Abstract:This paper introduces two subsidyschemes in a supply chain environment consisting of a manufacturer and aretailer. The manufacturer sells a single type of products to the retailer, whothen fulfills the customer demand of multiple classes. The retailer adopts abase stock policy to periodically replenish the inventory on an infinitehorizon. By the inventory rationing policy, the retailer either fulfills demandimmediately, or backorders the demand to wait for next cycle. The retailerselects a cycle time that balances the set up cost, the holding cost anddiscounting cost. In the meantime, the manufacturer incurs the production costand fixed setup cost for each cycle. In order to reduce the average cost on thetime horizon, the manufacturer provides the holding cost subsidy and backorderingcost subsidy schemes to induce the retailer to increase the cycle time. Wederive the retailer’s optimal rationing policy, and show that there exists aunique optimal cycle time. The numerical analysis shows that both the holdingcost subsidy and backordering cost subsidy schemes may provide the retailerwith an incentive to extend the cycle, and manufacturer and retailer maybenefit significantly from adopting the subsidy schemes. Thenumeric analysis also shows that the two subsidy schemes can be usefulcomplements in certain circumstances.Lastly, we provide some guidelinesand insights on how to choose the effective subsidy schemes.
1. Introduction
Effectivecoordinate the supply chain system has been one of the most challenging issuesfacing both the practitioners and the academicians for years. Especially in theglobal operations, such as offshore manufacturing system, the product istypically sourced and manufactured in a single foreign supplier, and thenshipped back to domestic warehouses for sale and distribution (Simchi-Levi,2008). In this environment, the challenges for the suppliers are how to reducethe per-unit transportation cost through higher truckload utilization. As aresult, the supplier would like to have large lot sizes. Unfortunately, typicaldemand doesn’t come in large lot sizes, so large lot sizes lead to highinventory. To achieve the scale of economic in transportation or production,the manufacturer needs a second financial lever in addition to the wholesaleprice, such as sharing the retailer’s holding cost or providing some promotionsto the end customers. Although these subsidy schemes are common in many industries,the poorly designed schemes may not fail to induce the customer to increase thecycle time, but create additional subsidy cost burdens.
Motivatedby this story, this paper considers two subsidy schemes, including the holdingcost subsidy (HCS) and backorder cost subsidy (BCS) schemes, utilized in a twoechelon supply chain consisting of a manufacturer and a retailer. Themanufacturer sells a single product replenished on a periodic basis to theretailer, which then satisfies the demand of multiple customer classes. By therationing policy, the retailer either fulfills demand immediately or delays thedemand to next cycle. Under the holding cost and / or backorder cost subsidies,the retailer would like to increase the order cycle, and then the manufacturerwould benefit from increased cycle time by reducing the per-unit setup cost. Itis assumed that the manufacturer and the retailer are independently owned, andboth the two aim at maximizing their own expected profits. Then, the problem ofthe manufacturer is how to choose and design the subsidy schemes to maximizeher average profit.