Time constrained maximal covering salesman problem with weighted demands and partial coverage

Abstract

In a routing framework, it may not be viable to visit every single customer separately due to resource limitations or efficiency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in which the aim is to find a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide flow and cut formulations and derive valid inequalities. Since the connectivity constraints and the proposed valid inequalities are exponential in the size of the problem, we devise different branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the effectiveness of the proposed valid inequalities in terms of strengthening the linear relaxation bounds as well as speeding up the solution procedure. Moreover, the results indicate the superiority of using a branch-and-cut methodology over a flow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments.

A Two-Echelon Cooperated Routing Problem for a Ground Vehicle and Its Carried Unmanned Aerial Vehicle

“…Mufalli [ 10 ] constructed a new mathematical model for UAV routing to collect data from simultaneous sensors. Similar research on data collection was investigated by Ozbaygin [ 11 ], which was studied as a time-constrained maximal covering salesman problem. Avellar [ 12 ] developed a group of UAVs for area coverage and Vanegas [ 13 ] researched the routing problem with environmental uncertainty.…”

Mixed-integer programming approaches for the time-constrained maximal covering routing problem

“…In Naji-Azimi and Salari (2014), the authors presented a flowbased MIP model and some heuristics for the TCMCSP ( Amiri and Salari ( 2019) is basically the extension of the approaches in Naji-Azimi and Salari (2014) to the TCMCRP). In Ozbaygin et al (2016), an exact solution algorithm based on GSECs for a variant of the TCMCSP was proposed.…”

“…The following variable fixing exploits the distance limit L, similar ideas have been used in Bianchessi et al (2018); Dang et al (2013); El-Hajj et al (2016) for the TOP and in Ozbaygin et al (2016) for the TCMCSP, they can be seen as specialcase of the path inequalities for the OP proposed in Fischetti et al (1998).…”

Exact algorithms for budgeted prize-collecting covering subgraph problems

“…It distinguishes between customer vertices and facility vertices, and seeks to find a tour through the facility vertices such that its routing cost is not greater than a given budget, and it maximizes the number of customers who are not further away from the closest visited facility than a given value. The TCMCSP in its original form does not involve prizes, but it was extended to a budgeted prize-collecting problem by Ozbaygin et al [44], who introduced the TCMCSP with partial cover: no distinction is made between customers and facilities, and every vertex has its own prize, to be collected entirely if the vertex is in the tour, or instead partially if the vertex lies within a given distance from a vertex in the tour. v. Lastly, the Connected Facility Location (conFL) problem arises when a graph consists of facility vertices and customer vertices, and costs are associated to opening facilities, assigning customers to facilities and connecting the facilities.…”

“…profit associated with a customer that is referred to a pick-up point rather than served directly, can be considered to be only a certain fraction of the profit in case of home delivery, mainly due to a loss of goodwill from the part of the customer. Specifically for this setting, a more accurate objective is the total collected profit; the resulting maximization problem is known as the Time Constrained Maximum Covering Salesman problem (TCMCSP) [42,44].…”