Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

Abstract

Abstract:We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single-period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function.For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win-win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor-managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor-managed delivery arrangement that potentially improves the centralized solution.Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single-period setting.

Quantifying the value of buyer–vendor coordination: Analytical and numerical results under different replenishment cost structures

“…In order to illustrate how this observation enables us to use our analytical results on Goyal's Problem, let us consider a specific instance of Problem II in Table 7, i.e., the problem instance where R = 2.5 and the other model parameters are in Range 3 so that the corresponding IR value remains constant at 13.203% over P P 256. As we have noted at the end of Section 4.2, when the truck capacity is sufficiently large, we can use Proposition 4 to compute IR by adding the per truck cost R to fixed replenishment costs, i.e., by substituting K w = 312.6 + 2.5 = 324.1 and K r = 160 + 2.5 = 162.5 in Expression (14). It follows from Expressions (9) and (11) that n à d ¼ 2 and n à c ¼ 1, and hence, Expression (14) leads to IR ¼ 13:203%, which is the same as our experimental result in Table 7.…”

“…As we have noted at the end of Section 4.2, when the truck capacity is sufficiently large, we can use Proposition 4 to compute IR by adding the per truck cost R to fixed replenishment costs, i.e., by substituting K w = 312.6 + 2.5 = 324.1 and K r = 160 + 2.5 = 162.5 in Expression (14). It follows from Expressions (9) and (11) that n à d ¼ 2 and n à c ¼ 1, and hence, Expression (14) leads to IR ¼ 13:203%, which is the same as our experimental result in Table 7.…”

“…Despite a growing interest in channel coordination over the past few decades [1,4,9,10,15,12,14], no detailed analytical or numerical results measuring its impact on system performance have been reported in the literature. For this reason, we revisit the classical buyer-vendor coordination problem introduced by Goyal [4] (called Goyal's Problem from now on) and extended by Toptal et al [13].…”

Transportation pricing of a truckload carrier

“…While many of the papers in this area consider the problem in a single echelon setting (e.g., Aucamp, 1982;Lee, 1986;Tersine and Barman, 1994;Shinn et al, 1996;Burwell et al, 1997;Hwang et al, 1990;Jaruphongsa et al, 2005;Mendoza and Ventura, 2008;Rieksts and Ventura, 2008;Toptal, 2009), relatively recent papers model and solve the replenishment problems of multiple echelons under transportation considerations (see Hoque and Goyal, 2000;Çetinkaya and Lee, 2002;Chan et al, 2002;Toptal et al, 2003;Toptal and Çetinkaya, 2006;Rieksts and Ventura, 2010).…”

“…Aucamp (1982), Lee (1986), Çetinkaya and Lee (2002), Toptal et al (2003), Toptal and Çetinkaya (2006) are examples of papers that assume a single mode of transportation, in the form of a truckload shipment. They use a multiple set-ups structure to model this form of shipment.…”