ON THE (T,SJ) POLICY IN AN INTEGRATED PRODUCTION INVENTORY MODEL WITH TIME-PROPORTIONAL DEMAND

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 that is not always the case.