Advanced backtracking search optimization algorithm for a new joint replenishment problem under trade credit with grouping constraint

In the real business situation, suppliers usually provide retailers with forward financing to decrease inventory or increase demand. Moreover, some heterogeneous goods are not allowed to transport together, or a penalty cost is incurred when heterogeneous goods are transported at the same time. This research proposes a practical multi-item joint replenishment problem (JRP) by considering trade credit and grouping constraint in accordance with the practical situation. The JRP aims to find reasonable item replenishment frequencies and each group's basic replenishment cycle time so that the overall cost can be minimized. Four intelligent algorithms, which include an advanced backtracking search optimization algorithm (ABSA), genetic algorithm (GA), differential evolution (DE) and backtracking search optimization algorithm (BSA), are provided to solve this problem. Findings of contrastive example verify that ABSA is superior to GA, DE, and BSA, which have been validated to be effective algorithms. Randomly generated problems are used to test the performance of ABSA. Results indicate ABSA is more effective and stable to resolve the proposed JRP than the other algorithms. ABSA is a good solution for the proposed JRP with heterogeneous items under trade credits.