A binary-continuous invasive weed optimization algorithm for a vendor selection problem

This paper introduces a novel and practical vendor selection problem of a firm that cooperates with multiple geographically dispersed stores. In this problem, the firm entrusts some of its business process to external vendors, and each store can split the ordered quantity between one or more potential vendors, represented as a multi-sourcing strategies. Moreover, the Cobb-Douglas demand function is utilised to establish a relationship between the market demand and the selling price; representing price-sensitive demand. This paper seeks to choose the best vendors, to allocate the stores to them, and to find the optimal values for inventory-related decisions. The approach is based on the integration of the vendor selection problem and the inventory-related decisions in order to generate additional opportunities for system-wide operational efficiency and cost-effectiveness. The aim is to minimise total cost of the firm consisting of costs associated with the vendor selection and inventory-related decisions. A novel meta-heuristic called the binary-continuous invasive weed optimization (BCIWO) algorithm that is capable of solving both binary and continuous optimization problems is developed to solve the complicated NP-hard problem. As there is no benchmark available in the literature, an efficient genetic algorithm enhanced by a multi-parent crossover operator is designed to solve the problem in order to validate the results obtained using BCIWO. The algorithms are tuned using the response surface methodology, based on which their performances are analyzed statistically. Finally, the applicability of the proposed approach and the solution methodologies are demonstrated.