given set of multipliers to achieve a feasible schedule.

[1]  S. Eilon Economic Batch-Size Determination for Multi-Product Scheduling , 1959 .

[2]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[3]  J. H. Krone A Note on Economic Lot Sizes for Multi-Purpose Equipment , 1964 .

[4]  William L. Maxwell,et al.  The scheduling of economic lot sizes , 1964 .

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

[6]  William Beranek,et al.  Financial Implications of Lot-Size Inventory Models , 1967 .

[7]  Salah E. Elmaghraby The machine sequencing problem – review and extensions , 1968 .

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

[9]  Kenneth R. Baker Note---On Madigan's Approach to the Deterministic Multi-Product Production and Inventory Problem , 1970 .

[10]  Thom J. Hodgson,et al.  Addendum to Stankard and Gupta's Note on Lot Size Scheduling , 1970 .

[11]  Robert W. Haessler Letter to the Editor—A Note on Scheduling a Multi-Product Single Machine System for an Infinite Planning Period , 1971 .

[12]  S. K. Goyal Scheduling a Multi-Product Single Machine System , 1973 .

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

[14]  L. Zurich,et al.  Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[15]  George L. Adler,et al.  The Effects of Learning on Optimal Lot Size Determination—Multiple Product Case , 1974 .

[16]  Hamdy A. Taha,et al.  Integer Programming: Theory, Applications, and Computations , 1975 .

[17]  E. Newson Multi-Item Lot Size Scheduling by Heuristic Part I: With Fixed Resources , 1975 .

[18]  Robert F. Williams Note---A Dominance Relation in Dynamic Lot Sizing , 1975 .

[19]  S. K. Goyal Scheduling a multi-product single machine system A new approach , 1975 .

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