The single depot multiple set orienteering problem

Abstract

In this article, we present the single Depot multiple Set Orienteering Problem (sDmSOP), a new variant of the classical Set Orienteering Problem (SOP). A significant feature of sDmSOP is the presence of many travelers who set off from the same depot and return there at the end of their journey. The objective of the problem is to maximize the profit while remaining within the budget; hence the challenge at hand involves searching multiple paths among the mutually clustered sets for travelers. A set’s profit can be collected with a single node visit only. Supply-chain management, the bus delivery problem, etc., are just a few examples where the sDmSOP has proven useful. By simulating the instances of the Generalized Traveling Salesman Problem (GTSP) using GAMS 37.1.0, we determine the optimal profit for GTSP instances for some small and medium instances which follow the triangular and symmetric properties. We find that the use of multiple travelers is beneficial for both service provid ers and customers, as it allows service providers to offer their services to customers at a lower cost because the service provider gets a significant amount of profit using multiple travelers