Coordinating the Optimal Discount Schedules of Supplier and Carrier

Transportation is important in making supply chain decisions. With the careful consideration of transportation expenses, the performance of each supply chain member, as well as the entire supply chain, could be improved significantly. The purpose of this research is: 1) to explore and identify the various situations that relate to replenishment and transportation activities; and 2) to reveal the strength of the connection between purchase quantity and transportation discounts, and integrate the two discounts to enhance supplychain coordination. The problem is analyzed and categorized into four representative cases, depending on transportation. To aid the supplier or the carrier to determine the discount that should be offered, in light of the buyer’s reaction to that discount, decision models are proposed under three different circumstances. First, assuming a single product, we investigate the quantity discounts from the supplier’s perspective, via a noncooperative game-theoretical approach and also a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer’s best reaction. The Stackelberg equilibrium and the Pareto-optimal solution set are derived for the noncooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than noncooperatively. Moreover, we extend our model in several directions: (a) the product is transported by a private fleet; (b) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and iii (c) the case of multiple (heterogeneous) buyers. Numerical examples are employed, here and throughout the thesis, to illustrate the practical applications of the models presented and the sensitivity to model parameters. Secondly, we consider a situation with a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier’s point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier’s discount policy. The third approach studies the case in which transportation of the goods by a common carrier (a public, for-hire trucking company) is integrated in the quantity discount decisions. In reality, it is quite difficult for the carrier to determine the proper transportation discount, especially in the case of LTL (less-than-truckload) trucking. This is not only because of the “phantom freight” phenomenon, caused by possible over-declaration of the weight by the shipper, but also due to the fact that the discount relates to both transportation and inventory issues. In this research, we study the problem of coordinating the transportation and quantity discount decisions from the perspectives of the parties who offer the discounts, rather than the ones that take them. By comparison of the noncooperative and cooperative models, we show that cooperation provides better overall results, not only to each party, but iv also to the entire supply chain. To divide the extra payoffs gained from that cooperation, we further conduct a coalition analysis, based upon the concept of “Shapley Value. ” A detailed algorithm and numerical examples are provided to illustrate the solution procedure. Finally, the thesis concludes with comprehensive remarks. We summarize the contributions of this thesis, show the overall results obtained here, and present the directions that our research may take in the future.