Development of a joint economic lot size model with stochastic demand within non-equal shipments

The majority of the studies on the integrated vendor-buyer inventory problem assume that the shipments are equal. in this paper, shipments are considered to be nonequal. both demand and delivery times are also assumed to be stochastic. moreover, unsatisfied demand can be back ordered and lost, and a service level constraint is considered. the objective is to minimize both buyer and vendor costs at the same time. the problem is solved by an exact heuristic algorithm. to validate performance of the algorithm, the results are compared with those of the lingo solver. finally, a set of numerical problems are applied to compare the results in the integrated and independent forms.