Abstract
In this work, a supply chain with coordination mechanism consisting single vendor and buyer is considered. Further, instead of price sensitive linear or deterministic demand function, a price-sensitive non-linear demand function is introduced in this paper. To find the inventory cost, penalty cost and transportation cost, it is considered that the production and shipping functions of vendor are continuously harmonized and occur at the same rate. In this integrated supply chain, the Buyer’s Linear Program (LP), vendor’s Integer Program (IP) and coordinated Mixed Integer Program (MIP) models are formulated. Numerical examples presented in this research, which include the sensitivity of the key parameters to illustrate the models. The solution procedures demonstrate that the individual profit as well as joint profit could be increased by coordination mechanism even though the demand function is non-linear. In addition, the results illustrate that Buyer’s selling price with consumers purchasing price could be decreased which may increase the demand of the end market. Finally, a conclusion is drawn in favor of the coordinated supply chain with non-linear price sensitive demand function.
Highlights
The classical objective of logistics is to be able to have the right products in the right quantity, at the right place, at the right moment at minimal cost
Without coordination a supply chain system cannot be optimal as a whole since each party will only try to enhance his own profits
An exponential price sensitive demand function comprises an explicit term for price elasticity that incorporates non-linear effects of pricing and is easy to manipulate mathematically is introduced
Summary
The classical objective of logistics is to be able to have the right products in the right quantity, at the right place, at the right moment at minimal cost. Efforts to produce an efficient supply chain are centered on managing logistical flow and inventory. In overcoming many of the new challenges of the comprehensive enterprise, the coordination of members along the supply chain is vital. Without coordination a supply chain system cannot be optimal as a whole since each party will only try to enhance his own profits. That is why to ensure the optimal system and to satisfy customer demands in today’s competitive markets, significant information needs to be shared along the supply chain. The concept of Joint Economic Lot Sizing (JELS) is introduced to filter traditional methods for independent inventory control and to find a more profitable joint production and inventory policy
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