Development of Heuristic Approaches for Last-Mile Delivery TSP with a Truck and Multiple Drones

Unmanned Aerial Vehicles (UAVs) are gaining momentum in many civil and military sectors. An example is represented by the logistics sector, where UAVs have been proven to be able to improve the efficiency of the process itself, as their cooperation with trucks can decrease the delivery time and reduce fuel consumption. In this paper, we first state a mathematical formulation of the Travelling Salesman Problem (TSP) applied to logistic routing, where a truck cooperates synchronously with multiple UAVs for parcel delivery. Then, we propose, implement, and compare different sub-optimal routing approaches to the formulated mFSTSP (multiple Flying Sidekick Travelling Salesman Problem) since the inherent combinatorial computational complexity of the problem makes it unattractable for commercial Mixed-Integer Linear Programming (MILP) solvers. A local search algorithm, two hybrid genetic algorithms that permutate feasible and infeasible solutions, and an alternative ad-hoc greedy method are evaluated in terms of the total delivery time of the output schedule. For the sake of the evaluation, the savings in terms of delivery time over the well-documented truck-only TSP solution are investigated for each proposed routing solution, and this is repeated for two different scenarios. Monte Carlo simulations corroborate the results

Developments in linear and integer programming

In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies

Zero-one IP problems: Polyhedral descriptions & cutting plane procedures

A systematic way for tightening an IP formulation is by employing classes of linear inequalities that define facets of the convex hull of the feasible integer points of the respective problems. Describing as well as identifying these inequalities will help in the efficiency of the LP-based cutting plane methods. In this report, we review classes of inequalities that partially described zero-one poly topes such as the 0-1 knapsack polytope, the set packing polytope and the travelling salesman polytope. Facets or valid inequalities derived from the 0-1 knapsack and the set packing polytopes are algorithmically identifie

Centralized versus market-based approaches to mobile task allocation problem: State-of-the-art

Centralized approach has been adopted for finding solutions to resource allocation problems (RAPs) in many real-life applications. On the other hand, market-based approach has been proposed as an alternative to solve the problem due to recent advancement in ICT technologies. In spite of the existence of some efforts to review the pros and cons of each approach in RAPs, the studies cannot be directly applied to specific problem domains like mobile task allocation problem which is characterised with high level of uncertainty on the availability of resources (workers). This paper aims to review existing studies on task allocation problems(TAPs) focusing on those two approaches and their comparison and identify major issues that need to be resolved for comparing the two approaches in mobile task allocation problems. Mobile Task Allocation Problem (MTAP) is defined and its problematic structures are explained in relation with task allocation to mobile workers. Solutions produced by each approach to some applications and variations of MTAP are also discussed and compared. Finally, some future research directions are identified in order to compare both approaches in function of uncertainty emerging from the mobile nature of the MTAP

A hybrid heuristic solving the traveling salesman problem

This paper presents a new hybrid heuristic for solving the Traveling Salesman Problem, The algorithm is designed on the frame of a general optimization procedure which acts upon two steps, iteratively. In first step of the global search, a feasible tour is constructed based on insertion approach. In the second step the feasible tour found at the first step, is improved by a local search optimization procedure. The second part of the paper presents the performances of the proposed heuristic algorithm, on several test instances. The statistical analysis shows the effectiveness of the local search optimization procedure, in the graphical representation.peer-reviewe

Exact algorithms for the order picking problem

Order picking is the problem of collecting a set of products in a warehouse in a minimum amount of time. It is currently a major bottleneck in supply-chain because of its cost in time and labor force. This article presents two exact and effective algorithms for this problem. Firstly, a sparse formulation in mixed-integer programming is strengthened by preprocessing and valid inequalities. Secondly, a dynamic programming approach generalizing known algorithms for two or three cross-aisles is proposed and evaluated experimentally. Performances of these algorithms are reported and compared with the Traveling Salesman Problem (TSP) solver Concorde

The 2-period balanced traveling salesman problem

In the 2-period Balanced Traveling Salesman Problem (2B-TSP), the customers must be visited over a period of two days: some must be visited daily, and the others on alternate days (even or odd days); moreover, the number of customers visited in every tour must be balancedâ, i.e. it must be the same or, alternatively, the difference between the maximum and the minimum number of visited customers must be less than a given threshold. The salesman's objective is to minimize the total distance travelled over the two tours. Although this problem may be viewed as a particular case of the Period Traveling Salesman Problem, in the 2-period Balanced TSP the assumptions allow for emphasizing on routing aspects, more than on the assignment of the customers to the various days of the period. The paper proposes two heuristic algorithms particularly suited for the case of Euclidean distances between the customers. Computational experiences and a comparison between the two algorithms are also given.