Traveling Salesman Problem with a Drone Station

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 산업공학과, 2018. 2. 문일경.The importance of drone delivery services is increasing. However, the operational aspects of drone delivery services have not been studied extensively. Specifically, with respect to truck-drone systems, researchers have not given sufficient attention to drone facilities because of the limited drone flight range around a distribution center. In this paper, we propose a truck-drone system to overcome the flight-range limitation. We define a drone station as the facility where drones and charging devices are stored, usually far away from the package distribution center. The traveling salesman problem with a drone station (TSP-DS) is developed based on mixed integer programming. Fundamental features of the TSP-DS are analyzed and route distortion is defined. We show that the model can be divided into independent traveling salesman and parallel identical machine scheduling problems for which we derive two solution approaches. Computational experiments with randomly generated instances show the characteristics of the TSP-DS and suggest that our decomposition approaches effectively deal with TSP-DS complexity problems.Chapter 1. Introduction 1 Chapter 2. Literature Review 5 Chapter 3. Truck-drone routing Problem 9 3.1 Notation 10 3.2 Mathematical formulation 12 Chapter 4. Fundamental Features of the TSP-DS 14 4.1 Route distortion 14 4.2 Condition for the elimination of route distortion 18 4.3 Decomposition of the TSP-DS 20 Chapter 5. Computational Experiments 24 5.1 Computation times 25 5.2 Comparison between the TSP-DS and TSP 28 5.3 Number of drones in a drone station 30 5.4 Discussion 32 Chapter 6. Conclusions 33 References 35 초록 40Maste

Valid inequalities for unrelated parallel machines scheduling with precedence constraints

International audienceThis paper deals with the mathematical modeling of a scheduling problem for unrelated parallel machines with precedence constraints in order to minimize the makespan (Cmax). This study was motivated by the quality of the Integer Program based on the interval graph. Three families of inequalities are proposed. The first two inequalities based on the idea of the precedence jobs and the third based on the shortest processing time(SPT). We studied the validity of the new inequalities and strength them by checking the linear combination. After an exhaustive computational and statistical analysis we can conclude that the addition of these inequalities decreases the computational requirements to obtain the optimal solution in many cases