Optimal pricing and lot sizing in VMI model

Article history: Received 1 January 2010 Received in revised form 10 March 2010 Accepted 1 April 2010 Available online 30 April 2010 Vendor Managed Inventory (VMI) is one of the effective techniques for managing the inventory in supply chain. VMI models have been proven to reduce the cost of inventory compared with traditional economic order quantity method under some conditions such as constant demand and production expenditure. However, the modeling of the VMI problem has never been studied under some realistic assumptions such as price dependent demand. In this paper, three problem formulations are proposed. In the first problem formulation, we study a VMI problem with one buyer and one supplier when demand is considered to be a function of price and price elasticity to demand, and production cost is also a function of demand. The proposed model is formulated and solved in a form of geometric programming. For the second and the third models, we consider VMI problem with two buyers and two suppliers assuming that each buyer centre is relatively close to the other buyer centre. Each supplier has only one product which is different from the product of the other supplier. Two suppliers cooperate in customer relationship management and two buyers cooperate in supplier relationship management as well, so the suppliers send the orders of two buyers by one vehicle, simultaneously. For the third model, an additional assumption which is practically applicable and reasonable is considered. For all the proposed models, the optimal solution is compared with the traditional one. We demonstrate the implementation of our proposed models using some numerical examples. © 2010 Growing Science Ltd. All rights reserved.