Determining the best optimization method for large scale probabilistic supplier selection problem integrated with inventory management

In logistics and supply chain management, a problem of supplier selection is an optimization problem where the number of variables is growing exponentially which will produce a large-scale optimization problem. A right choice of the used method to solve is needed according to the performance of the method. This paper is considered to compare and analyse how the performance of some classic numerical optimization methods which are interior point, SQP, SQP-legacy and active-set to solve a large-scale optimization problem of a probabilistic supplier selection problem with inventory management. Word “probabilistic” in this case is referring to that the problem is involving some uncertain parameters approached by random variable (probabilistic parameter). We used the existing mathematical model of probabilistic supplier selection problem with inventory management provided in our previous works that only considering few numbers of decision variable then the occurred optimization problem is a small-scale problem that can be solved efficiently by analytical method or numerical method. Then, in this paper we resolved this model with huge number of decision variable indicated by the number of the supplier and time period that is large by using an existing numerical optimization method to analyse how the decision variable, is it reliable to be used or not. We generate some randomly data to simulate the problem and the results. From our computational experiment, the optimal decision variables obtained by the used methods are acceptable to be used as the decision that can be used to be applied by the decision maker. Based on the relative error given by these methods, the active set was given the best performance which means that active-set method is the best choice to solve.