Extensions of the Planning Horizon Theorem in the Dynamic Lot Size Model

Abstract

This paper considers an N period production planning problem in which a sequence of known demands d 1, d 2,..., d N must be satisfied. The cost of production in period t consists of a setup cost K t plus a marginal cost per unit c t. The cost of carrying a unit of inventory into period t is h t - 1 . An optimal policy is a production plan that satisfies demand at minimum cost. The main results of the paper are a theorem that decreases the computational effort required to find optimal policies and a theorem that establishes the existence of planning horizons. The results of these two theorems are combined in a forward algorithm for the efficient solution of the problem.

Facets and algorithms for capacitated lot sizing

“…Zangwill (1966), who extended the results of Wagner and Whitin to allow backordering of demand, also introduced a network representation of the problem (1969). Zabel (1964) and Eppen, Gould and Pashigian (1969) improved the planning horizon results of Wagner and Whitin. Zangwill (1969) and Kalymon (1970) extended the results to include multiple facilities.…”

Single item lot sizing problems

“…The problem was also studied by Zabel [109], Eppen et al [30] and Lundin and Morton [67]. However, their implementations did not improve the complexity of the WW algorithm.…”

The sensitivity of set-up cost estimation on the problem of joint lot sizing and scheduling

“…In step 1, the sequence-independent set-up costs are estimated using the ISCE. For example, if the AVE ISCE is used, the initial set-up cost for item i in period t would be In step 2, using the estimated set-up costs, the solution to the lot-sizing problem is determined using the extension to the Wagner-Whitin algorithm developed by Eppen et al (1969). With lot sizes determined, step 3 finds the solution to the scheduling problem by using a branch-and-bound mixed integer program.…”