Robust Salesforce Compensation with Inventory Considerations

Project: Research

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The proposed project is partially motivated by salesforce contracting in supply chains in practice. Salesforceis a key factor for the excellence of supply chain management as it directly generates demand. For example,the average expenditure on salesforce cost accounts for 10%?40% of firms’ sales revenue (Albers and Mantrala2008). To be competitive, firms must provide appropriate incentives to motivate sales agents. Traditionally,salesforce contracting hinges on two key assumptions: unlimited inventory supply and complete informationon the demand model. This project aims to propose a new modeling framework and techniques to analyzesalesforce contracting in supply chains by taking into account of limited inventory and model uncertainty togain insights on how to achieve efficient and effective contracts for sales agents.We will consider salesforce contracting with limited inventory and parameter uncertainty. That is, a firmmust decide the order quantity before the selling season. Any unfulfilled demand is lost, i.e., there is thedemand censoring effect (the firm cannot observe the demand exceeding its inventory level). Moreover, thedemand distribution is contingent on the effort exerted by the sales agent and we assume that the ability ofthe agent is unknown and in an uncertainty set. In the presence of the parameter uncertainty, the firm adoptsa worst-case criterion, i.e., the firm would like to choose a contract such that the incentive compatibilitycondition holds for any values of the parameters in the uncertainty set and the firm chooses a minmaxcriterion to eveluate its performance. It remains unclear how the demand censoring effect and the parameteruncertainty affect the optimal robust contract.In the existing literature, typically we assume that the firm knows the exact demand model. However, inreality, no model is given and often we estimate the demand model through historical sales data. As a result,we tend to have some degree of ambiguity over the exact values of the parameters in the demand model,e.g., usually we obtain a confidence region instead of a point estimation. If a demand model is misspecified,then the resulting contract may not work. Hence, it is important to understand what types of contracts arerobust to the parameter uncertainty.By exploiting the recent progresses in robust optimization, we are able to find a robust counterpart of therobust contracting problem under our setting. To obtain insights, we consider the firm and the agent arefinancially risk neutral. Interestingly, based on the preliminary results, under the minmax criterion we find alinear contract—paying the agent a base payment and a reward proportional to sales output (or commissionbased reward) is robust even in the presence of demand censoring effect. Moreover, no other contracts arerobust. In other words, a simple contract is robust while a complex nonlinear contract is not robust. Ourresult provides a new explanation on the popularity of the linear contracts in practice even in the presenceof limited inventory. We believe that we can also obtain additional important guidelines and insights on howthe parameter uncertainty affects the commission rate, the optimal order quantity and profitability of thefirm.Preliminary analytical results are presented in this proposal along with the tasks for achieving our statedresearch goals. Our preliminary results on related problems and the techniques developed during thoseexperiences have encouraged us to take up the challenge described.


Project number9042727
Grant typeGRF
Effective start/end date1/12/1826/11/21