The multi-depot multiple set orienteering problem: an integer linear programming formulation

Abstract

In this article, we introduce a novel variant of the single Depot multiple Set Orienteering Problem (sDmSOP), which we refer to as the multi-Depot multiple Set Orienteering Problem (mDmSOP). We suggest the integer linear program (ILP) of the mDmSOP also, and analyze the impact of the Sub-tour Elimination Constraints (SECs) based on the Miller–Tucker–Zemlin (MTZ) and the Gavish-Graves (GG) model on it. The mDmSOP is most frequently encountered in distribution logistics. In mDmSOP, a fleet of travelers is utilized to serve a set of customers from a number of depots, with each traveler associated with a specific depot. The challenge is to choose the routes for each traveler to maximize the profit within a specific budget, while the profit can be earned from a set of customers only once by visiting exactly one customer. We show the simulation results conducted on the General Algebraic Modeling System (GAMS) 39.0.2, which is used to model and analyze linear, non-linear, mixed-integer, and other complex optimization problems. The Generalized Traveling Salesman Problem (GTSP) instances of up to 200 vertices are taken as the input data set for the simulations. The results show that the MTZ-based formulation takes less time than the GG-based formulation to converge to the optimal solution for the mDmSOP.