Designing routes to minimize fleet operating costs

A route-planner must try to schedule the delivaries by a fleet of vehicles such that customer requirements are met and management objectives are satisfied. In most cases, the number of feasible arrangements is legion, and calculations relating to individual vehicle loads, mileages, delivery times, etc. are tedious, allowing only a small fraction of possible route plans to be established and compared. The problem presents an ideal opportunity for computer application, not least to ensure that solutions are timely and error free.Several algorithms have been developed to improve the quality of vehicle routes, but in practice only those that rely on simple selection rules have found widespread acceptance, due to the innate complexity of the calculations that follow from a more rigorous approach and to the great variety of customer, vehicle, and operational characteristics that distinguish transport systems and which must be accomodated.The method presented here is based upon the well-known ‘savings’ criterion, but avoids many of its deficiencies by employing a random selection mode and producing (efficiently) a large sample of schedules from which to choose the most suitable. In particular, this allows greater flexibility in defining management objectives, and has led to substantial reductions in both fleet sizes and distances travelled, compared to published results, for a set of nine test cases each involving more than 200 customer locations.     

Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand

This paper proposes a short-term liner ship fleet planning problem by taking into account container transshipment and uncertain container shipment demand. Given a liner shipping service network comprising a number of ship routes, the problem is to determine the numbers and types of ships required in the fleet and assign each of these ships to a particular ship route to maximize the expected value of the total profit over a short-term planning horizon. These decisions have to be made prior to knowing the exact container shipment demand, which is affected by some unpredictable and uncontrollable factors. This paper thus formulates this realistic short-term planning problem as a two-stage stochastic integer programming model. A solution algorithm, integrating the sample average approximation with a dual decomposition and Lagrangian relaxation approach, is then proposed. Finally, a numerical example is used to evaluate the performance of the proposed model and solution algorithm.     

Liner ship fleet deployment with week-dependent container shipment demand

This paper addresses a practical liner ship fleet deployment problem with week-dependent container shipment demand and transit time constraint, namely, maximum allowable transit time in container routing between a pair of ports. It first uses the space–time network approach to generate practical container routes subject to the transit time constraints. This paper proceeds to formulate the fleet deployment problem based on the practical container routes generated. In view of the intractability of the formulation, two relaxation models providing lower bounds are built: one requires known container shipment demand at the fleet deployment stage, and the other assumes constant container shipment demand over the planning horizon. An efficient global optimization algorithm is subsequently proposed. Extensive numerical experiments on the shipping data of a global liner shipping company demonstrate the applicability of the proposed model and algorithm.     

An approach for analysing transportation costs and a case study

One of the important parameters in the determination of optimal transportation system is economy. Therefore, a realistic method based on the technical, economical and operational parameters of various transportation modes, namely, road, railway, and sea routes is required in the analysis of costs. This method will take into consideration the probable price escalations during the lifetime of a certain transportation system. The cost of a unit of cargo or passenger per route length should be considered since it is an indicator of economics. In this paper, an approach for transportation cost analysis based on the economic analysis of the alternative modes of cargo or passenger transportation, is presented.     

Stowage planning in maritime container transportation

We consider a stowage-planning problem of arranging containers on a container ship in the maritime transportation system. Since containers are accessible only from the top of the stack, temporary unloading and reloading of containers, called shifting, is unavoidable if a container required to be unloaded at the current port is stacked under containers to be unloaded at later ports on the route of the ship. The objective of the stowage planning problem is to minimize the time required for shifting and crane movements on a tour of a container ship while maintaining the stability of the ship. For the problem, we develop a heuristic solution method in which the problem is divided into two subproblems, one for assigning container groups into the holds and one for determining a loading pattern of containers assigned to each hold. The former subproblem is solved by a greedy heuristic based on the transportation simplex method, while the latter is solved by a tree search method. These two subproblems are solved iteratively using information obtained from solutions of each other. To see the performance of the suggested algorithm, computational tests are performed on problem instances generated based on information obtained from an ocean container liner. Results show that the suggested algorithm works better than existing algorithms.     

Minimizing setup costs for parallel multi-purpose machines under load-balancing constraint

This article focuses on the minimization of the setup costs of a workshop modeled with parallel multi-purpose machines. Any admissible workshop configuration has to ensure that a load-balanced production plan meeting a given demand exists. This problem is shown to be NP-hard in the strong sense, and is stated as a mixed integer linear program. It is shown that under some hypotheses, it can be stated as a transportation problem and solved in polynomial time. An upper bound and lower bound are proposed, as well as a performance ratio assessment that is reached only when degenerate optimal solutions to the transportation problem exist.     

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.     

Minimizing earliness and tardiness costs in stochastic scheduling

We address the single-machine stochastic scheduling problem with an objective of minimizing total expected earliness and tardiness costs, assuming that processing times follow normal distributions and due dates are decisions. We develop a branch and bound algorithm to find optimal solutions to this problem and report the results of computational experiments. We also test some heuristic procedures and find that surprisingly good performance can be achieved by a list schedule followed by an adjacent pairwise interchange procedure.     

Joint optimization of fleet size and maintenance capacity in a fork-join cyclical transportation system

This article presents an asset management-oriented multi-criteria methodology for the joint estimation of a mobile equipment fleet size, and the maintenance capacity to be allocated in a productive system. Using a business-centred life-cycle perspective, we propose an integrated analytical model and evaluate it using global cost rate, availability and throughput as performance indicators. The global cost components include: (i) opportunity costs associated with lost production, (ii) vehicle idle time costs, and (iii) maintenance resources idle time costs. This multi-criteria approach allows a balanced scorecard to be built that identifies the main trade-offs in the system. The methodology uses an improved closed network queueing model approach to describe the production and maintenance areas. We test the proposed methodology using an underground mining operation case study. The decision variables are the size of a load-haul-dump fleet and specialized maintenance crew levels. Our model achieves savings of 20.6% in global cost terms with respect to a benchmark case. We also optimize the system to achieve desired targets of vehicle availability and system throughput (based on system utilization). The results show increments of 7.1% in vehicle availability and 13.5% in system throughput with respect to baseline case. For the case studied, these criteria also have a maximum, which allows for further improvement if desired. The results also show the importance of using balanced performance measures in the decision process. A multi-criteria optimization was also performed, showing the Pareto front of considered indicators. We discuss the trade-offs among different criteria, and the implications in finding balanced solutions. The proposed analytical approach is easy to implement and requires low computational effort. It also allows for an easy re-evaluation of resources when the business cycle changes and relevant exogenous factors vary.     

Integrated fleet mix and routing decision for hazmat transportation: A developing country perspective

In developing countries, truck purchase cost is the dominant criteria for fleet acquisition-related decisions. However, we contend that other cost factors such as loss due to the number of en route truck stoppages based on a truck type and recovery cost associated with a route choice decision, should also be considered for deciding the fleet mix and minimizing the overall costs for long-haul shipments. The resulting non-linear model, with integer variables for the number and type of trucks, and the route choices, is solved via genetic algorithm. Using real data from a bulk liquid hazmat transporter, the trade-offs between the cost of travel, loss due to number of truck stoppages, and the long-term recovery cost associated with the risk of exposure due to a hazmat carrier accident are discussed. The numerical experiments show that when factors related to public safety and truck stoppages are taken into account for transportation, the lowest total cost and optimal route choice do not align with the cheapest truck type option; rather, the optimal solution corresponds to another truck type and route with total costs significantly less than the total costs associated with the cheapest truck type. Our model challenges the current truck purchasing strategy adopted in developing countries using the cheapest truck criteria.     

Optimization of production allocation and transportation of customer orders for a leading forest products company

A leading manufacturer of forest products with several production facilities located in geographical proximity to each other has recently acquired a number of new production plants in other regions/countries to increase its production capacity and expand its national and international markets. With the addition of this new capacity, the company wanted to know how to best allocate customer orders to its various mills to minimize the total cost of production and transportation. We developed mixed-integer programming models to jointly optimize production allocation and transportation of customer orders on a weekly basis. The models were run with real order files and the test results indicated the potential for significant cost savings over the company’s current practices. The company further customized the models, integrated them into their IT system and implemented them successfully. Besides the actual cost savings for the company, the whole process from the initial step of analyzing the problem, to developing, testing, customizing, integrating and finally implementing the models provided enhanced intelligence to sales staff.     

Benchmarking the operating efficiency of Asia container ports

The aim of this paper is to explore the operating efficiency, the scale efficiency targets, and the variability of DEA efficiency estimates of Asian container ports. This study applies data envelopment analysis (DEA) with the traditional DEA model, most productive scale size concept, returns to scale approach, and bootstrap method to assess the operating performance, set scale efficient targets, and determine efficiency rankings of Asian container ports. The results of this study can provide port managers with insights into resource allocation, competitive advantages, as well as optimization of the operating performance. The potential applications and strengths of DEA in assessing the Asian container ports are highlighted.     

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.     

Minimizing the expected discounted time to ruin for a company managing N distinct funds with a “superclaims”process

1.IntroductionOne of the central problems in classical ruin theory of a( non- life) insurance businesshas been the determination of the initial reserve size to ensure minimal probability of ruinover some time interval.If the comulative claims process X ( t) is compouns Possion,and ifthe premium rate,p.is a constant,then for an initial reserve u,the( Levy) processR( t) =u + pt- X( t) ( 1 )defines the‘risk- reserve’ or state of the company attime t.the company is ruined at epoch T=T( u) wher…     

Integrated scheduling of crane handling and truck transportation in a maritime container terminal

This paper studies the interactions between crane handling and truck transportation in a maritime container terminal by addressing them simultaneously. Yard trucks are shared among different ships, which helps to reduce empty truck trips in the terminal area. The problem is formulated as a constraint programming model and a three-stage algorithm is developed. At the first stage, crane schedules are generated by a heuristic method. At the second stage, the multiple-truck routing problem is solved based on the precedence relations of the transportation tasks derived from the first stage. At the last stage a complete solution is constructed by using a disjunctive graph. The three procedures are linked by an iterative structure, which facilitates the search for a good solution. The computational results indicate that the three-stage algorithm is effective for finding high-quality solutions and can efficiently solve large problems.     

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.     

Exact solution methods for uncapacitated location problems with convex transportation costs

In this paper we study exact solution methods for uncapacitated facility location problems where the transportation costs are nonlinear and convex. An exact linearization of the costs is made, enabling the formulation of the problem as an extended, linear pure zero–one location model. A branch-and-bound method based on a dual ascent and adjustment procedure is developed, and compared to application of a modified Benders decomposition method. The specific application studied is the simple plant location problem (SPLP) with spatial interaction, which is a model suitable for location of public facilities. Previously approximate solution methods have been used for this problem, while we in this paper investigate exact solution methods. Computational results are presented.     

Estimation of the ruin probability of an insurance company operating on a BS-market

We obtain an estimate for the ruin probability of an insurance company that invests a part of its capital in stocks and puts the rest of the capital in a bank account. An insurance premium is established depending on the capital of the insurance company. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1443–1453, November, 2007.     

A multi-agent inventory problem with general transportation costs

This paper addresses the cost allocation problem that arises from an inventory system with multiple item and several agents that place joint orders according to an EOQ policy. In this setting, the cost per a new order has two components: a fixed cost and a variable cost. We assume that the variable part is given by a general function, not necessarily additive. We obtain the optimal policy and we evaluate some proposals of allocation rule for the ordering costs.     

A model for allocated versus actual costs in assignment and transportation problems

We present a simple mathematical model which will relate the actual cost spent in accomplishing a task to the dollars budgeted for that task. In the specific instances of assignment and transportation problems we show how to minimize total dollars spent given total dollars allocated. We show furthermore how to quantitatively measure the work done along each arc in such problems. The total work, which will measure how fixed costs are realized across various arcs for a given prescribed effort, can then be minimized. It is shown that this, in general, leads to a third type of optimal solution which is different from those optimal solutions obtained by minimizing either total cost or total dollars allocated.