A three level joint location-inventory problem with correlated demand, shortages and periodic review system: Robust meta-heuristics

•Considering a three-echelon location-inventory problem with correlated demand.•Proposing a new coordinated location-inventory model with shortages and periodic review system.•Formulating the management problem as an MINLP.•Solving the model using a genetic algorithm and simulated annealing with the decoding scheme.•Demonstrating the presented model and solution methods effectively.

This paper considers a location-inventory problem in the three-level supply chain where demand across the retailers is assumed to be correlated and inventory shortages are allowed. For better monitoring the stock status, a periodic review of inventory level is taken into account. In order to overcome the joint location-inventory problem, this paper proposes an optimization model based on a mixed integer non-linear programming (MINLP) whose objective function is the minimization of the total supply chain costs. To solve the designed MINLP model, two meta-heuristic algorithms are presented, including genetic algorithm (GA) and simulated annealing (SA) with an appropriate decoding scheme. Since the performance of meta-heuristic algorithms depends on setting the parameters; therefore, the Taguchi method is used to set parameters of the developed solving algorithms. Finally, the proposed algorithms have been used to several numerical test problems that indicate the higher performance of the GA compared with the SA in terms of objective function.