Inventory service-level optimization in a distribution network design problem using heterogeneous fleet

Dimensionality-reduction Procedure for the Capacitated p-Median Transportation Inventory Problem

“…It is a very uncommon restriction in supply chain, because vehicles usually can supply product to different customers in a route. Hence, the LIRP published in Carmona-Benitez et al [14] is not a routing problem because it does not solve routing decisions, it is a transportation problem, because it solves transportation decisions, reason why, in this paper, the CLITraP-HTF is classified as a transportation problem.…”

“…However, their model has three limitations: first, their model assumes that the lead times (L) are the same for all customer facilities no matter who is the supplier facility, but in a real life problem, lead times are different depending the distance between origin facilities and destination facilities; second, their model assumes that the variability of the demand over lead time (σ DL ) does not change when a facility is chosen to be a DC, however, in a real-life problem, the σ DL changes when a facility is assigned to be a DC; third, in their model product enters the network through only one supplier facility, but in a real-life problem, product could enter through different facilities. In this paper, the LIRP proposed in Carmona-Benitez et al [14] is modified to overcome these limitations in Section 2.3, and it is called CLITraP-HTF.…”

“…The LIRP presented by Carmona-Benitez et al [14] is based on a real company distribution problem, where vehicles are not allowed to supply more than one facility per trip because the hazardous material (hazmat) product they distribute is not divisible by law. It is a very uncommon restriction in supply chain, because vehicles usually can supply product to different customers in a route.…”

“…The optimum value of n ij is an integer variable different from zero because the amount of product to transport from facility i {O ∪ V} to facility j V every T * j is equal to Λ j T * j and to n ij q ij (Equation (28)). Λ j T * j is different from zero because Equations (24) and (14) indicate that T * j and Λ j are positive and different from zero respectively.…”

“…From Equation (31), the optimum transportation cost W w=1 C ijw n ijw is achieved when W w=1 n ijw = 1, because the amount of product to transport from facility i {O ∪ V} to facility j V every T * j using vehicle w W is equal to Λ j T * j and to n ijw q ijw . Λ j T * j is different from zero because Equations (24) and (14) indicate that T * j and Λ j are positive and different from zero respectively. Hence, only one shipment using one type of vehicle from the heterogeneous fleet of vehicles w W is used to transport product from facility i {O ∪ V} to facility j V every T j , even if Λ j in facility j V increases or decreases, or whether facility j V is chosen to be a DC or not.…”