A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints

This paper develops a multiproduct economic production quantity inventory model for a vendor–buyer system in which several products are manufactured on a single machine. The vendor delivers the products to customer in small batches. The number of orders must be a discrete value. Moreover, benefitting from a just-in-time policy, the buyer decides the size of the delivered batches. Due to the fact that several products are manufactured on one machine, this makes that the production capacity be considered as a constraint. The aim of this study is to determine the optimal cycle length and the number of delivered batches for each product so that the total inventory cost is minimized. The problem under study is modeled as a mixed integer nonlinear programing problem considering maximum number of orders, capacity and budget constraints. Three different methods are developed and employed to solve this problem: an exact method, a heuristic algorithm and a hybrid genetic algorithm. Based on the results, the three algorithms have near efficiency with different running times. The results shows that the heuristic algorithm obtains a good solution in a short time and the hybrid genetic algorithm finds solutions with higher quality in an acceptable time. Finally, a sensitivity analysis is done to evaluate the effect of changes in the parameters of problem.