Mathematical Modeling of the Two-Echelon Location Routing Problem with Simultaneous Pickup and Delivery and Parcel Locker

This study considers an extension model of the Two-Echelon Location Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD), namely the Two-Echelon Location Routing Problem with Simultaneous Pickup and Delivery and Parcel Locker (2E-LRPSPD-PL). 2E-LRPSPD-PL deals with the accumulation of routing plan and facilities' locations decisions, i.e., satellite and parcel lockers. The first echelon of 2E-LRPSPD-PL consists of one depot, opened satellites, and opened parcel lockers. While the second echelon is described by opened satellites which create routes to fulfill demands of home service customers and by opened parcel lockers which accommodate the demands of parcel locker customers. We propose two-indexed Mixed Integer Linear Programming (MILP) formulation to describe the problem. CPLEX solver is employed to solve small to medium test instances of the 2E-LRPSPD-PL. The computational result shows that CPLEX effectively results in an optimum solution for small instances of 2E-LRPSPD-PL. Furthermore, in the execution of small to medium test instances, some scenarios regarding the number of parcel locker customers are considered to analyze their impact toward the model.