Development of a two-level trade credit model with shortage for deteriorating products using hybrid metaheuristic algorithm

In the classical inventory systems, it was implicitly assumed that the buyer pays to the vendor at the time of receiving the items. In real world, however, the vendor usually allows the buyer to defer payment. Among different types of delay in payment, trade credit has attracted many researches’ attention and still has great potential for further studies. For example, most of the previous studies have considered constant demand, while the demand in real market is dependent to several factors such as price, time, inventory, etc. Besides, for simplicity in modelling and solving, the researchers often ignore shortage and deterioration rate which are parts and parcels of today’s business. Two-level trade credit is another potential area for exploration. It is referred to the case that not only the vendor offers credit period to the buyer, but also the buyer allows its customers to delay payment. Furthermore, most of the previous studies have considered Economic Order Quantity (EOQ) model of a single member of the supply chain. However, assuming the Economic Production Quantity (EPQ) and formulating the integrated inventory system of the buyer and the vendor would be more practical. Considering these possibilities, this research develops a new inventory model for a supplier and a manufacturer under a two-level trade credit contract. The market demand is considered price dependent, and backorder and deterioration are also assumed. Moreover, the traditional inventory model and one-level trade credit are developed to make a comparison of the results and investigate the effects of delay in payment on the inventory system. The formulated models aim at helping the supply chain decision makers to determine the best delay strategy and find the optimal values for replenishment policy and manufacturer’s selling price, with the objective of maximising the supply chain total net profit. A hybrid metaheuristic algorithm which combines Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm, is then developed to solve the established models. In order to evaluate the solutions of the hybrid algorithm, the models are also solved by a global optimization solver,Branch-And-Reduce Optimization Navigator (BARON). Furthermore, the models and the solution methods are verified by applying numerical examples and real data from industry. The results of the proposed inventory systems are finally compared to explore the effects of trade credit on the supply chain net profit and the variables’ sensitivity to the parameters are analysed. The examples demonstrate that although two-level trade credit is mostly more profitable for the supply chain and the manufacturer, the supplier benefits from a traditional supply chain. Besides, having obtained a p-value of 0.241 which is greater than 0.05 in a paired sample t-test shows that there is no difference between the results of BARON and the hybrid GA-PSO. This proves the capability of the developed hybrid algorithm in solving the formulated model.

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