Joint determination of the lot size and number of shipments for a family of integrated vendor–buyer systems considering defective products

In this paper we present two solution procedures to obtain the solution for a family of economic production quantity inventory models for an integrated vendor–buyer system considering that production system generates defective products, in which the number of shipments must be a discrete value and that the lot size can take continuous (case 1) or integer (case 2) values. These solution procedures provide a more realistic approach for solving a family of inventory models. Previous works only derive the optimal lot size considering the number of shipments as a given value or derive both the lot size and the number of shipments considering both decision variables as continuous. The number of shipments takes integer values in real life and thus it must be considered as a discrete variable. This paper revisits and solves previous inventory models considering the variables (lot size and number of shipments) according to their real-life nature.

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