Development of location-inventory model based on all-unit quantity discount policy

Distribution network design is one of the main issues in supply chain management. Two key decisions that must be determined to design a distribution network are facility allocation decisions and inventory control decisions. Despite the interaction exists between these two decisions, traditional methods ignored simultaneously optimizing them in a supply chain. Therefore, the obtained results are expected to be suboptimal in many situations. To deal with this problem, in recent years, joint location-inventory models are developed to simultaneously determine the inventory control decisions and facility locations decision of a distribution network. Majority of the previous joint location-inventory models considered the simplest inventory model that is economic order quantity (EOQ) to replenish the demands of retailers. However, a very common policy offered by suppliers is quantity discount that provides the buyers the opportunity of purchasing in larger quantities and reducing their total cost. When quantity discount is available the buyers need to trade-off between reduction in purchasing and ordering cost and increase in the inventory cost in order to find the optimal order quantity. However, EOQ (Q, r) model is not capable of doing such comparison and the buyers need to apply quantity discount models to find the optimal order quantity. Nevertheless, so far quantity discount has not been considered as inventory policy in joint location-inventory models. Thus, this research has formulated and solved a joint location-inventory problem, while all-unit quantity discount is considered as the inventory policy of distribution network. In order to solve the model, two heuristics and one enumeration algorithm are developed. It is shown that considering quantity discount instead of EOQ policy saves the total cost up to 4.5%. In addition, the network configurations are hown to be different under two policies. To investigate the performance of the developed heuristic algorithms, results of the heuristics in terms of total cost and computational time (CPU time) are compared with results obtained by enumeration algorithm and results obtained by Lingo 12.0 software. Results of the developed heuristics are up to 92% betters that the results that the enumeration algorithm find in 24 hours, and 88% better than the results obtained by Lingo.

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