A tabu search heuristic for the vehicle routing problem with private fleet and common carrier

This paper describes a tabu search heuristic for a vehicle routing problem where the owner of a private fleet can either visit a customer with one of his vehicles or assign the customer to a common carrier. The owner’s objective is to minimize the variable and fixed costs for operating his fleet plus the total costs charged by the common carrier. The proposed tabu search is shown to outperform the best approach reported in the literature on 34 benchmark instances with a homogeneous fleet.     

A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers

The purpose of this article is to propose a perturbation metaheuristic for the vehicle routing problem with private fleet and common carrier (VRPPC). This problem consists of serving all customers in such a way that (1) each customer is served exactly once either by a private fleet vehicle or by a common carrier vehicle, (2) all routes associated with the private fleet start and end at the depot, (3) each private fleet vehicle performs only one route, (4) the total demand of any route does not exceed the capacity of the vehicle assigned to it, and (5) the total cost is minimized. This article describes a new metaheuristic for the VRPPC, which uses a perturbation procedure in the construction and improvement phases and also performs exchanges between the sets of customers served by the private fleet and the common carrier. Extensive computational results show the superiority of the proposed metaheuristic over previous methods.     

A tabu search heuristic for the split delivery vehicle routing problem with production and demand calendars

The purpose of this article is to propose a tabu search heuristic for the split delivery Vehicle Routing Problem with Production and Demand Calendars (VRPPDC). This new problem consists of determining which customers will be served by a common carrier, as well as the delivery routes for those served by the private fleet, in order to minimize the overall transportation and inventory costs. We first model this problem and then propose a simple decomposition procedure that can be used to provide a starting solution. Next, we introduce a new tabu search heuristic and we describe two new neighbor reduction strategies. Finally, we present the results of our extensive computational tests. According to these tests, our reduction strategies are efficient not only at reducing computing time but also at improving the overall solution quality.     

Alternate mode dispatching: the impact of cost minimisation

When a shipper may use a variety of trucks to ship less-than-truckload shipments, shipping cost is the relevant criterion for evaluating alternate dispatches. This point is demonstrated by optimally solving 15 dispatching problems from industry in two ways, once minimising distance, and second time minimising costs, when a mixed private fleet and a common carrier are available. The distance minimising dispatches are, on the average, 35% more expensive than the corresponding cost minimising ones, but part of this difference stems from assumptions which are necessary to compare these two criteria.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

Planung der geringsten Kosten täglicher lokaler Lieferungen. Ein Beispiel für die Anwendung der Dynamischen Planung

Zusammenfassung Die Planung der täglichen Lieferung von Waren vom Erzeuger zum Verbraucher unter Benützung von Transportunternehmen und des firmeneigenen Lastwagenparkes stellt ein ziemlich schwieriges alltägliches Entscheidungsproblem dar, da die Variablen der Zuweisung diskret und normalerweise zahlreich sind. Bei verschieden großen Lastwagenparks ist im Hinblick auf die geringsten Gesamt-Lieferkosten nicht unbedingt jene Zuteilung von Lieferaufträgen die günstigste, bei welcher die eigenen Lastwagen täglich voll ausgelastet werden, und die von Tag zu Tag anzusetzenden Lieferungen können hinsichtlich ihrer Art und Anzahl stark variieren.Ein solches Planungsproblem wurde im Detail studiert. Die vorliegende Unterlage enthält die Ergebnisse dieser Untersuchung.Mit Hilfe von Rekursionsmethoden (Dynamische Planung) und unter genauer Berücksichtigung der speziellen Eigenschaften der betreffenden Kostenfunktion kann man eine einfache Regel für die Wahl jener Lieferpläne, die ein ungefähres Optimum darstellen, finden, sowie einen Ausdruck für die Grenze der Abweichung von den genauen sich ergebenden Mindestkosten festlegen. Klarerweise ist diese Grenze sehr eng gesteckt, und es ist weder wünschenswert noch notwendig, die Planung auf die genauen Mindestkosten abzustellen, vor allem im Hinblick auf die Tatsache, daß der Möglichkeit, präzise Kosteninformationen zu erhalten, praktische Grenzen gesetzt sind und es sehr schwer ist, täglich eine genaue Berechnung des Optimalplanes durchzuführen.Sobald eine Entscheidungsregel für einen annähernd optimalen Tages-Lieferplan aufgestellt ist, ergibt sich natürlich die Frage der Optimalgröße des eigenen Lastwagenparks. Man kann für verschiedene hypothetische Größen des Wagenparks Kostenvergleichsberechnungen in bezug auf die im unmittelbar vergangenen Jahr vorhandene Liefersituation anstellen, wobei man die Entscheidungsregel für den annähernd optimalen Lieferplan als Grundlage für die Bestimmung der Mindest-Betriebskosten für jeden einzelnen Wagenpark nimmt und Lastwagen von Jahr zu Jahr aus dem Dienst zieht oder neu ankauft, um den Wagenpark in der Nähe der Optimalgröße zu halten. Der hier vorgeschlagene Planungsabschnitt, nämlich ein Jahr, kann länger oder kürzer gewählt werden, je nach den näheren Umständen des Marktes und den Usancen bei Kapitalinvestitionen und deren Versicherung. Auf diese Weise kann man erreichen, daß die Leiferkosten ziemlich in der Nähe des Minimums gehalten werden, vorausgesetzt daß die saisonbedingten Schwankungen in der durchschnittlichen Anzahl und der Art der täglichen Lieferungen nicht von Planungsperiode (d. h. Jahr) zu Planungsperiode allzu sehr verschieden sind. Wenn die Unterschiede von Jahr zu Jahr groß sind, kann die Aufgabe, einen optimalen Wagenpark zu finden, tatsächlich sehr kompliziert werden, da die Vorhersage der saisonbedingten Schwankungen im durchschnittlichen Tagesvolumen allein nicht genügt, sondern evtl. auch Änderungen in der Art (d. h. Lieferzeit und Lieferumfang) der Lieferungen ebenfalls vorhergesagt werden müssen.Gleichgültig, wie genau die Optimalgröße des Lastwagenparks bestimmt werden kann, bleibt es doch wichtig, eine annähernd optimale Entscheidungsregel für die Verteilung der täglichen Lieferungen auf eigene Lastwagen und Transportunternehmen zu finden. Die Einsatzentscheidung muß Tag für Tag getroffen werden, gleichgültig, wie zutreffend die Entscheidung über die Investition in firmeneigenen Lastwagen war; dabei kann es um beträchtliche Geldsummen gehen, vor allem in unserem Beispiel, wo die Lieferkosten einen wesentlichen Teil der Gesamtkosten ausmachten. In manchen Fällen lassen sich die größten Einsparungen durch eine richtige Einschätzung der Optimalgröße des firmeneigenen Lastwagenparks erzielen.

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Summary The scheduling, between common carrier and private fleet truck, of local delivery of product from manufacturer to customer is a daily decision problem of some complexity, because the assignment variables are discreet and ordinarily many in number. For any given size of private truck fleet, the most efficient assignment of deliveries (in the sense of least total delivery costs) is not necessarily one in which a private fleet is used to capacity each day, and the deliveries to be scheduled each day may be highly variable in number and kind.This scheduling problem has been studied in detail for a manufacturer of glass containers. The results of this study are reported herein.By use of recursion methods (Dynamic programming) and explicit consideration of the special properties of the cost function involved, a simple decision rule is found for scheduling deliveries which is approximately optimum, and an expression is given for a bound upon the deviation from exact minimum cost thereby entailed. The bound is evidently small and an exact minimum cost scheduling is neither desirable nor required, particularly in view of the practical limitations of getting precise cost data and the difficulties of making daily an exact calculation of optimum scheduling.Having determined an approximately optimum daily scheduling decision rule, the question of optimum private, truck fleet size naturally arises. Comparative cost calculations may be made for various hypothetical private fleet sizes related to the deliveries encountered during an immediately previous year, using the near optimum daily scheduling rule as a basis for determining minimum operating costs connected with each fleet size, and private trucks may be retired or purchased annually to control the private fleet at near optimum size. The planning period suggested, i. e. one year, may be increased or decreased, depending upon the market circumstances and practices used for making and underwriting capital investments. The control thus obtained will be comparatively close to a minimum for delivery costs, provided the seasonal variation of average daily number and character of deliveries do not fluctuate violently from one planning period (e. g. year) to the next. If the annual variation is great, the problem of optimizing fleet size may be complex indeed, because forecasts of the seasonal variation of average daily volume alone are not sufficient. Changes in the character (i. e. destination and related volume of goods) of deliveries may have to be forecasted.Regardless of how well an optimum fleet size can be determined, it is important to have an approximately optimum daily decision rule for assignment of deliveries between private truck and common carrier. The operating decision to be made arises day by day, no matter how well the decision for investment in company trucks has been made, and considerable funds may be at stake, particularly in the case study presented here where delivery costs are a substantial part of total costs. The largest savings may be derived, in some instances, from correctly assessing the optimum size of private truck fleet.

     

An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls

In this article, a visual interactive approach based on a new greedy randomised adaptive memory programming search (GRAMPS) algorithm is proposed to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) and a new extension of the HFFVRP, which is called heterogeneous fixed fleet vehicle routing problem with backhauls (HFFVRPB). This problem involves two different sets of customers. Backhaul customers are pickup points and linehaul customers are delivery points that are to be serviced from a single depot by a heterogeneous fixed fleet of vehicles, each of which is restricted in the capacity it can carry, with different variable travelling costs.     

Scheduling policies for a repair shop problem

In this paper, we analyze a repair shop serving several fleets of machines that fail from time to time. To reduce downtime costs, a continuous-review spare machine inventory is kept for each fleet. A spare machine, if available on stock, is installed instantaneously in place of a broken machine. When a repaired machine is returned from the repair shop, it is placed in inventory for future use if the fleet has the required number of machines operating. Since the repair shop is shared by different fleets, choosing which type of broken machine to repair is crucial to minimize downtime and holding costs. The optimal policy of this problem is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost and base-stock level for each spare machine inventory. As an alternative, we propose the dynamic Myopic(R) policy, which is easy to implement, yielding costs very close to the optimal. Most of the time it outperforms the static first-come-first-served, and preemptive-resume priority policies. Additionally, via our numerical study, we demonstrate that repair shop pooling is better than reserving a repair shop for each fleet.     

A reactive variable neighborhood tabu search for the heterogeneous fleet vehicle routing problem with time windows

This paper presents a solution methodology for the heterogeneous fleet vehicle routing problem with time windows. The objective is to minimize the total distribution costs, or similarly to determine the optimal fleet size and mix that minimizes both the total distance travelled by vehicles and the fixed vehicle costs, such that all problem’s constraints are satisfied. The problem is solved using a two-phase solution framework based upon a hybridized Tabu Search, within a new Reactive Variable Neighborhood Search metaheuristic algorithm. Computational experiments on benchmark data sets yield high quality solutions, illustrating the effectiveness of the approach and its applicability to realistic routing problems. This work is supported by the General Secretariat for Research and Technology of the Hellenic Ministry of Development under contract GSRT NM-67.     

Incorporating the pricing decisions into the dynamic fleet management problem

This paper presents a model to coordinate the pricing and fleet management decisions of a freight carrier. We consider a setting where the loads faced by the carrier over a certain time horizon are deterministic functions of the prices. We want to find what prices the carrier should charge so that its pricing and fleet management decisions jointly maximize the profits. Our solution approach is an iterative one. At each iteration, we solve the fleet management problem with fixed prices, and then, adjust these prices by using the primal-dual solution to the fleet management problem so as to obtain ‘better’ prices. Computational experiments show that our approach yields high-quality solutions and can efficiently be applied on large problems.     

Minimizing fleet operating costs for a container transportation company

This paper focuses on a fleet management problem that arises in container trucking industry. From the container transportation company perspective, the present and future operating costs to minimize can be divided in three components: the routing costs, the resource (i.e., driver and truck) assignment costs and the container repositioning costs (i.e., the costs of restoring a given container fleet distribution over the serviced territory, as requested by the shippers that own the containers).This real-world problem has been modeled as an integer programming problem. The proposed solution approach is based on the decomposition of this problem in three simpler sub-problems associated to each of the costs considered above.Numerical experiments on randomly generated instances, as well as on a real-world data set of an Italian container trucking company, are presented.     

Dynamic fleet scheduling with uncertain demand and customer flexibility

We develop a dynamic fleet scheduling model that demonstrates how a carrier can improve fleet utilization. The fleet scheduling model presented by Lee et?al. (Eur J Oper Res 218(1):261–269, 2012) minimizes (1) a carrier’s fleet size and (2) the penalty associated with the alternative delivery times selected. The model is static since requests are collected over time and processed together. In this paper we present a stochastic, dynamic version of the fleet reduction model. As demand is revealed throughout an order horizon, decisions are made in stages by sampling anticipated demand to avoid recourse penalties in later stages. Based on computational experiments we find the following:

1. Modeling stochasticity improves the quality of solutions relative to the analogous model that does not include stochasticity. Counter-intuitively, an order lead-time distribution in which most loads are requested early can negatively impact optimal solution costs.
2. The stochastic model produces good results without requiring prohibitively large numbers of demand scenarios.
3. Consignees that place orders early in the order horizon are more often assigned their requested delivery times than those who place orders late.

     

A worst-case analysis for the split delivery vehicle routing problem with minimum delivery amounts

In the vehicle routing problem (VRP), a fleet of vehicles must service the demands of customers in a least-cost way. In the split delivery vehicle routing problem (SDVRP), multiple vehicles can service the same customer by splitting the deliveries. By allowing split deliveries, savings in travel costs of up to 50 % are possible, and this bound is tight. Recently, a variant of the SDVRP, the split delivery vehicle routing problem with minimum delivery amounts (SDVRP-MDA), has been introduced. In the SDVRP-MDA, split deliveries are allowed only if at least a minimum fraction of a customer’s demand is delivered by each visiting vehicle. We perform a worst-case analysis on the SDVRP-MDA to determine tight bounds on the maximum possible savings.     

The multiple frequency delivery operations in the time-definite delivery industry

The pure hub-and-spoke network is an efficient network structure for time-definite freight delivery common carriers. Centres perform pickup and delivery functions, while hubs consolidate partial loads. This substantially reduces the transportation costs with only a small increase in the handling cost. In Taiwan, as well as in the US, carriers run their delivery operations once a day. As a result, the feeder fleet is under-utilized. This research studied the impact of multiple frequency delivery operations on the feeder fleet size. We formulated line-haul operations planning for multiple frequency delivery operations as an integer programme. We developed an α-optimal implicit enumeration algorithm and used two small networks from the third largest carrier in Taiwan for numerical testing. The results demonstrated a smaller feeder fleet size compared with the single frequency delivery operations.     

Balancing fleet size and repositioning costs in LTL trucking

This paper develops an optimization modeling approach for analyzing the trade-off between the cost of a larger fleet of tractors and the cost of repositioning tractors for a trucking company operating a consolidation network, such as a less-than-truckload (LTL) company. Specifically, we analyze the value of using extra tractor repositioning moves (in addition to the ones required to balance resources throughout the network) to reduce the fixed costs of owning or leasing a tractor fleet during a planning horizon. We develop network flow optimization models, some with side constraints and nonlinear objective functions, using event-based, time-expanded networks to determine appropriate fleet sizes and extra repositioning moves under different repositioning strategies, and we compare the optimal costs of the strategies. For repositioning costs, two different cost schemes are explored: one linear and one nonlinear. Computational experiments using real data from a national LTL carrier compare the total system costs obtained with four different strategies and show that extra repositioning may indeed enable fleet size reductions and concomitant cost savings.     

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

The two-dimensional loading heterogeneous fleet vehicle routing problem (2L-HFVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles. These vehicles have different capacities, fixed and variable operating costs, length and width in dimension, and two-dimensional loading constraints. The objective of this problem is to minimize transportation cost of designed routes, according to which vehicles are used, to satisfy the customer demand. In this study, we proposed a simulated annealing with heuristic local search (SA_HLS) to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints in 2L-HFVRP. To speed up the search process, a data structure was used to record the information related to loading feasibility. The effectiveness of SA_HLS was tested on benchmark instances derived from the two-dimensional loading vehicle routing problem (2L-CVRP). In addition, the performance of SA_HLS was also compared with three other 2L-CVRP models and four HFVRP methods found in the literature.     

Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints

In this paper, we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel; the resulting problem is called the multiple traveling repairmen problem with distance constraints (MTRPD). In the MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once. The objective is to minimize the total waiting time of all customers after the vehicles leave the depot. To optimally solve the MTRPD, we propose a new exact branch-and-price-and-cut algorithm, where the column generation pricing subproblem is a resource-constrained elementary shortest-path problem with cumulative costs. An ad hoc label-setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem. Computational results show the effectiveness of the proposed method. The optimal solutions to 179 out of 180 test instances are reported in this paper. Our computational results serve as benchmarks for future researchers on the problem.     

Periodic airline fleet assignment with time windows,spacing constraints,and time dependent revenues

Given the sets of flights and aircraft of an airline carrier, the fleet assignment problem consists of assigning the most profitable aircraft type to each flight. In this paper we propose a model for the periodic fleet assignment problem with time windows in which departure times are also determined. Anticipated profits depend on the schedule and the selection of aircraft types. In addition, short spacings between consecutive flights which serve the same origin–destination pair of airports are penalized. We propose a non-linear integer multi-commodity network flow formulation. We develop new branch-and-bound strategies which are embedded in our branch-and-price solution strategy. Finally, we present computational results for periodic daily schedules on three real-world data sets.     

Vehicle routing considerations in distribution system design

In Distribution System Design, one minimizes total costs related to the number, locations and sizes of warehouses, and the assignment of warehouses to customers. The resulting system, while optimal in a strategic sense, may not be the best choice if operational aspects such as vehicle routing are also considered.We formulate a multicommodity, capacitated distribution planning model as anon-linear, mixed integer program. Distribution from factories to customers is two-staged via depots (warehouses) whose number and location must be chosen. Vehicle routes from depots to customers are established by considering the “fleet size and mix” problem, which also incorporates strategic decisions on fleet makeup and vehicle numbers of each type. This problem is solved as a generalized assignment problem, within an algorithm for the overall distribution/routing problem that is based on Benders decomposition. We furnish two version of our algorithm denoted Technique I and II. The latter is an enhaancement of the former and is employed at the user's discretion. Computer solution of test problems is discussed.     

A simulation study of the fleet sizing problem arising in offshore anchor handling operations

A fleet sizing problem arising in anchor handling operations related to movement of offshore mobile units is presented in this paper. Typically, the intensity of these operations is unevenly spread throughout the year. The operations are performed by dedicated vessels, which can be hired either on the long-term basis or on the spot market. Spot rates are frequently a magnitude higher than long-term rates, and vessels are hired on the spot market if there is a shortage of long-term vessels to cover the ongoing anchor handling operations. Deciding the cost-optimal fleet of vessels on the long-term hire to cover future operations is a problem facing offshore oil and gas operators. This decision has a heavy economic impact as anchor handling vessels are among the most expensive ones. The problem is highly stochastic because durations of anchor handling operations vary and depend on uncertain weather conditions. Moreover, future spot rates for anchor handling vessels are extremely volatile. The objective of this paper is to describe a simulation model for the fleet sizing problem. The study was initiated by the largest Norwegian offshore oil and gas operator and has received considerable acceptance among the planners.