Abstract: A generalized economic production quantity model with deteriorating items over a finite planning horizon is considered in this paper. The unit production cost, the production rate and the demand rate are assumed to be known and continuous functions of time, and the forgetting effect of setup cost is incorporated into the problem. Shortages are not allowed in this model. A mixed-integer constraint optimization mathematical model in which the objective is to minimize the total cost is established and the conditions of the optimal solution for this problem are derived. A discrete variable in the total cost function is relaxed to the continuous variable and this technique is used to prove the uniqueness and optimality of the optimal solution for a special case. In addition, the optimal solution of the special case is regarded as the initial condition to simplify the search process of finding the optimal solution of the generalized problem. Finally, a numerical example is provided to illustrate the results.

Key words: operations research, inventory model, convex function, deterioration, time-varying cost