Soft time-windows for a bi-objective vendor selection problem under a multi-sourcing strategy: Binary-continuous differential evolution

• A bi-objective vendor selection problem with inventory-related decisions is modeled.
• A soft time-window mechanism and a multi-sourcing strategy are studied.
• The objectives are minimization of the total cost and delivery schedule violation.
• A trade-off between the proposed objectives is established.
• A binary-continuous differential evolution is developed.

This paper introduces a novel and practical integration of the inventory control and vendor selection problems for a manufacturing system that provides multiple products for several stores located in different places. The replenishment policy of each store is the economic order quantity under a multi-sourcing strategy in which the demand rate decreases as the selling price increases. In this strategy, the ordered quantity of each store for each product can be replenished by a set of selected vendors among all. In addition, the selected vendors can deliver the required products within a certain time window based on a soft time-window mechanism. The aim is to minimize the total system cost and delivery schedule violations, simultaneously. A trade-off between the two objectives is generated using the min–max approach to obtain near fair non-dominated solutions. As the problem is known to be NP-hard, a novel meta-heuristic algorithm called binary-continuous differential evolution (BCDE) is developed to make the original differential evolution capable of solving both binary and continuous optimization problems. Moreover, an improved genetic algorithm with a multi-parent crossover operator is designed to solve the problem. While the applicability of the proposed approach and the solution methodologies are demonstrated, the solution algorithms are tuned and their performances are analyzed and compared statistically. Finally, sensitivity analyses on the size of the soft time-window and the bandwidth factor of the BCDE algorithm are conducted.

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