The latency location-or-routing problem

This paper introduces the latency location-or-routing problem (LLoRP); a variant of the location-or-routing problem (LoRP) and an extension of the latency location-routing problem. The LLoRP consists of selecting (opening) a set of depots to serve a set of customers, which can be visited as part of routes also to be decided. The maximum number of depots to open is assumed to be exogenous. For the customers lying within a certain coverage range from an open depot, direct service is an alternative. A set of capacitated homogeneous vehicles is available to be assigned to the selected depots as needed. The goal is to minimize the sum of the waiting times of the customers for being served (latency). Several customer-centric applications of the LLoRP are discussed. Three mixed-integer-linear-programming formulations are developed and two lower bounds on the optimal latency value are devised. A tradeoff between LLoRP and LoRP is considered within a bi-objective modeling framework that is tackled using the ε−constrained method. An outcome of this analysis are compact formulations for the standard LoRP. This type of model is in itself a novelty for that problem. Finally, extensive computational results are discussed to assess the relevance of the LLoRP and the efficacy of the models and bounds proposed. The results highlight multiple distinguishing features of the LLoRP while identifying the most promising optimization models to use. They also provide strong evidence for the relevance of looking into tradeoff solutions when a cost-oriented objective becomes of interest in addition to latency.