# Solving the multi-buyer joint replenishment problem with simulated annealing method

 Author: Lam, Chi-kin Title: Solving the multi-buyer joint replenishment problem with simulated annealing method Degree: M.Sc. Year: 2001 Subject: Inventory control -- Mathematical modelsSimulated annealing (Mathematics)Hong Kong Polytechnic University -- Dissertations Department: Multi-disciplinary StudiesDept. of Applied Mathematics Pages: 104 leaves : ill. ; 30 cm Language: English InnoPac Record: http://library.polyu.edu.hk/record=b1569115 URI: http://theses.lib.polyu.edu.hk/handle/200/3197 Abstract: The Joint Replenishment Problem (JRP) is a Multi-Item inventory problem of coordinating the replenishment of a group of items that may be jointly ordered from a single supplier. Each time an order is placed, a major ordering cost is incurred, independent of the number of items ordered. Furthermore, a minor ordering cost is incurred whenever an item is included in a replenishment order. Joint replenishment of a group of items reduces the number of times that the major ordering cost is charged, and so this saves costs. In some cases, a group of buyers can be coordinated to order items from a single supplier. Then, the JRP problem is extended from a Single-Buyer Multi-Item JRP to a Multi-Buyer Multi-Item (MBMI) JRP. Some algorithms had been developed to solve the JRP. However, those algorithms become inefficient when the size of the problem becomes large. A better approach is to solve the problem with meta heuristic search. In this project, the Simulated Annealing (SA) method is employed. We have implemented the SA method in a computer program and applied to a form-ordering problem of a leading bank in Hong Kong. The goal of the problem is to minimize the ordering and inventory cost by coordinating 100 branches in the replenishment of 26 types of forms. This is a typical MBMI JRP. With the use of SA, this problem is solved in around 8 seconds in a personal computer. The model of the MBMI JRP is further extended to coordinate the vendor and buyers together. The new model is implemented by a computer program and applied to the form-ordering problem. To investigate the performance of the new model, it is compared with other production/replenishment schemes. The results show that the new model can achieve a significant cost saving in the forms-order problem.

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