Replenishment decisions under an all-units discount schedule and stepwise freight costs

Abstract

a b s t r a c tIn this study, we analyze the replenishment decisions under a general replenishment cost structure that includes stepwise freight costs and all-units quantity discounts. We first formulate a general model that accounts for a larger class of problems and prove several useful properties of the expected profit function. We later utilize these properties to develop a computational solution approach to find the optimal order quantity. As an application of the general results, we study the replenishment decisions in the single-period, i.e., the Newsboy, problem considering several scenarios that model the cost considerations either for the buyer or for both the buyer and the vendor.

Economic and environmental considerations in a continuous review inventory control system with integrated transportation decisions

“…In particular, we include explicit truck costs, capacities, and emissions in case of TL transportation. As noted before, TL transportation costs have been previously modeled in integrated inventory control and transportation studies (see, e.g., Aucamp, 1982;Lee, 1986;Toptal et al, 2003;Toptal and Çetinkaya, 2006;Toptal, 2009;Toptal and Bingol, 2011;Konur and Toptal, 2012). In calculating the TL transportation emissions, we explicitly consider the freight trucks and their loads.…”

“…On the other hand, in TL transportation, the retailer is charged on the number of trucks used for transportation, which requires explicit transportation modeling. TL transportation has been integrated with inventory control decisions in the supply chain and logistics literature (see, e.g., Aucamp, 1982;Lee, 1986;Toptal et al, 2003;Toptal and Çetinkaya, 2006;Toptal, 2009;Toptal and Bingol, 2011;Konur and Toptal, 2012). Following the modeling approach in these studies, we model TL transportation explicitly by taking per truck costs and per truck capacities into account.…”

Models for Ordering Multiple Products Subject to Multiple Constraints, Quantity and Freight Discounts

“…Mendoza and Ventura [12] developed exact algorithms for deciding economic lot sizes under all-units and incremental quantity discounts and two modes of transportation: truck load and less than truck load. Toptal [13] developed a model for lot sizing decisions involving stepwise freight costs and all-units quantity discounts.…”

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).…”