A Two-Echelon Inventory System with Quantity Discounts and Transshipments

Abstract

<p>Analysis and optimization of inventory systems allows retailers (e.g. Best Buy) and suppliers (e.g. Apple) to serve customers effectively while simultaneously keeping costs low. Transshipment within an echelon allows for structured sharing of product inventory between locations that have independent demands. The possible advantages gained from allowing transshipments within a multilocation inventory system are that it can allow for lower overall stock levels, cost savings, service level improvements and expanded availability of markets. When a supplier offers a quantity discount to two retailers based on a two-block tariff the response function for each retailer is transformed from a single curve, to a family of two curves. The derivation of the equilibriums for this situation allows for four possible equilibrium points. Two of these have symmetry properties. Significantly, the other two equilibrium points, which are mirror images of each other, prescribe non-symmetric inventory positions for the two retailers. The existence of these equilibrium points are dependent on the choice of the quantity discount parameters offered by the supplier to the two retailers. Under the appropriate conditions we show that the retailers choose optimal ordering quantities that have the following properties: <br></br> <br></br>1.Satisfy the first-order equilibrium conditions. <br></br>2.Are not symmetric for the two retailers, even though the quantity discount offered to the two retailers by the supplier is identical, and all costs are symmetric for the two retailers. <br></br>3.Result in improved profits for each retailer over the symmetric equilibrium solutions. <br></br>4.Result in improved profits for the supplier. <br></br> <br></br>Through the setting of the appropriate quantity discount scheme, the supplier can achieve a range of system performance outcomes, based on their strategic preferences. This research adds to the current literature on transshipment systems by identifying new strategic advantages to engaging in transshipments in inventory systems that include quantity-based purchasing discounts.</p><p>This presentation occurred at the Wright State University Campus-Wide Celebration of Research, Scholarship and Creative Activities on April 8, 2011</p>