Abstract: Out-of-stock situations are inevitable in the multi-product joint inventory replenishment of retail commodities. Customers have several different responses to stock-out, such as abandoning purchase, delaying purchase or buying alternatives. Customer Response to Stock-out (CRS) differs among different product categories, which has a great impact on the inventory control of commodities and their alternatives. The single set of out-of-stock item and its substitute under multi-constraint is investigated, and various models have been explored in joint replenishment by prior empirical studies. However, the seemingly contradictory findings from the related studies indicate that there can be multiple sets in joint replenishment, which is still under-explored in extant literature. Moreover, there still exists irrational use of resources that some items can't satisfy the demand while others have surplus supplies. There is a lack of research into multi-item two-stage JIT joint replenishment considering comprehensive utilization of resources and maximization of revenue.
In the view of these, the research is extended into a two-stage JIT joint replenishment of retail commodities from two aspects, taking the impact of CRS and resource restrictions on ordering decisions into account. First, the joint order strategy under the resource restriction condition is suggested according to the JIT inventory principle. Second, the product group is extended from one group to multiple groups in accord with CRS rule. On this basis, a multi-product two-stage JIT joint replenishment model considering CRS is established with the goal of maximizing the retailer's revenue. According to the characteristics of the above model, the imperialist competition algorithm (ICA) is improved in terms of initial solution generation and revolution mode of colonial countries, to obtain the approximate optimal solution more quickly. A total of 9 groups of 18 products are selected from the Gruen survey report, and the model and the solutionare verified by numerical examples in three scales:scale 1 (small:including 6 kinds of products), scale 2 (medium:including 12 kinds of products) and scale 3 (large:including 18 kinds of products).
The results show that compared with the ordering method without considering CRS, the multi-product two-stage JIT combined ordering method with CRS consideration can not only improve the retailer's total revenue, but also improve the customer's service level. The results also show that the unit resource opportunity income and the unit residual resource opportunity income are the main factors to decide how to allocate resources effectively. If the opportunity benefits of unit inventory resource in peer group are approximate each other, no replacement would be made in peer group. While, if the opportunity benefits of unit inventory resource in peer group vary significantly and are higher than those in other groups, substitution and stock-out would be shown in the group. More specifically, if the opportunity benefits of unit surplus resource are lower than the opportunity benefits of unit resource in other groups, the surplus resources of the product would be transferred to other out-of-stock products. The findings of the research could provide references to the decision making of multi-item/two-stage JIT joint replenishment for retailers.

Key words: customer response to stock-out, multi-item/two-stage, JIT joint replenishment, product substitution, improved imperialist competitive algorithm