A solution to the multiple set-up problem with dynamic demand

Abstract In this note, we study an important practical problem, the classic dynamic lot size model with set-up cost including a fixed cost and freight cost, where the freight cost is proportional to the number of containers used. This freight cost is the additional multiple set-up cost. We solve the T-period problem in O(T44) effort using dynamic programming, Handled by the Editor-in-Chief.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  W. Zangwill.  A Deterministic Multi-Period Production Scheduling Model with Backlogging , 1966 .

[3]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[4]  Matthew J. Sobel,et al.  Smoothing Start-Up and Shut-Down Costs: Concave Case , 1970 .

[5]  Steven A. Lippman.  Economic Order Quantities and Multiple Set-Up Costs , 1971 .

[6]  Stephen F. Love.  Bounded Production and Inventory Models with Piecewise Concave Costs , 1973 .

[7]  C. Swoveland.  A Deterministic Multi-Period Production Planning Model with Piecewise Concave Production and Holding-Backorder Costs , 1975 .

[8]  K. R. Baker,et al.  An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints , 1978 .

[9]  Katarzyna Iwaniec.  An Inventory Model with Full Load Ordering , 1979 .

[10]  J. K. Lenstra,et al.  Deterministic Production Planning: Algorithms and Complexity , 1980 .

[11]  Donald C. Aucamp.  Nonlinear freight costs in the EOQ problem , 1982 .

[12]  Hanan Luss,et al.  Production planning with time-dependent capacity bounds , 1982 .

[13]  Donald C. Aucamp,et al.  A solution to the multiple set-up problem , 1984 .

[14]  Gabriel R. Bitran,et al.  Approximation Methods for the Uncapacitated Dynamic Lot Size Problem , 1984 .

[15]  Chung-Yee Lee,et al.  The Economic Order Quantity for Freight Discount Costs , 1986 .

[16]  A. Federgruen,et al.  The dynamic lot size model with quantity discount , 1990 .