Güneş Erdoğan

Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem

The generalized vehicle routing problem (GVRP) consists of finding a set of routes for a number of capacitated vehicles on a graph where the vertices are partitioned into clusters with given demands, such that the total cost of travel is minimized and all demands are met. This paper describes and compares four new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential-size sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented.

An Exact Algorithm for the Static Rebalancing Problem arising in Bicycle Sharing Systems

Bicycle sharing systems can significantly reduce traffic, pollution, and the need for parking spaces in city centers. One of the keys to success for a bicycle sharing system is the efficiency of rebalancing operations, where the number of bicycles in each station has to be restored to its target value by a truck through pickup and delivery operations. The Static Bicycle Rebalancing Problem aims to determine a minimum cost sequence of stations to be visited by a single vehicle as well as the amount of bicycles to be collected or delivered at each station. Multiple visits to a station are allowed, as well as using stations as temporary storage. This paper presents an exact algorithm for the problem and results of computational tests on benchmark instances from the literature. The computational experiments show that instances with up to 60 stations can be solved to optimality within 2 hours of computing time.

Scheduling ambulance crews for maximum coverage

This paper addresses the problem of scheduling ambulance crews in order to maximize the coverage throughout a planning horizon. The problem includes the subproblem of locating ambulances to maximize expected coverage with probabilistic response times, for which a tabu search algorithm is developed. The proposed tabu search algorithm is empirically shown to outperform previous approaches for this subproblem. Two integer programming models that use the output of the tabu search algorithm are constructed for the main problem. Computational experiments with real data are conducted. A comparison of the results of the models is presented.

The static bicycle relocation problem with demand intervals

This study introduces the Static Bicycle Relocation Problem with Demand Intervals (SBRP-DI), a variant of the One Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP). In the SBRP-DI, the stations are required to have an inventory of bicycles lying between given lower and upper bounds and initially have an inventory which does not necessarily lie between these bounds. The problem consists of redistributing the bicycles among the stations, using a single capacitated vehicle, so that the bounding constraints are satisfied and the repositioning cost is minimized. The real-world application of this problem arises in rebalancing operations for shared bicycle systems. The repositioning subproblem associated with a fixed route is shown to be a minimum cost network problem, even in the presence of handling costs. An integer programming formulation for the SBRP-DI are presented, together with valid inequalities adapted from constraints derived in the context of other routing problems and a Benders decomposition scheme. Computational results for instances adapted from the 1-PDTSP are provided for two branch-and-cut algorithms, the first one for the full formulation, and the second one with the Benders decomposition.

The pickup and delivery traveling salesman problem with first-in-first-out loading

This paper addresses a variation of the traveling salesman problem with pickup and delivery in which loading and unloading operations have to be executed in a first-in-first-out fashion. It provides an integer programming formulation of the problem. It also describes five operators for improving a feasible solution, and two heuristics that utilize these operators: a probabilistic tabu search algorithm, and an iterated local search algorithm. The heuristics are evaluated on data adapted from TSPLIB instances.

Hybrid metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This paper presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a hybrid genetic search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored, by means of bi-directional dynamic programming, sequence concatenation, and appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale instances. Recommendations on the choice of algorithm are provided, based on average cluster size.

The Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs

This paper introduces a new variant of the one-to-many-to-one single vehicle pickup and delivery problems (SVPDP) that incorporates the handling cost incurred when rearranging the load at the customer locations. The simultaneous optimization of routing and handling costs is difficult, and the resulting loading patterns are hard to implement in practice. However, this option makes economical sense in contexts where the routing cost dominates the handling cost. We have proposed some simplified policies applicable to such contexts. The first is a two-phase heuristic in which the tour having minimum routing cost is initially determined by optimally solving an SVPDP, and the optimal handling policy is then determined for that tour. In addition, branch-and-cut algorithms based on integer linear programming formulations are proposed, in which routing and handling decisions are simultaneously optimized, but the handling decisions are restricted to three simplified policies. The formulations are strengthened by means of problem specific valid inequalities. The proposed methods have been extensively tested on instances involving up to 25 customers and hundreds of items. Our results show the impact of the handling aspect on the customer sequencing and indicate that the simplified handling policies favorably compare with the optimal one.

A branch-and-cut algorithm for quadratic assignment problems based on linearizations

Abstract The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this study, we focus on the Koopmans–Beckmann formulation and exploit the structure of the flow and distance matrices based on a flow-based linearization technique that we propose. We present two new IP formulations based on the flow-based linearization technique that require fewer variables and yield stronger lower bounds than existing formulations. We strengthen the formulations with valid inequalities and report computational experience with a branch-and-cut algorithm. The proposed method performs quite well on QAPLIB instances for which certain metrics (indices) that we proposed that are related to the degree of difficulty of solving the problem are relatively high ( ⩾ 0.3 ). Many of the well-known instances up to size 25 from the QAPLIB (e.g. nug24, chr25a) are in this class and solved in a matter of days on a single PC using the proposed algorithm.

The orienteering problem with variable profits

This article introduces, models, and solves a generalization of the orienteering problem, called the the orienteering problem with variable profits (OPVP). The OPVP is defined on a complete undirected graph G = (V,E), with a depot at vertex 0. Every vertex i∈V \{0} has a profit pi to be collected, and an associated collection parameter αi∈[0, 1]. The vehicle may make a number of “passes,” collecting 100αi percent of the remaining profit at each pass. In an alternative model, the vehicle may spend a continuous amount of time at every vertex, collecting a percentage of the profit given by a function of the time spent. The objective is to determine a maximal profit tour for the vehicle, starting and ending at the depot, and not exceeding a travel time limit.

The Attractive Traveling Salesman Problem

In the Attractive Traveling Salesman Problem the vertex set is partitioned into facility vertices and customer vertices. A maximum profit tour must be constructed on a subset of the facility vertices. Profit is computed through an attraction function: every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer vertices, and the attractiveness of the facility vertex. A gravity model is used for computing the profit attraction. The problem is formulated as an integer non-linear program. A linearization is proposed and strengthened through the introduction of valid inequalities, and a branch-and-cut algorithm is developed. A tabu search algorithm is also implemented. Computational results are reported.