1,044 research outputs found

    Optimizing departure times in vehicle routes

    Get PDF
    Most solution methods for the vehicle routing problem with time\ud windows (VRPTW) develop routes from the earliest feasible departure time. However, in practice, temporal traffic congestions make\ud that such solutions are not optimal with respect to minimizing the\ud total duty time. Furthermore, VRPTW solutions do not account for\ud complex driving hours regulations, which severely restrict the daily\ud travel time available for a truck driver. To deal with these problems,\ud we consider the vehicle departure time optimization (VDO) problem\ud as a post-processing step of solving a VRPTW. We propose an ILP-formulation that minimizes the total duty time. The obtained solutions are feasible with respect to driving hours regulations and they\ud account for temporal traffic congestions by modeling time-dependent\ud travel times. For the latter, we assume a piecewise constant speed\ud function. Computational experiments show that problem instances\ud of realistic sizes can be solved to optimality within practical computation times. Furthermore, duty time reductions of 8 percent can\ud be achieved. Finally, the results show that ignoring time-dependent\ud travel times and driving hours regulations during the development of\ud vehicle routes leads to many infeasible vehicle routes. Therefore, vehicle routing methods should account for these real-life restrictions

    Diffusion limits for shortest remaining processing time queues

    Full text link
    We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.Comment: 19 pages; revised, fixed typos. To appear in Stochastic System

    The Multi-Depot Minimum Latency Problem with Inter-Depot Routes

    Get PDF
    The Minimum Latency Problem (MLP) is a class of routing problems that seeks to minimize the wait times (latencies) of a set of customers in a system. Similar to its counterparts in the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), the MLP is NP-hard. Unlike these other problem classes, however, the MLP is customer-oriented and thus has impactful potential for better serving customers in settings where they are the highest priority. While the VRP is very widely researched and applied to many industry settings to reduce travel times and costs for service-providers, the MLP is a more recent problem and does not have nearly the body of literature supporting it as found in the VRP. However, it is gaining significant attention recently because of its application to such areas as disaster relief logistics, which are a growing problem area in a global context and have potential for meaningful improvements that translate into reduced suffering and saved lives. An effective combination of MLP\u27s and route minimizing objectives can help relief agencies provide aid efficiently and within a manageable cost. To further the body of literature on the MLP and its applications to such settings, a new variant is introduced here called the Multi-Depot Minimum Latency Problem with Inter-Depot Routes (MDMLPI). This problem seeks to minimize the cumulative arrival times at all customers in a system being serviced by multiple vehicles and depots. Vehicles depart from one central depot and have the option of refilling their supply at a number of intermediate depots. While the equivalent problem has been studied using a VRP objective function, this is a new variant of the MLP. As such, a mathematical model is introduced along with several heuristics to provide the first solution approaches to solving it. Two objectives are considered in this work: minimizing latency, or arrival times at each customer, and minimizing weighted latency, which is the product of customer need and arrival time at that customer. The case of weighted latency carries additional significance as it may correspond to a larger number of customers at one location, thus adding emphasis to the speed with which they are serviced. Additionally, a discussion on fairness and application to disaster relief settings is maintained throughout. To reflect this, standard deviation among latencies is also evaluated as a measure of fairness in each of the solution approaches. Two heuristic approaches, as well as a second-phase adjustment to be applied to each, are introduced. The first is based on an auction policy in which customers bid to be the next stop on a vehicle\u27s tour. The second uses a procedure, referred to as an insertion technique, in which customers are inserted one-by-one into a partial routing solution such that each addition minimizes the (weighted) latency impact of that single customer. The second-phase modification takes the initial solutions achieved in the first two heuristics and considers the (weighted) latency impact of repositioning nodes one at a time. This is implemented to remove potential inefficient routing placements from the original solutions that can have compounding effects for all ensuing stops on the tour. Each of these is implemented on ten test instances. A nearest neighbor (greedy) policy and previous solutions to these instances with a VRP objective function are used as benchmarks. Both heuristics perform well in comparison to these benchmarks. Neither heuristic appears to perform clearly better than the other, although the auction policy achieves slightly better averages for the performance measures. When applying the second-phase adjustment, improvements are achieved and lead to even greater reductions in latency and standard deviation for both objectives. The value of these latency reductions is thoroughly demonstrated and a call for further research regarding customer-oriented objectives and evaluation of fairness in routing solutions is discussed. Finally, upon conclusion of the results presented in this work, several promising areas for future work and existing gaps in the literature are highlighted. As the body of literature surrounding the MLP is small yet growing, these areas constitute strong directions with important relevance to Operations Research, Humanitarian Logistics, Production Systems, and more

    The commodity-split multi-compartment capacitated arc routing problem

    Get PDF

    Integrated network routing and scheduling problem for salt trucks with replenishment before snowfall

    Get PDF
    Kar yağışı öncesinde ve sırasında yolların zamanında tuzlanması, trafik güvenliğini iyileştirmek ve trafik sıkışıklığını önlemek için önemli bir önleyici faaliyettir. Bu çalışmada, bir şehir yolu ağındaki tuz kamyonlarının rotalama ve çizelgeleme problemi ele alınmıştır. Ele alınan problem İstanbul Büyükşehir Belediyesinin yoğun kar yağışı durumlarında karşılaştığı bir operasyonel problemdir ve periyodik olarak çözülmelidir. Problemde, araç filosu tuz kapasitesi açısından heterojen araçlardan oluşmaktadır ve birden fazla tuz ikmal noktası bulunmaktadır. Hava şartları gerektirdiğinde, tuzlanması gereken yollar ve bu yollar için öncelik seviyeleri belirlenmektedir. Amaç, ağın farklı noktalarında konumlanmış olan araçların, tuzlanması gereken tüm yolları tuzlayacak şekilde ve yolların ağırlıklı tamamlanma süresini en küçükleyerek rotalanması ve çizelgelenmesidir. Tuza ihtiyacı olan her yol tek bir araç tarafından tuzlanmalıdır. Araçlar tuzlanması gereken bir yolu tuzlama yapmadan sadece geçiş yapmak amacıyla da kullanılabilir. Araçlar, tuzları bittiğinde tuz ikmal noktalarını ziyaret etmelidir. Problemin çözümü için ilk olarak bir karma tam sayılı programlama modeli geliştirilmiştir. Problem büyüklüğü arttıkça modelin performansının hızla düştüğü gözlemlenmiş ve iki aşamalı bir sezgisel yöntem geliştirilmiştir. Sezgiselin ilk aşamasında yapıcı algoritma ile olurlu bir başlangıç çözümü elde edilmektedir, ikinci aşamasında bulunan başlangıç çözümü bir komşuluk arama algoritması ile geliştirilmektedir. Çözüm yaklaşımımızın verimliliği, gerçek hayat yol ağlarını yansıtan rastgele oluşturulmuş örnekler üzerinde analiz edilmiştir.Timely salting of roads before the snowfall is an important preventive activity for improving traffic safety and avoiding traffic congestions. We study the problem of routing and scheduling of salt trucks on a city road network. The problem is motivated by the operational problem that the Istanbul Metropolitan Municipality face in case of a heavy snowfall, and thereby should be solved in a periodic manner.In this problem, the vehicle fleet consists of heterogeneous vehicles that differ in salt capacity and there are multiple salt replenishment points. At the beginning of the current planning horizon, given a set of salt needing roads with different urgency levels, the vehicles start from different points of the network (i.e., their final locations at the end of the former planning horizon) and should cover all salt needing roads with the objective of minimizing the total weighted completion time of salting operation of each service needing arc. Each service needing arc should be serviced by exactly one vehicle, however, can be traversed for deadheading by a vehicle as part of its route.Vehicles visit replenishment points when they run out of salt. We first develop a Mixed-Integer Programming model for the problem. Since the performance of the model degrades rapidly as the problem size increases, we propose a simulated annealing metaheuristic, which obtains an initial solution by a constructive heuristic in the first phase, and then improves the solution in the next phase. The efficiency of our solution approach is evaluated on randomly generated instances reflecting real life road networks
    corecore