On the ( t, Sj) policy in an integrated production/inventory model with time-proportional demand

Abstract

In this paper, we consider a two-level continuous time lotsizing problem with setup costs, inventory holding costs and time-proportional demand for a single end product and the raw materials used for manufacturing it. We analyze a ( t, S j ) ordering policy for the production of the end product, where at every equal and fixed scheduling cycle, t, a variable production quantity, S j , is produced during the j-th cycle. With the objective of minimizing the integrated total relevant cost, we formulate a mathematical programming problem to determine simultaneously the economic batch sizes for the end product and the economic order sizes for the raw materials. A heuristic is developed using the Lagrangian multiplier, and its solution compares very well with the exact solution. We compare the numerical results with the equal batch sizing policy, i.e., the ( s, Q) policy, which is expected to be outperformed by the ( t, S j ) policy, and find that is not always the case.