Bike-sharing systems allow people to rent a bicycle at one of many automatic rental stations scattered around the city, use them for a short journey and return them at any station in the city. A crucial factor for the success of a bikesharing system is its ability to meet the fluctuating demand for bicycles and for vacant lockers at each station. This is achieved by means of a repositioning operation, which consists of removing bicycles from some stations and transferring them to other stations, using a dedicated fleet of trucks. Operating such a fleet in a large bike-sharing system is an intricate problem consisting of decisions regarding the routes that the vehicles should follow and the number of bicycles that should be removed or placed at each station on each visit of the vehicles. In this paper, we present our modeling approach to the problem that generalizes existing routing models in the literature. This is done by introducing a unique convex objective function as well as time-related considerations. We present two mixed integer linear program formulations, discuss the assumptions associated with each, strengthen them by several valid inequalities and dominance rules, and compare their performances through an extensive numerical study. The results indicate that one of the formulations is very effective in obtaining high quality solutions to real life instances of the problem consisting of up to 104 stations and two vehicles. Finally, we draw insights on the characteristics of good solutions.
This paper is concerned with the general dynamic lot size model, or (generalized) Wagner-Whitin model. Let n denote the number of periods into which the planning horizon is divided. We describe a simple forward algorithm which solves the general model in 0(n log n) time and 0(n) space, as opposed to the well-known shortest path algorithm advocated over the last 30 years with 0(n 2) time. A linear, i.e., 0(n)-time and space algorithm is obtained for two important special cases: (a) models without speculative motives for carrying stock, i.e., where in each interval of time the per unit order cost increases by less than the cost of carrying a unit in stock; (b) models with nondecreasing setup costs. We also derive conditions for the existence of monotone optimal policies and relate these to known (planning horizon and other) results from the literature.dynamic lot sizing models, dynamic programming, complexity
T he period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). In this paper, we consider a variation of the PVRP in which service frequency is a decision of the model. We refer to this problem as the PVRP with service choice (PVRP-SC). We explore modeling issues that arise when service choice is introduced, and suggest efficient solution methods. Contributions are made both in modeling this new variation of the PVRP and in introducing an exact solution method for the PVRP-SC. In addition, we propose a heuristic variation of the exact method to be used for larger problem instances. Computational tests show that adding service choice can improve system efficiency and customer service. We also present general insights on the impact of node distribution on the value of service choice.
In this paper we develop an optimal and a heuristic algorithm for the problem of designing a¯exible assembly line when several equipment alternatives are available. The design problem addresses the questions of selecting the equipment and assigning tasks to workstations, when precedence constraints exist among tasks. The objective is to minimize total equipment costs, given a predetermined cycle time (derived from the required production rate). We develop an exact branch and bound algorithm which is capable of solving practical problems of moderate size. The algorithm's eciency is enhanced due to the development of good lower bounds, as well as the use of some dominance rules to reduce the size of the branch and bound tree. We also suggest the use of a branch-and-bound-based heuristic procedure for large problems, and analyze the design and performance of this heuristic.
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