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

In the present article, a production-inventory model is developedover an infinite plan ning horizon where the demand varies linearlywith time, unit production cost is taken as a function of theproduction rate, and shortages in inventory are permitted andare fully back-ordered. The machine production rate, which isassumed to be flexible, is treated as a decision variable. Theassociated nonlinear programming problem is modified by usingthe barrier-function method, and then a search technique isused to find the solution numerically. The analysis of the presentmodel of the production system points to optimality under conditionsthat are commonly recognized as ‘just in time’.