An economic production lot-size model with shortages and time-dependent demand

In the present article, a production–inventory mode is developed over an infinite planning horizon where the demand varies linearly with time, unit production cost is taken as a function of the production rate, and shortages in inventory are permitted and are fully back-ordered. The machine production rate, which is assumed to be flexible, is treated as a decision variable. The associated nonlinear programming problem is modified by using the barrier-function method, and then a search technique is used to find the solution numerically. The analysis of the present model of the production system points to optimality under conditions that are commonly recognized as ‘just in time’.