Incorporating quantity discounts to the EOQ model with transportation costs

Transportation pricing of a truckload carrier

“…Their focus is to find the optimal replenishment quantities to minimize the sum of transportation and inventory related costs. See, for example, Aucamp (1982), Lee (1986), Lee (1989), Tersine and Barman (1994), Çetinkaya and Lee (2002), Jaruphongsa et al (2005), Mendoza and Ventura (2008). The papers in the latter body of research, study the pricing of transportation services within the context of fleet management.…”

“…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).…”

“…In some recent studies, a combination of TL and LTL shipments is modeled. See, for example, Mendoza and Ventura (2008), Rieksts and Ventura (2008), Rieksts and Ventura (2010). These three studies allow the utilization of a TL carrier and an LTL carrier simultaneously for the shipment of the replenishment quantity.…”

“…Our modeling of transportation costs is similar to the one in these studies (i.e., Mendoza and Ventura, 2008;Rieksts and Ventura, 2008;Rieksts and Ventura, 2010). Mainly, we assume that the TL carrier charges a fixed shipping price per truck whether it is fully or partially loaded, and the LTL carrier charges a constant price for each unit shipped.…”

“…Rieksts and Ventura (2008) solve the classical Economic Order Quantity (EOQ) model assuming the availability of a TL and an LTL carrier for inbound shipments. Mendoza and Ventura (2008) extend this model to consider a general whole price structure, given by either an all-units or an incremental quantity discount schedule. Rieksts and Ventura (2010) study a two-echelon system consisting of a warehouse and a retailer, and model the transportation costs from the warehouse to the retailer allowing both TL and LTL shipments.…”