Decision Support
Impact of cost uncertainty on pricing decisions under risk aversion

https://doi.org/10.1016/j.ejor.2016.02.034Get rights and content

Highlights

  • We identify the root causes of cost uncertainty in service.

  • We investigate the impact of cost and demand uncertainties on pricing decisions under risk aversion.

  • Cost uncertainty increases price, whereas demand uncertainty reduces it.

  • We establish an optimal cost contingency policy under a sequential service engagement process.

Abstract

This paper studies cost uncertainty in services. Despite the fact that the service sector has become the largest component of gross domestic products in most developed economies, cost uncertainty and its impact on pricing decisions have not received much attention in the literature. In this paper, we first identify the root causes of cost uncertainty in services. Using the distinctive characteristics of services defined in the literature, we show why cost uncertainty, which has been widely neglected in the manufacturing dominated literature, is pervasive in services. Next, we investigate how cost uncertainty affects a risk-averse service provider’s pricing decisions in a make-to-order setting. Using the expected utility theory framework, we show that cost uncertainty increases the optimal price, whereas demand uncertainty reduces it. As a result of the countervailing impacts, the optimal price under risk aversion may be larger or smaller than the optimal risk-neutral price. Next, we study the problem of optimizing cost contingency in service contract pricing. We show that the optimal cost contingency decreases as the profit of the contract increases even when the utility function exhibits an increasing absolute risk aversion. Finally, we introduce various strategies to mitigate the risk of cost uncertainty observed in practice, and propose new research problems.

Introduction

When engaging on a service contract, service providers are uncertain about the cost of delivering the service. For example, consider a software development service provider that bids for an application development project. In the software development outsourcing industry, fixed-price contract, under which a buyer pay a fixed fee to a service provider, is one of the most common forms of contracts (Gopal, Sivaramakrishnan, Krishnan, & Mukhopadhyay 2003). To offer a fixed-price contract for the software development project, the service provider first estimates the labor and other costs to develop the application, and determines the price based on this estimate. The total labor hours required to complete the project, which determine the actual cost of the service, are difficult to estimate in advance. In software development projects, project requirements involve significant uncertainties, which often cause cost overruns (Kraut & Streeter 1995). Anecdotal examples from other service industries such as the business process outsourcing industry and the construction service industry also highlight the significance of cost uncertainty in services. (Flyvbjerg, Holm, Buhl, 2004, Blomberg, Boyette, Chandra, Oh, Zhou, Strong, et al., 2014).

Cost uncertainty yields a substantial risk in service profitability, and thus has a huge impact on the service provider’s pricing and contracting decisions. Despite its importance, cost uncertainty has not received much attention in the pricing and contracting literature. This oversight is in a sharp contrast to demand uncertainty, which has been studied extensively (see, e.g., Özer & Phillips 2010). As Shoemaker and Mattila (2009) pointed out, most existing pricing frameworks were developed in the context of consumer goods. Karmarkar and Pitbladdo (1995) argue that the very nature of service markets depends on distinctive characteristics of services. Hence, the existing pricing frameworks cannot properly address the problem of service pricing. The service sector now accounts for about 80 percent of the United States economy (New York Times 2010). Thus, cost uncertainty and its impact on pricing decisions are important subjects to explore.

In this paper, we first introduce cost uncertainty in services. The characteristics of services have been well explored in the literature. We show how each of the defining characteristics of services yields cost uncertainty, which also explains why cost uncertainty does not usually arise in manufacturing. Next, we investigate the impact of cost uncertainty on pricing decisions made by a risk-averse service provider in a make-to-order setting. In our model, the service provider starts delivering the service after the demand is realized, and thus quantity (production) decisions are made trivially. Using the expected utility theory framework, we model the problem of pricing under cost and demand uncertainties, and show how the two sources of uncertainty affect the optimal pricing decision. Next, we study the problem of optimizing cost contingency in service contract pricing. We show how the properties of the potential contract affect the optimal cost contingency. Finally, we introduce various strategies that service providers employ in practice to mitigate the risk of cost uncertainty, and propose new research problems.

This paper is closely related to the literature on pricing under demand uncertainty and risk aversion. In the economics and operations literature, how a seller’s risk aversion and demand uncertainty affect pricing decisions has captured some attention (e.g., Leland, 1972, Agrawal, Seshadri, 2000, Colombo, Labrecciosa, 2012, Rubio-Herrero, Baykal-Gürsoy, Jaśkiewicz, 2015). This literature, however, consistently assumes that cost is certain (or zero), and hence the impact of cost uncertainty has not been explored. The impact of risk aversion and demand uncertainty on the optimal inventory (production) decisions has been studied extensively in the operations literature (see, e.g., Ahmed, Çakmak, Shapiro, 2007, Wang, Webster, Suresh, 2009, Choi, Ruszczyński, 2011). This stream of work, however, considers neither the pricing decision nor the uncertainty in cost. We contribute to the literature by introducing cost uncertainty in services, and investigating its impact on pricing decisions under risk aversion.

The pricing literature has shown that the impact of demand uncertainty on the optimal pricing decision sharply depends on the demand uncertainty model (Agrawal, Seshadri, 2000, Xu, Chen, Xu, 2010). Hence, we solve the problem under three different demand uncertainty models: valuation uncertainty, additive demand uncertainty, and multiplicative demand uncertainty. We show that under all demand uncertainty models, cost uncertainty consistently increases the optimal price, whereas the impact of demand uncertainty varies depending on the model. We defer all proofs to the appendix.

Section snippets

Cost uncertainty in services

In this section, we explore what makes service costs uncertain. As we discussed in the previous section, cost uncertainty has been neglected in the manufacturing centered pricing literature. This oversight implies that the causes of cost uncertainty are closely related to distinctive characteristics of service. The characteristics of service have been well studied in the literature. As summarized by Sampson and Froehle (2006), there are five defining characteristics of service: intangibility,

Impact of cost uncertainty on pricing decisions

In the previous section, we explored why costs are uncertain when making pricing decisions for a service. In this section, we investigate the impact of cost uncertainty on a risk-averse service provider’s pricing decisions in the make-to-order setting. It has been shown in the literature that the impact of demand uncertainty on pricing decisions sharply depends on the demand model (e.g., Leland, 1972, Agrawal, Seshadri, 2000, Xu, Chen, Xu, 2010, Colombo, Labrecciosa, 2012). For example, under

Optimizing cost contingency in service contract pricing

When a large service enterprise agrees on a new service contract with a client, the engagement process consists of solution design, quality assurance, and pricing phases (Councill, Hacigumus, Johns, Kreulen, Lehman, Rhodes, et al., 2009, Oh, Strong, Chandra, Blomberg, 2014b). During the solution design phase, technical solution architects develop a service delivery plan and estimate the cost of the service. During the quality assurance phase, risk assessment experts quantify the risk level of

Strategies to mitigate cost uncertainty

Cost uncertainty can cause a considerable financial risk to service providers. The total contract price of a large IT outsourcing service can be multi-billion dollars (Spohrer et al. 2007). In such large service contracts, underestimated costs can easily result in multi-million dollar losses. Thus effectively managing the risk of cost uncertainty is an important problem for service providers. Adding a cost contingency in a fixed price contract studied in the previous section is one such risk

Conclusion

In this paper, we have studied cost uncertainty in services. Using the characteristics of service, we show why cost uncertainties arise in services. By studying simple analytic models of pricing under cost and demand uncertainties in the make-to-order setting, we have shown that cost uncertainty always increases the price, where as the impact of demand uncertainty depends on the uncertainty model. We have shown that under the uncertain valuation and additive demand uncertainty models, demand

Acknowledgment

The authors thank Prof. Borgonovo and the two anonymous reviewers for constructive suggestions.

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