Production and distribution planning, scheduling and routing problem in a yogurt supply chain under robust fuzzy uncertainty: a case study

Abstract

Regarding the gradual evolution of the food industry and all challenges it faces, like the high perishability of the product, managing the food industry supply chain has become an attractive issue for researchers and decision-makers. Over time the integration of uncertain aspects has continuously gained importance for managerial decision-making. Among these, the industry of yogurt products is one of the most challenging industries. In this study, we investigate the problem of production and distribution planning, scheduling, and routing in the yogurt industry supply chain network. The problem is a multi-product, single plant, multi-distribution center, multi-period, and multi-transportation track. A mixed-integer non- linear programming (MINLP) model is presented to minimize the total costs, including production, setup, overtime, unmet demand, and transportation. Besides, a robust fuzzy programming approach is applied to the problem under uncertainty. A meta-heuristic approach based on the Genetic algorithm was developed to solve the problem. In addition, the required modifications to make GA applicable are the problem mentioned. Tested experiments indicate that the proposed algorithm has an average gap of less than 0.4 percent from the optimal solution within a reasonable time. A real-world case is considered, and the proposed GA method compared to CPLEX and the results show the effectiveness of the model and the average objective function had approximately a 10% improvement.