Three-stage supply chain allocation with fixed cost

Purpose - The purpose of this paper is of two-fold. First, the authors propose the application of genetic algorithm (GA)-based heuristic for solving a distribution allocation problem for a three-stage supply chain with fixed cost. Second, a methodology for parameter design in GA is discussed which can lead to better performance of the algorithm. Design/methodology/approach - A mathematical model is formulated as an integer-programming problem. The model is solved using GA-based heuristic and illustrated with a numerical example. An investigation is made for determining the best combination of the parameters of GA using factorial design procedure. Findings - The optimum population size for the selected problem size is found to be 100. The mutation probability for a better solution is 0.30. The objective function value at the above mentioned levels is better than that obtained at the other combinations. Research limitations/implications - This work provides a good insight about the fixed cost transportation problem (FCTP) in a three-stage supply chain and design of numerical parameters for GA. The model developed assumes a single product environment in a single period. Hence, the present study can be extended to a multi-product, multi-period, and varying demand environment. In the parameter design, three distinct numerical parameters are considered. The parameters, population size and mutation probability are set at four levels and the parameter, crossover probability is set at three levels. More levels can be selected so that more combinations can be experimented. Originality/value - The paper presents the formulation and solution of a distribution-allocation problem in a three-stage supply chain with fixed cost for a transportation route.