A two-warehouse inventory model for deteriorating items with partially backlogged demand rate under trade credit policies

This work presents a two-storage inventory model developed considering the effect of deterioration of items, partial advanced payment and two-level trade credit financing policies ignoring the relationship between the credit periods offered for retailers as well as customers by the supplier and retailer respectively. Here, demand is dependent on freshness period of the items, credit period (offered by the retailer) of customers and item’s selling price. Here, shortages are permitted with partially backlogged. According to the length of credit period for retailer, three scenarios are investigated. Then these scenarios are discussed in details and the corresponding models are formulated with the objectives to determine the optimal policy by optimizing the average profit of each scenario subject to some constraints. The corresponding optimization problems of different scenarios are non-linear in nature and those problems are solved with the help of differential evolution (DE) algorithm and other eight existing metaheuristic algorithms. To validate the model, three numerical examples are considered and solved. The results obtained from DE algorithm are compared statistically with that of other algorithms. For justification of the comparison and also the verification of the statistical significance of DE algorithm, two different tests, viz. Friedman and analysis of variance (ANOVA) tests are carried out for the numerical examples. Finally, sensitivity analyses are conducted and the effects of different system parameters on best found (optimal) policy are presented graphically.