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

In this paper, the authors 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. They analyze a (t,Sj) ordering policy for the production of the end product, where at every equal and fixed scheduling cycle, t, a variable production quantity, Sj, is produced during the j-th cycle. With the objective of minimizing the integrated total relevant cost, the authors formulate a mathematical programming problem to determine simultaneously the economic batch sizes for the end product and the economic order sizes for the raw A heuristic is developed using the Lagrangian multiplier, and its solution compares very well with the exact solution. The authors compare the numerical results with the equal batch sizing policy, i.e., the (s,Q) policy, which is expected to be outperfromed by the (t,Sj) policy, and find that that is not always the case.