A multi-objective mathematical model for the multi-warehouse order picking system using Benders decomposition algorithm

The order-picking problem is important as one of the warehouse's logistics activities. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders quickly. This paper aims to provide a multi-objective mathematical programming model for integrating the decisions of batching, routing, and scheduling of selectors with the packaging problem in a multi-warehouse environment. The objective functions include depreciation of the delivery times and total order picking costs.

In this research, first, by reviewing the literature in the field of order picking, the research gaps of the problem have been identified. Then, taking into account the main constraints of the problem, a multi-objective mathematical model has been formulated for the multi-warehouse order-picking problem. The classic Benders decomposition algorithm and the accelerated Benders decomposition algorithm have been used to solve the problem. The data related to the warehouses of a company producing sanitary products in Iran was used as a case study to validate the applicability of the proposed model, and its results were reported in the article.

The proposed model's results indicate that CPLEX can solve these problems up to small sizes in an acceptable time. Also, the numerical results show the performance of the Benders decomposition algorithm and the accelerated Benders algorithm as suitable alternatives for solving the model in large-sized problems. The calculation results obtained from the implementation of the solution methods for the proposed model showed that in terms of the number of iterations and the calculation time, the accelerated Benders algorithm had better results than the classic Benders algorithm.

Originality/Value:

 In this research, the order-picking problem with the integrity of operational decisions has been formulated as a multi-objective mathematical model for a multi-warehouse environment for the first time. Also, in this article regarding the solution method, exact solution approaches have been used for the first time considering the structure of the problem. The computation results show that the proposed algorithms are efficient and suitable methods for problem-solving.