A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

Heuristics for the multi-depot petrol station replenishment problem with time windows

In the multi-depot petrol station replenishment problem with time windows (MPSRPTW), the delivery of petroleum products stored in a number of different petroleum depots to a set of petrol distribution stations has to be optimized. Each depot has its own fleet of heterogeneous and compartmented tank trucks. Stations specify their demand by indicating the minimum and maximum quantities to be delivered for each ordered product and require the delivery within a predetermined time window. Several inter-related decisions must be made simultaneously in order to solve the problem. For this problem, the set of feasible routes to deliver all the demands, the departure depot for each route, the quantities of each product to be delivered, the assignment of these routes to trucks, the time schedule for each trip, and the loading of the ordered products to different tanks of the trucks used need to be determined. In this paper, we propose a mathematical model that selects, among a set of feasible trips, the subset that allows the delivery of all the demands while maximizing the overall daily net revenue. If this model is provided with all possible feasible trips, it determines the optimal solution for the corresponding MPSRPTW. However, since the number of such trips is often huge, we developed a procedure to generate a restricted set of promising feasible trips. Using this restricted set, the model produces a good but not necessarily optimal solution. Thus the proposed solution process can be seen as a heuristic. We report the results of the extensive numerical tests carried out to assess the performance of the proposed heuristic. In addition, we show that, for the special case of only one depot, the proposed heuristic outperforms a previously published solution method.     

An intermodal multicommodity routing problem with scheduled services

We study a multicommodity routing problem faced by an intermodal service operator that uses ground and maritime transportation. Given a planning horizon, a?set of commodities to be picked up at their release times and to be delivered not later than their duedates, the problem is to decide on routes for these commodities using trucks and scheduled and capacitated maritime services at minimum cost of transportation and stocking at the seaports. Two mixed integer programming formulations and valid inequalities are proposed for this problem. The results of a computational study to evaluate the strength of the linear programming relaxations and the solution times are reported.     

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.     

A column generation approach for determining optimal fleet mix,schedules, and transshipment facility locations for a vessel transportation problem

This paper presents a column generation approach for a storage replenishment transportation-scheduling problem. The problem is concerned with determining an optimal combination of multiple-vessel schedules to transport a product from multiple sources to different destinations based on demand and storage information at the destinations, along with cost-effective optimal strategic locations for temporary transshipment storage facilities. Such problems are faced by oil/trucking companies that own a fleet of vessels (oil tankers or trucks) and have the option of chartering additional vessels to transport a product (crude oil or gasoline) to customers (storage facilities or gas stations) based on agreed upon contracts. An integer-programing model that determines a minimum-cost operation of vessels based on implicitly representing feasible shipping schedules is developed in this paper. Due to the moderate number of constraints but an overwhelming number of columns in the model, a column generation approach is devised to solve the continuous relaxation of the model, which is then coordinated with a sequential fixing heuristic in order to solve the discrete problem. Computational results are presented for a range of test problems to demonstrate the efficacy of the proposed approach.     

A two-phase algorithm for the partial accessibility constrained vehicle routing problem

In the partial accessibility constrained vehicle routing problem, a route can be covered by two types of vehicles, i.e. truck or truck + trailer. Some customers are accessible by both vehicle types, whereas others solely by trucks. After introducing an integer programming formulation for the problem, we describe a two-phase heuristic method which extends a classical vehicle routing algorithm. Since it is necessary to solve a combinatorial problem that has some similarities with the generalized assignment problem, we propose an enumerative procedure in which bounds are obtained from a Lagrangian relaxation. The routine provides very encouraging results on a set of test problems.     

Yard crane scheduling in port container terminals

Yard cranes are the most popular container handling equipment for loading containers onto or unloading containers from trucks in container yards of land scarce port container terminals. However, such equipment is bulky, and very often generates bottlenecks in the container flow in a terminal because of their slow operations. Hence, it is essential to develop good yard crane work schedules to ensure a high terminal throughput. This paper studies the problem of scheduling a yard crane to perform a given set of loading/unloading jobs with different ready times. The objective is to minimize the sum of job waiting times. A branch and bound algorithm is proposed to solve the scheduling problem optimally. Efficient and effective algorithms are proposed to find lower bounds and upper bounds. The performance of the proposed branch and bound algorithm is evaluated by a set of test problems generated based on real life data. The results show that the algorithm can find the optimal sequence for most problems of realistic sizes.     

A Constraint-Based Method for Project Scheduling with Time Windows

This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.     

A column generation algorithm for tactical timber transportation planning

We present a tactical wood flow model that appears in the context of the Canadian forestry industry, and describe the implementation of a decision support system created for use by an industrial partner. In this problem, mill demands and harvested volumes of a heterogeneous set of log types are given over a multi-period planning horizon. Wood can be stored at the forest roadside before delivery at a financial cost. Rather than solve this as a network linear programme on the basis of out-and-back deliveries, we choose to model this problem as a generalization of a log-truck scheduling problem. By routing and scheduling the trucks in the resolution, this allows us to both anticipate potential backhaul opportunities for cost and fuel savings, and also minimize queuing times at log-loaders, management of which is a major concern in the industry. We model this problem as a mixed integer linear programme and solve it via column generation. The methodology is tested on several case studies.     

Dynamic Plots in Virtual Negotiations

Advanced information and communications technology provides the basis for continuous monitoring of, and rapid data exchange about, crucial operations. Of special interest are those conflict situations where organizations continuously readjust mutually affecting decisions, considering the competitors' choices, but without communicating verbally. An example refers to trucking companies who base their decisions, which trucks to assign to different routes, on the competitors' assignments. To support the decision process for these types of virtual negotiation settings, a new dynamic plot approach is proposed. Dynamic plots can be used to visualize the decision topology of all parties and the impact of making a decision on all parties. Of special interest in this paper are dynamic plots with an individual stability equilibrium, where competitors do not revise their decisions unless a change in the market occurs. Dynamic plots for 2 × 2 conflict situations are discussed first, followed by a discussion of 3 × 3 conflict situations. The paper closes with a discussion of a computer implementation and empirical evidence of virtual negotiations with dynamic plots. The results of these virtual negotiations suggest that dynamic plots stimulate virtual negotiations and support efficiency, equity, and system optimum for these types of real-time negotiations.     

Constructing Good Solutions for the Spanish School Timetabling Problem

In the school timetabling problem a set of lessons (combinations of classes, teachers, subjects and rooms) has to be scheduled within the school week. Considering classes, teachers and rooms as resources for the lessons, the problem may be viewed as the scheduling of a project subject to resource constraints. We have developed an algorithm with three phases. In Phase I an initial solution is built by using the scheme of parallel heuristic algorithm with priority rules, but imbedding at each period the construction of a maximum cardinality independent set on a resource graph. In Phase II a tabu search procedure starts from the solution of Phase I and obtains a feasible solution to the problem. The solution obtained is improved in Phase III. Several procedures based on the calculation of negative cost cycles and shortest paths in a solution graph are used to get more compact timetables.The algorithms have been imbedded in a package designed to solve the problem for Spanish secondary schools. The computational results show its performance on a set of real problems. Nevertheless, it can be applied to more general problems and results on a set of large random problems are also provided.     

Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach

We study a vehicle routing problem with soft time windows and stochastic travel times. In this problem, we consider stochastic travel times to obtain routes which are both efficient and reliable. In our problem setting, soft time windows allow early and late servicing at customers by incurring some penalty costs. The objective is to minimize the sum of transportation costs and service costs. Transportation costs result from three elements which are the total distance traveled, the number of vehicles used and the total expected overtime of the drivers. Service costs are incurred for early and late arrivals; these correspond to time-window violations at the customers. We apply a column generation procedure to solve this problem. The master problem can be modeled as a classical set partitioning problem. The pricing subproblem, for each vehicle, corresponds to an elementary shortest path problem with resource constraints. To generate an integer solution, we embed our column generation procedure within a branch-and-price method. Computational results obtained by experimenting with well-known problem instances are reported.     

A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.     

A stochastic dynamic traveling salesman problem with hard time windows

Just-in-time (JIT) trucking service, i.e., arriving at customers within specified time windows, has become the norm for freight carriers in all stages of supply chains. In this paper, a JIT pickup/delivery problem is formulated as a stochastic dynamic traveling salesman problem with time windows (SDTSPTW). At a customer location, the vehicle either picks up goods for or delivers goods from the depot, but does not provide moving service to transfer goods from one location to another. Such routing problems are NP-hard in deterministic settings, and in our context, complicated further by the stochastic, dynamic nature of the problem. This paper develops an efficient heuristic for the SDTSPTW with hard time windows. The heuristic is shown to be useful both in controlled numerical experiments and in applying to a real-life trucking problem.     

解非线性约束拟凸规划的一个梯度投影法

目前国内外所流行的梯度投影法(包括Rosen的原有算法和一些修正算法)还存在以下几个问题:一、要增加Polak程序以保证算法的收僉性。二、在计算投影梯度时,每步一般要作两次投影。三、对于非线性约束问题,负梯度投影方向是不可行的,因此必须在此方向的基础上构造出能保证算法收歛的新可行下降方向。而目前为构造出这个新方向所作的计算都比较复杂。 1981年[5]提出了一个处理线性约束条件的梯度投影法,基本上解决了线     

Optimizing single-terminal dispatch of large volume trips to trucks

In this paper, we consider the problem of delivering large volumes of products from a single supplier to a set of commercial outlets with the use of a non-homogeneous fleet of trucks. The non-homogeneity implies different costs and, hence, traditional methods which measure miles, hours, and/or number of trucks are not appropriate. The problem may be modeled as an elastic generalized assignment problem. A special purpose branch and bound algorithm is developed and a set of real-world distribution problems and solved.     

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig–Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by intervals instead of by fixed values. The flexible cargo sizes have consequences for the times used in the ports because both the loading and unloading times depend on the cargo sizes. We found it computationally hard to find exact solutions to the subproblems, so our method does not guarantee to find the optimum over all solutions. To be able to say something about how good our solution is, we generate a bound on the difference between the true optimal objective and the objective in our solution. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that our Dantzig–Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.     

On the flow of a non-Newtonian fluid between rotating,coaxial discs

In recent times, workers in numerical methods for non-Newtonian flows have been concerned with the high Weissenberg number problem. This problem which may be caused by a number of different things, manifests itself in the failure of numerical methods at some finite and often small Weissenberg number.This paper is concerned with the torsional flow of an Oldroyd-B fluid. The kinematics is restricted to that commonly referred to as Von Kármán kinematics. These restrictions allow the reduction of the problem to a set of ordinary differential equations. The problem is then solved with finite differences using well-known branch following and jumping techniques.The solution of this set of equations is discussed, and it is found that the solutions either lose stability at subcritical bifurcation points, or fold back on themselves at limit points. Either of these will cause a high Weissenberg number problem.Comparisons are also made with the known solutions to the Newtonian problem by considering small values of the Weissenberg number.     

The stop-and-drop problem in nonprofit food distribution networks

In this paper, we introduce the stop-and-drop problem (SDRP), a new variant of location-routing problems, that is mostly applicable to nonprofit food distribution networks. In these distribution problems, there is a central warehouse that contains food items to be delivered to agencies serving the people in need. The food is delivered by trucks to multiple sites in the service area and partner agencies travel to these sites to pick up their food. The tactical decision problem in this setting involves how to jointly select a set of delivery sites, assign agencies to these sites, and schedule routes for the delivery vehicles. The problem is modeled as an integrated mixed-integer program for which we delineate a two-phase sequential solution approach. We also propose two Benders decomposition-based solution procedures, namely a linear programming relaxation based Benders implementation and a logic-based Benders decomposition heuristic. We show through a set of realistic problem instances that given a fixed time limit, these decomposition based methods perform better than both the standard branch-and-bound solution and the two-phase approach. The general problem and the realistic instances used in the computational study are motivated by interactions with food banks in southeastern United States.     

Balancing stochastic two-sided assembly lines: A chance-constrained,piecewise-linear,mixed integer program and a simulated annealing algorithm

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of a production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, the task times are assumed to be deterministic. However, in real life applications, especially in manual assembly lines, the tasks may have varying execution times defined as a probability distribution. The task time variation may result from machine breakdowns, loss of motivation, lack of training, non-qualified operators, complex tasks, environment, etc. In this paper, the problem of balancing two-sided assembly lines with stochastic task times (STALBP) is considered. A chance-constrained, piecewise-linear, mixed integer program (CPMIP) is proposed to model and solve the problem. As a solution approach a simulated annealing (SA) algorithm is proposed. To assess the effectiveness of CPMIP and SA algorithm, a set of test problems are solved. Finally, computational results indicating the effectiveness of CPMIP and SA algorithm are reported.