A joint economic lot size model for a supplier-manufacturer-retailers supply chain of an agricultural product

Smooth supply of processed agricultural products to the market is necessary for survival of human beings. Minimization of the management cost of these products plays an important role in delivering them to customers with reasonable prices. Although single-manufacturer single-retailer two-tier supply chain (SC) models are available in the literature, there is a lack of a three-tier SC model concerning agricultural products. This study presents a three-tier joint economic lot size SC model of delivering agricultural products, consisting of a single seasonal supplier, a single manufacturer and multiple retailers. The demand of a product is assumed to be a deterministic constant. The objective is to find the number of shipments and shipments sizes in a cycle from the supplier to the recipient to minimize the total cost of ordering, setup, shipment and holding. The model is solved following both the algebraic and the differentiation methods. They are found to provide the same solution theoretically. Also, we develop an algorithm to find integer number of shipments to manufacturer and retailers in obtaining the minimal total cost solution to the problem. A sensitivity analysis on a solution of a numerical problem shows that a manager can control the frequency of shipments with an extra cost.