A sustainable production inventory model for growing items with trade credit policy under partial backlogging

Abstract

Most countries rely on the growth of commodity industries to sustain their economies. The growing commodity industries produce livestock such as sheep, pigs, chickens, and fish. The purpose of this paper is to develop a mathematical model for growing items with linear demand and deteriorating items. Most of the inventory models are considered with constant rate of deterioration. The paper explores deterioration rates changing with time and partially backlog shortages allowed. Furthermore, it is assumed that live newborn items are fed until their weight has grown to a customer-preferred level during breeding periods. Afterward, they are slaughtered and turned into deteriorating products susceptible to customer demand during consumption. This model is optimised by devising an analytical solution procedure to determine the appropriate purchasing quantity of the newborn animals and the breeding period. Numerical examples are provided, for a type of poultry, to illustrate the model. To study how model parameters affect the result of the objective function and decision variables, we do a sensitivity analysis.