Time-based procurement

Abstract

This study investigates the design of a time-based procurement contract when a supplier possesses private information about intrinsic completion time and may choose to exert time reduction effort. We first derive the optimal (complex) contract for the buyer, and then evaluate the performance of a (simple) fixed-price and fixed-time (FPFT) contract. Our analysis shows that the structure of the optimal time-based contract and the performance of an FPFT contract depend largely on time reduction forms. Specifically, if time reduction follows a multiplicative model, the optimal contract induces the intrinsically slow supplier to reduce time, and offers a fixed payment to the intrinsically fast supplier. This result is opposite to what could occur when time reduction follows an additive model. We also show that, in a specific multiplicative model, the FPFT contract achieves at least eight-ninth of the available surplus for the buyer, whereas the performance of an FPFT contract deteriorates dramatically in an additive model. In response to this underperformance, we then propose an enhanced linear contract, and demonstrate that, using this contract, the buyer loses no more than one-sixteenth of the available surplus. Our results shed light on the important effect of time reduction forms on time-based contract design.

Introduction

Time is money. Intense global competition and rapid technological advances have made speed a competitive advantage. To succeed, companies must identify new opportunities and launch new products or services to the marketplace ahead of their competitors. Perhaps in no industry does speed matter as much as in the consumer electronics industry. For example, a delay in launching a product can result in a decline in sales ranging from 5.92% to 10.99% (Hendricks and Singhal, 2008) and a loss of 5.25% of the firm's share price (Hendricks and Singhal, 1997). The construction industry is another good example in which time and speed matter. Because a typical construction project requires debt financing, any reduction in time could directly lower the borrowing cost. According to Konchar and Sanvido (1998), the median construction cost in the USA is $1140 per square meter, and the median construction speed is 438 square meters per month. Consider a residential project with a size of 100,000 square meters. Suppose that 75% of the construction cost is debt financed, and the prevalent interest rate of commercial loans is 4.8% per annum. Then a property developer such as D.R. Horton could save as much as 342,000 in interest expenses if the completion time is reduced by just one month.

In the face of increasing time-to-market pressure, numerous organizations are turning to outsourcing to gain competitive advantage over their competitors. For example, Pannos Kalaritis, the vice president of operations for Irix Pharmaceuticals, says that outsourcing process development can accelerate a drug's development by allowing a pharmaceutical company to continue research, while a contractor works on process optimization (Lerner, 2002). Time has been an important criterion when organizations source services for critical construction projects, new product design, enterprise resource planning (ERP) software, and so forth. In public sectors, the time to complete a project significantly affects consumers’ wellbeing and social welfare. For example, the social cost caused by a delay in highway repair jobs could be as high as several million dollars per day (Lewis and Bajari, 2011).

A contractor (or supplier) can usually speed up job completion by shifting resources from other jobs, hiring more workers, using equipments more intensively, or scheduling overtime. After recognizing such possibilities, a number of organizations offer explicit time incentive to their contractors. This paper studies a situation in which a buyer purchases an item (product or service) from a supplier, and benefits from fast delivery. The question is how to design time-based incentive that is offered to the supplier. This same model also applies to an outsourcing setting, in which a firm outsources a job (project or process) to a contractor and is concerned with designing a time-based contract to incentivize the contractor to complete the job as early as possible.

Incentive-based contracts have seen widespread applications in practice, and can make time reduction rewarding for both buyers and suppliers. For example, on January 17, 1994, a 6.8-magnitude earthquake struck the Los Angeles basin near the suburb of Northbridge and caused 60 deaths, thousands of injuries, and billions of dollars in property damage. Nowhere was the destructive power of nature more evident than in the collapsed sections of the freeway system that disrupted the daily commute of an estimated 1 million local residents. The Northbridge earthquake posed one of the greatest challenges to California Department of Transportation (CalTrans) in its nearly 100-year history. To expedite the recovery process, Governor Pete Wilson signed an emergency declaration allowing CalTrans to streamline contracting procedures and offer attractive incentive for completing work ahead of schedule. The time incentive scheme proved to be a powerful motivator for the freeway reconstruction contractors. C.C. Myers, Inc., pulled out a stunning feat by repairing the damaged freeways 74 days ahead of schedule and was awarded a 14.8 million bonus (Baxter, 1994). Despite the difficulties and expenses incurred by around-the-clock freeway building, most local residents cheered CalTran's quake recovery efforts.

In this study, we consider a procurement model in which a supplier possesses private information about intrinsic completion time and is able to invest in time reduction effort. In practice, it is difficult (and sometimes impossible) for a buyer to observe the effort exerted by the supplier. However, the actual time when the supplier delivers the good or service is always observable and verifiable. Therefore, the buyer can write a time-based contract to achieve the optimal procurement outcome. Based on the principal-agent literature, this paper is concerned with how to incentivize the supplier to reduce time when the supplier has private information regarding intrinsic completion time and exerts private effort in time reduction.

An important question is how to model time reduction since this will directly affect the buyer's utility, and hence the optimal time-based procurement contract. We consider two time reduction models: (1) multiplicative model, in which the reduced time is increasing in the intrinsic time with the same level of effort, implying that it is easier to reduce the completion time if the initial time is shorter and (2) additive model, in which the reduced time does not depend on the intrinsic time. These two models are likely to emerge in various circumstances. Consider a multi-level residential building as an example. The use of fast-drying cements can reduce the drying time for each level by 1 day, which is independent of the intrinsic time. On the other hand, the use of concurrent design (e.g., Jayaram and Malhotra, 2010) or laddering technique (e.g., Larson and Gray, 2011) can also reduce the completion time. Laddering means that project activities are broken into segments so that the following activity can begin sooner and not delay the work. Suppose that it takes the contractor to trench, lay pipe, and refill in 9 days (with 3 days for each activity). The contractor can break these three activities into three segments such that it can start to lay pipe when the first segment of trenching is completed, start to refill when the first segment of laying pipe is completed, and so forth. The total time would reduce from 9 to 5 days. In this case, the reduced time is increasing in the intrinsic time. In summary, different options to reduce completion time can lead to the additive or multiplicative model.

For each model, we first design the optimal time-based procurement contract, and then assess the performance of a simple but often used contract, namely the fixed-price and fixed-time (FPFT) contract. Under this contract, the buyer agrees to pay the supplier a fixed payment if the supplier is able to complete the job within a fixed amount of time. The results and insights in this paper are rich. First, we demonstrate that whether the time reduction is multiplicative or additive significantly changes the form of optimal payment (as a function of actual completion time). In particular, when the time reduction follows an additive model, it is optimal for the buyer to induce a fast supplier to reduce time by using a convex payment function. In contrast, when the time reduction follows a multiplicative model, it is optimal for the buyer to induce a slow supplier to reduce time by using a concave payment function. In practice, a convex payment function is reminiscent of a contract that offers a large bonus for each unit of reduced time; whereas a concave payment function is reminiscent of a contract that stipulates a firm delivery time. Both contract forms are being used in modern procurement systems (see Larson and Gray, 2011, Lewis and Bajari, 2011). In this sense, our research provides a holistic economic explanation on the use of time-based incentive. In addition, the results suggest that the buyer may suffer from long delays or high costs if a payment function based on an incorrect assumption is applied.

Second, we show that the performance of some simple contracts critically depends on the cost of exerting effort and whether time reduction is multiplicative or additive. In particular, when time reduction follows a multiplicative model, we demonstrate that by using an FPFT contract, the buyer may lose no more than 1/9 of the achievable surplus secured by an optimal contract. However, when time reduction follows an additive model, the performance of an FPFT contract deteriorates especially when the cost of exerting effort is medium or high. In response to this underperformance, we propose an enhanced linear contract, and demonstrate that the performance ratio of this enhanced contract is at least 15/16.

Our results highlight the importance of identifying time reduction forms. In practice, it may be difficult for a buyer to recognize which model the time reduction follows. A rule of thumb is to consider whether the time that can be possibly reduced depends on the initial time. If the reduced time is affected by the intrinsic time, then time reduction is likely to follow a multiplicative model; otherwise, it may follow an additive model. Then based on the conjecture of time reduction, the buyer designs an appropriate time-based contract.

This study is broadly related to the literature on principal-agent models with incomplete information (which leads to adverse selection) and hidden action (which leads to moral hazard). For a general review on this topic, we refer readers to Bolton and Dewatripont (2005). In the following literature review, we will focus our attention on the most relevant articles, which study how to incentivize suppliers to reduce their production costs. The two influential papers in this area were written by Barron and Myerson (1982), where the agent's production cost is unobservable, and Laffont and Tirole (1986), where the agent's production cost is observable. In Laffont and Tirole (1986) and numerous subsequent studies, the agent's cost is assumed to be additive with respect to the agent's effort. Specifically, the agent privately observes the intrinsic cost and chooses to invest in cost reduction. The principal observes the agent's realized cost, which equals the intrinsic cost minus the agent's private effort.

Our study differs from the above literature in that we consider a procurement mechanism design problem with time reduction. Time reduction is distinct from cost reduction in that the former may be of multiplicative or additive form, while the latter is of additive form (as the literature suggests). More importantly, we find that the optimal payment function has contrasting properties for these two models, which has not been reported in the existing studies.

In the operations management literature, several papers study the issue of on-time delivery, whereas we focus on inducing the supplier to reduce time. Grout and Christy (1993) study a just-in-time environment, in which the supplier determines when to start the production, and show that a bonus contract improves on-time delivery. Grout (1998) shows that the use of delivery windows does not always improve on-time delivery. Cachon and Zhang (2006) consider a procurement problem in which the supplier possesses private information about capacity cost. Recognizing that the reserved capacity determines the delivery time, Cachon and Zhang characterize the optimal procurement mechanisms and evaluate the performance of two simple contracts. Dai et al. (2012) study the contracting problem in a vaccine supply chain by integrating various industrial features such as product design, uncertain delivery, and time-sensitive demand. We contribute to this literature by identifying the impact of time reduction on optimal contracts and developing theoretical bounds on the forgone surplus when an FPFT contract is used.

The remainder of this paper is organized as follows: Section 2 presents the model setup, and Section 3 derives the optimal time-based contracts for the multiplicative model and the additive model. Then we evaluate the performance of the FPFT contract in Section 4, and finally we summarize the main findings and discuss the future research in Section 5. All the proofs are related to the Appendix. We also study a time-based auction to achieve the optimal procurement outcome if there are multiple suppliers competing for the buyer's business. This together with other extensions is provided in the Online Supplement.