Search

In many practical applications, transportation issues are crucial to Maintaining the supply from the source to the destination is the goal of this issue. The Transportation Problem is frequently utilized to take on a real-world problem. Due to some unanticipated circumstances, unpredictability and imprecision will always exist in the actual world. In this study I have, use robust ranking technique for Defuzzification process, to which resource have the lowest shipping cost. The study to investigate the least transportation cost of zero suffix method is less than the heuristic method. [ABSTRACT FROM AUTHOR]

A transportation problem can be involving multiple objectives, multiple products, and multiple conveyances. These kinds of transportation problems are named multi-objective multi-attributes solid transportation problems (MMSTP). In this study, a solution based on goal programming has been proposed for MMSTP, in which the supply and demand are uncertain. Moreover, to handle uncertainty, different uncertainty parameters, which are between 0.6 and 0.9, have been used. Then, the results with obtained these parameters are compared by using cost function values. The results indicate that when the uncertainty parameter decreases, the cost increases. Finally, it is shown that an optimal solution can be found using this model through an example. [ABSTRACT FROM AUTHOR]

In this work, we analyse the transportation problem of a real-life situation by obtaining the optimal feasible solutions, thus carrying out the sensitivity analysis of the problem. The work utilises the data obtained from the Asejire and Ikeja plants of Coca-Cola company, aiming to aid decision- making regarding the best possible options to satisfy customers at the barest minimum cost of transportation. Rerunning the optimization of a problem is an expensive scheme for gathering and obtaining enough data required for a problem. Thus, to minimize the transportation cost, the sensitivity analysis of parameters is a good tool to determine the behaviour of some input parameters where the values of these parameters are varied arbitrarily such that optimal results are verified. Maple 18 Software is used to solve the problem and the result obtained is compared with the values evaluated from northwest corner method, least cost method and Vogel's approximation method. The study critically shows how a little change in a unit or more of any model parameter affects the expected results. [ABSTRACT FROM AUTHOR]

Uncertainties in oil demands have significant effects on the routing and scheduling of oil tankers and inevitably influence the pertinent fleet operational expenses, shortage and excess inventory penalties, and chartering costs. In this paper, we study a stochastic maritime scheduling transportation-inventory problem to transport crude oil from a source using a set of fully loaded heterogeneous vessels to be fully unloaded at a destination over a finite time horizon. Daily demands at the destination are normally distributed random variables and different penalties are imposed on the shortages/excesses in daily storage levels at the destination. The expected total cost of such a fleet operation, consists of the total vessels’ operational expenses, expected total penalties resulting from violating specified lower and upper bounds at the destination storage facility, and chartering expenses. We aim to simultaneously optimize the fleet schedules and maintain desirable daily storage levels to meet the stochastic demand requirements at the destination with acceptable reliability levels. We formulate the problem as a stochastic optimization model and then use chance constrained programming to convert it to an exact mixed-integer nonlinear program with a convex objective function and linear constraints. Solutions obtained via the proposed stochastic model and its deterministic counterpart are compared and analyzed to gain insights into the impact of the variations in demands and the probabilities of meeting demands on the overall operation and cost structure. [ABSTRACT FROM AUTHOR]

This article studies a capacitated fixed-charge multiperiod location–transportation problem in which, while the location and capacity of each facility must be determined immediately, the determination of the final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, namely using a budgeted uncertainty set, becomes a natural method for identifying meaningful decisions. Unfortunately, it is well known that these types of multiperiod robust decision problems are computationally intractable. To overcome this difficulty, we propose a set of tractable conservative approximations for the problem that each exploit to a different extent the idea of reducing the flexibility of the delayed decisions. While all of these approximation models outperform previous approximation models that have been proposed for this problem, each also has the potential to reach a different level of compromise between efficiency of resolution and quality of the solution. A row generation algorithm is also presented to address problem instances of realistic size. We also demonstrate that full flexibility is often unnecessary to reach nearly, or even exact, optimal robust locations and capacities for the facilities. Finally, we illustrate our findings with an extensive numerical study where we evaluate the effect of the amount of uncertainty on the performance and structure of each approximate solution that can be obtain d. [ABSTRACT FROM AUTHOR]

A coordinated calculation of two processes - locomotives turnover and servicing - is described. Locomotives turnover is calculated by optimization system Labyrinth and servicing by dynamic transportation problem. Service programs integrate these processes. A model of coordinated arrival of locomotives at servicing stations is proposed. The calculation consists of three interrelated steps. The first step is the calculation of the optimal locomotive turnover without considering servicing constraints. Service program SP-1 determines stations where forced stops will take place according to the necessity of servicing and forms the basic location of locomotives for further movement to servicing stations. The second step is the calculation of the optimal arrival of locomotives at servicing stations. Service program SP-2 provides location and release time of each locomotive after servicing. The third step is the calculation of a train schedule with the consideration for the location of stopped train sets and the appearance of locomotives after servicing. Servicing program SP-3 forms the united results. [ABSTRACT FROM AUTHOR]

It was shown in [J. R. Hoffman and R. P. Mahler, “Multitarget miss distance via optimal assignment,” IEEE Trans. Syst., Man, Cybern. A, Syst. Humans, vol. 34, no. 3, pp. 327–336, May 2004.] that the Wasserstein distance is equivalent to the mean optimal subpattern assignment (MOSPA) measure for empirical probability density functions. A more recent paper [M. Baum, K. Peter, and D. Uwe Hanebeck, “On Wasserstein barycenters and MMOSPA estimation,” IEEE Signal Process. Lett., vol. 22, no. 10, pp. 1511–1515, Oct. 2015.] extends on it by drawing new connections between the MOSPA concept, which is getting a foothold in the multitarget tracking community, and the Wasserstein distance, a metric widely used in theoretical statistics. However, the comparison between the two concepts has been overlooked. In this letter, we prove that the equivalence of Wasserstein distance with the MOSPA measure holds for general types of the probability density function. This nontrivial result allows us to leverage one recent finding in the computational geometry literature to show that the Minimum MOSPA (MMOSPA) estimates are the centroids of additive weighted Voronoi regions with a specific choice of the weights. [ABSTRACT FROM PUBLISHER]

Transportation CO 2 emissions are expected to increase in the following decades, and thus, new and better alternatives to reduce emissions are needed. Road transport emissions are explained by different factors, such as the type of vehicle, delivery operation and driving style. Because different cities may have conditions that are characterized by diversity in landforms, congestion, driving styles, etc., the importance of assigning the proper vehicle to serve a particular region within the city provides alternatives to reduce CO 2 emissions. In this article, we propose a new methodology that results in assigning trucks to deliver in areas such that the CO 2 emissions are minimized. Our methodology clusters the delivery areas based on the performance of the vehicle fleet by using the k -means algorithm and Tukey’s method. The output is then used to define the optimal CO 2 truck-area assignment. We illustrate the proposed approach for a parcel company that operates in Mexico City and demonstrate that it is a practical alternative to reduce transportation CO 2 emissions by matching vehicle type with delivery areas. [ABSTRACT FROM AUTHOR]

In this paper a method to obtain a non-dominated point for the multi-objective transportation problem is presented. The superiority of this method over the other existing methods is that the presented non-dominated point is the closest solution to the ideal solution of that problem. The presented method does not need to have the ideal point and other parameters to find this solution. Also, the calculative load of this method is less than other methods in the literature. [ABSTRACT FROM AUTHOR]

The fixed charge transportation problem generalizes the well-known transportation problem where the cost of sending goods from a source to a sink is composed of a fixed cost and a continuous cost proportional to the amount of goods sent. In this paper, we describe a new integer programming formulation with exponentially many variables corresponding to all possible flow patterns to sinks. We show that the linear relaxation of the new formulation is tighter than that of the standard mixed integer programming formulation. We describe different classes of valid inequalities for the new formulation and a column generation method to compute a valid lower bound embedded into an exact branch-and-price algorithm. Computational results on test problems from the literature show that the new algorithm outperforms the state-of-the-art exact methods from the literature and can solve instances with up to 70 sources and 70 sinks. [ABSTRACT FROM AUTHOR]

Given the locations of J customers, their demands and I capacitated facilities, the Capacitated Multi-facility Weber Problem (CMWP) is concerned with locating I facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost which is proportional to the distance between them. We propose two types of branch and bound algorithms for the ℓ distance CMWP with 1≤ r<∞. One of them is an allocation space based branch and bound algorithm for which a new branching variable selection strategy and new lower bounding procedures have been proposed. The other one is new and partitions the location space. Based on extensive computational experiments we can say that the proposed algorithms are promising and perform better than the existing ones. [ABSTRACT FROM AUTHOR]

This article presents a new harmony search optimization algorithm to solve a novel integer programming model developed for a consolidation network. In this network, a set of vehicles is used to transport goods from suppliers to their corresponding customers via two transportation systems: direct shipment and milk run logistics. The objective of this problem is to minimize the total shipping cost in the network, so it tries to reduce the number of required vehicles using an efficient vehicle routing strategy in the solution approach. Solving several numerical examples confirms that the proposed solution approach based on the harmony search algorithm performs much better than CPLEX in reducing both the shipping cost in the network and computational time requirement, especially for realistic size problem instances. [ABSTRACT FROM AUTHOR]

The article focuses on the minimum solution of the transportation problem of linear programming (TPLP) for Beijing's bus commuters, and calculated actual commuting and minimum commute for bus commuters in the Beijing city in China and mapped the corresponding commuting flows by utilizing bus users' origin and destination (OD) flow data in Beijing for 2008. It further mentions that graphical maps of OD movements are an innovative approach to demonstrating flows of actual travel patterns.

Transportation problem is one of the predominant areas of operations research, widely used as a decision making tool in engineering, business management and many other fields. In this paper, we present a brief literature review of transportation problem with its mathematical models in balanced and unbalanced cases. We report the basic feasible solution and hence the methods to attain optimal solution of the balanced transportation problem. Finally, we describe the primal-dual case of the problem with counter examples. [ABSTRACT FROM AUTHOR]

Most often, Lindo and QAM software are computer packages employed in Solving Transportation problems but the commands for these packages are difficult or not easily modifiable to suit general purpose. In this study we employed Visual Basic programme in Solving Transportation problems, which has the advantage of being modified or edited as the user desires. The application of this method was demonstrated using practical data from Kwara State Transportation Corporation and result compared with Lindo and QAM. We found that Visual Basic has viewer numbers of iteration at the optimal level. [ABSTRACT FROM AUTHOR]

Short-term scheduling for crude oil operations is a combinatorial problem and involves extreme detail. Thus, it is very complicated and, up to now, there is no efficient technique and software tool for it. To search for efficient techniques, a two-layer hierarchical solution is proposed for it. At the upper level, one finds a realizable refining schedule to optimize some objectives. At the lower level, a detailed schedule is obtained to realize it. A methodology has been presented to solve the lower level problem from a control perspective by the authors of this paper. In this paper, the upper level problem for finding optimal refining schedules is addressed, and a novel method is proposed based on the results obtained at the lower level. This method solves a linear programming problem to determine the maximal production rate and a transportation problem to optimally assign crude oil types and volume to the distillers. This way, the method is computationally very efficient. An industrial case study is presented to show the application of the proposed method. [ABSTRACT FROM PUBLISHER]

Considering that parameters of transportation problem have uncertainties, this paper developed a generalized fuzzy transportation problem with fuzzy supply, demand and costs. Based on the possibility theory and comprised with decision-makers' subjective and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives respectively. Finally, a practical case is presented to demonstrate the application of fuzzy transportation programming and to verify the validity of the method. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to propose a novel risk assessment approach that considers the inter-relationship between supply chain risks and the structure of network at the same time. To reduce the impact of the supply chain risk and enhance the flexibility of transportation route finding during the product delivery, the authors propose a way to model the risk propagation and how to integrate it with the supply chain network using Bayesian Belief Network (BBN). The key risk indicators (KRI) of each vertex and edge of the supply chain network which are measured or computed by the proposed approach can be utilized to develop the optimal transportation route in the execution phase. Design/methodology/approach – BBN is utilized to illustrate the relations among supply chain risks which may take place in a certain vertex. To apply the BBN to the supply chain network, the authors develop the framework to integrate BBN and the supply chain network by using the general functions that describe the characteristics of the risk factors and inter-relationships between vertices. Findings – By using the proposed risk assessment and dynamic route-finding approach, it is possible to reduce the unexpected cost from the supply chain risk and overcome the limitations of previous risk management strategies which focus on developing counter plans and assume the independency of supply chain risks. Practical implications – The proposed approach describes how to develop KRI-BBN to model the risk propagation and to integrate the KRI-BBN and supply chain network. The KRIs directly measured or computed by KRI-BBN in real time can be utilized to alternate supply chain execution plans such as inventory management, demand management and product flow management. Transportation problem considering risk is developed to show how to apply the proposed approach and numerical experiments are conducted to prove the cost effectiveness. Originality/value – The contribution of this paper lies in the way of developing KRI-BBN to assess the supply chain risk and modelling of the risk propagation by integrating KRI-BBN with supply chain network. With the proposed risk assessment approach, it is able to alternate the transportation route to minimize the unexpected cost and transportation cost simultaneously. [ABSTRACT FROM AUTHOR]

Abstract: Transportation network design problem (TNDP) aims to choose from among a set of alternatives (e.g., set of new arcs) which minimizes an objective (e.g., total travel time), while keeping consumption of resources (e.g., budget) within their limits. TNDP is formulated as a bilevel programming problem, which is difficult to solve on account of its combinatorial nature. Following a recent, heuristic by ant colony optimization (ACO), a hybridized ACO (HACO) has been devised and tested on the network of Sioux Falls, showing that the hybrid is more effective to solve the problem. In this paper, employing the heuristic of particle swarm optimization (PSO), an algorithm is designed to solve the TNDP. Application of the algorithm on the Sioux Falls test network shows that the performance of PSO algorithm is comparable with HACO. [Copyright &y& Elsevier]

Abstract: In this paper, single and multi-objective transportation models are formulated with fuzzy relations under the fuzzy logic. In the single-objective model, objective is to minimize the transportation cost. In this case, the amount of quantities transported from an origin to a destination depends on the corresponding transportation cost and this relation is verbally expressed in an imprecise sense i.e., by the words ‘low’, ‘medium’, ‘high’. For the multi-objective model, objectives are minimization of (i) total transportation cost and (ii) total time for transportation required for the system. Here, also the transported quantity from a source to a destination is determined on the basis of minimum total transportation cost as well as minimum transportation time. These relations are imprecise and stated by verbal words such as ‘very high’, ‘high’, ‘medium’, ‘low’ and ‘very low’. Both single objective and multi-objective problems using Real coded Genetic Algorithms (GA and MOGA) are developed and used to solve the single level and bi-level logical relations respectively. The models are illustrated with numerical data and optimum results are presented. [Copyright &y& Elsevier]

In this paper, we discuss modelling and solving some multiobjective optimization problems arising in biology. A class of comparison problems for string selection in molecular biology and a relocation problem in conservation biology are modelled as multiobjective optimization programmes. Some discussions about applications, solvability and different variants of the obtained models are given, as well. A crucial part of the study is based upon the Pareto optimization which refers to the Pareto solutions of multiobjective optimization problems. For such solution, improvement of some objective function can only be obtained at the expense of the deterioration of at least one other objective function. [ABSTRACT FROM AUTHOR]

Decision analysis is a structured approach to decisionmaking, which allows managers to gain enhanced insight and sharper intuition about the problems they face. Marginal analysis is a concept employed, in microeconomics where the marginal change in some parameter might be of interest to the decision-maker. A marginal change is a ration of very small addition or subtraction to the total quantity of some parameter. Marginal analysis is the analysis of the relationships between such changes in relation to the performance measure. Examples of marginal analysis are: marginal cost; marginal revenue; marginal product; marginal rate of substitution; marginal propensity to save, and so on. In optimization, the marginal analysis is employed primarily to explicate various changes in the parameters and their impact on optimal value. Sensitivity analysis, i.e., the analysis of the effect of small variations in system parameters on the output measures can be studied by computing the derivatives of the output measures with respect to the parameter. [ABSTRACT FROM AUTHOR]

The article discusses the Vehicle Routing Problem (VRP) which consists of designing best delivery or collection routes from a central depot to a set of geographically scattered customers. Each route starts and ends at a common location and some side constraints are satisfied. It further discusses the main known results for the classical VRP and the three main headings including exact algorithms, classical heuristics, and metaheuristics.

The vehicle routing problem with time windows (VRPTW) is an important problem in logistics. The problem is to serve a number of customers at minimum cost without violating the customers' time-window constraints or the vehicle-capacity constraint. In this paper, we propose a two-stage algorithm for the VRPTW. The algorithm first minimizes the number of vehicles with an ejection pool to hold temporarily unserved customers, which enables the algorithm to go through the infeasible solution space. Then it minimizes the total travel distance using a multi-start iterated hill-climbing algorithm with classical and new operators including generalized ejection chains, which enable the algorithm to search a larger neighborhood. We applied the algorithm to Solomon's 56 VRPTW instances and Gehring and Homberger's 300 extended instances. The experimental results showed that the algorithm is effective and efficient in reducing the number of vehicles and is also very competitive in terms of distance minimization. The m-VRPTW is a variant of the VRPTW in which a limited number of vehicles is available. A feasible solution to m-VRPTW may contain some unserved customers due to the insufficiency of vehicles. The primary objective of m-VRPTW is to maximize the number of customers served. We extended our VRPTW algorithm to solve m-VRPTW and the experimental results showed consistently good performance of the algorithm when compared with other methods. [ABSTRACT FROM AUTHOR]

Detailed analyses and comparisons of urban travel forecasts prepared by applying the state-of-practice sequential procedure and the solution of a combined network equilibrium model are presented. The sequential procedure for solving the trip distribution, mode choice and assignment problems with feedback is the current practice in most transportation planning agencies, although its important limitations are well known. The solution of a combined model, in contrast, results from a single mathematical formulation, which ensures a well-converged and consistent result. Using a real network, several methods for solving the sequential procedure with feedback are compared to the solution of the combined model ESTRAUS. The results of these methods are shown to have various levels of instability. The paper concludes with a call for a new paradigm of travel forecasting practice based on an internally consistent model formulation that can be solved to a level of precision suitable for comparing alternative scenarios. [ABSTRACT FROM AUTHOR]

The paper describes an approach to the vexing problem of transport planning and policy. It deals jointly with three questions, which in today's practice are addressed separately: How are hypotheses about transport problems and alternatives to their solution developed? How can a good plan or policy be identified? What is the process of implementing a transport plan or policy? In doing this the paper has the ambitious objective of proposing a new model and process for transport planning and policy. It is applicable in developed and developing countries and is not restricted to the transport sector. The paper builds on, and is a reinterpretation of two cornerstone transport planning and decision-making models – the CATS (Chicago Area Transportation Study) Planning and Design Model and Braybrooke and Lindblom's Disjointed Incrementalism. It advances a technique of experiential incrementalism (termed polisanalysis) to develop and implement plans and policies. It proposes that problems should be diagnosed by observation and continuous data collection; that their continuous analysis, finding the “cure”, and implementation take place through the method of experiential incrementalism. In this method interventions are grounded on the theories of neoinstitutional economics and psychoanalysis and derived using contact function, explained in the paper, which renders the method scientific replicability. Experiential incrementalism can employ a wider array of options in planning and policy than is presently thought possible. Like other scientific methods, its application requires rigorous training. [ABSTRACT FROM AUTHOR]

This paper describes an approach to solving a real-world problem which involves the transportation of multiple types of commodities from a number of sources to a number of destinations in discrete time periods, using a capacitated heterogeneous fleet of vehicles. The preliminary objective is to minimize the total number of discrete periods needed to complete the entire operation. The problem is first formulated as a mixed integer programme and its tractability is then greatly improved by reformulating it through backward decomposition into two separate models and solved iteratively. A heuristic approach harnessing specific features of the second approach is developed for solving large size problems to obtain near-optimal solutions within reasonable time. The design of the heuristic also takes into consideration the secondary objectives of minimizing the total vehicle capacity used and minimizing the total capacity of sources needed to satisfy the demands at the destinations. Computational results are provided for a variety of randomly generated problems as well as problems from the literature. The approach described here may be applied to the multi-period transportation of personnel and goods from multiple starting points to multiple destinations in both military and civilian applications. [ABSTRACT FROM AUTHOR]

Some instances of variational inequality models over polyhedral sets can be stated in a disaggregated or aggregated formulation related by an affine variable transformation. For such problems, we establish that sensitivity analysis results under parameterizations rely neither on the strict monotonicity properties of the problem in terms of the disaggregated variables, nor on any particular choice of their values at the solution. We show how to utilize the affine transformation to devise computational tools for calculating sensitivity results and apply them to the sensitivity analysis of elastic demand traffic equilibrium problems. The results reached show that sensitivity results do not rely on the choice of any particular route or commodity flow solution. Further, the sensitivity analysis, including the calculation of the gradient of the equilibrium link flow if it exists, can be performed by means of solving linearized traffic equilibrium problems. [ABSTRACT FROM AUTHOR]

In this paper, we undertake a detailed study of the bus stop problem in congested transit networks. In the first part of the paper, we present and discuss the bus stop models existing in the literature. In the second part, we propose a new general model for which we prove a number of good properties and we give equivalent formulations. Then, we examine two special cases of the general model. In the first case, the line capacities are considered limited and therefore they can not be exceeded by the on-board passenger flows. In the second case, the strict capacity constraints are relaxed in order to obtain a stop model that can be easily integrated into an assignment model to predict the global passenger behavior in transit networks. [ABSTRACT FROM AUTHOR]

This paper presents a new graph theoretic framework for the passenger assignment problem that encompasses simultaneously the departure time and the route choice. The implicit FIFO access to transit lines is taken into account by the concept of available capacity. This notion of flow priority has not been considered explicitly in previous models. A traffic equilibrium model is described and a computational procedure based on asymmetric boarding penalty functions is suggested. [ABSTRACT FROM AUTHOR]

One of the many problems faced by rail transportation companies is to optimize the utilization of the available stock of locomotives and cars. In this paper, we describe a decomposition method for the simultaneous assignment of locomotives and cars in the context of passenger transportation. Given a list of train legs and a fleet composed of several types of equipment, the problem is to determine a set of minimum cost equipment cycles such that every leg is covered using appropriate equipment. Linking constraints, which appear when both locomotives and cars are treated simultaneously, lead to a large integer programming formulation. We propose an exact algorithm, based on the Benders decomposition approach, that exploits the separability of the problem. Computational experiments carried on a number of real-life instances indicate that the method finds optimal solutions within short computing times. It also outperforms other approaches based on Lagrangian relaxation or Dantzig-Wolfe decomposition, as well as a simplex-based branch-and-bound method. [ABSTRACT FROM AUTHOR]

This paper discusses an element of forecasting with disaggregate demand models that has received little attention so far; namely, the extent to which the accuracy of the final prediction depends on the accuracy of the calibration process. The paper introduces a numerical technique to evaluate approximate confidence intervals for the expected number of people using a transportation facility and approximate prediction intervals for the actual usage. It is shown that, unless the magnitude of the variance of the estimated parameters is considerably small,the predictions that result may be biased and the resulting confidence intervals, inaccurate. The degree of accuracy that can be obtained with different parameter variances is illustrated numerically for the binary probit model. [ABSTRACT FROM AUTHOR]

Shadow prices derived from the optimal dual solution of a transportation problem give the rate at which the optimal cost changes when a warehouse capacity or market requirement is changed ceteris paribus. One of the limitations in interpreting shadow prices for managerial use is that they may be degenerate. i.e., their interpretation may be valid only over a zero range of the parameter to be varied. This paper provides an efficient procedure for computing all nondegenerate (or "real") shadow prices. The method involves breaking the optimal basis tree into subtress by dropping basic variables which are at their bounds, defining a measure of distance between the subtrees and solving a shortest path problem berween all pairs of subtrees. [ABSTRACT FROM AUTHOR]

We pursue the analysis of the Hub Operation Scheduling Problem (HOSP) over the finite and infinite horizons. The demand is assumed deterministic and stationary. We deduce the minimum fleet size V[subt] that satisfies all demands for 1 ≤ T ≤ ∞, as well as the optimal schedule that minimizes lost sales for a given fleet size smaller than V [subt]. Reintroducing the costs of empties and of delayed gales or, equivalently, the cost of empties and the gains from shipments, we resolve the issues of optimal allocation and optimal schedule over a horizon T ≤ ∞. Finally, we generalize the above results...still under the assumption of deterministic, stationary demands...first to the case in which each city communicates with its two "adjacent" cities (this is the "Wheel" problem) and then to the general network problem in which each terminal may communicate with any other terminal. [ABSTRACT FROM AUTHOR]

The problem considered is that of finding the location of a facility in the plane so that the maximum weighted rectilinear round-trip distance between the facility and N pairs of existing facilities is minimized. The round-trip distance is the total distance traveled starting from the new facility via a pair of existing facilities and back to the new facility. An efficient one-pass solution procedure is developed for finding all the optimal locations to the problem, and is compared computationally with the simplex method. Two special cases are investigated, namely, when the existing facilities lie on a line, and when all the weights are equal. [ABSTRACT FROM AUTHOR]

A schedule is a set of passages; is a 4-tuple p = (p1, p2, p3, p4) where p1, p2 denote departure and arrival terminals, p3, p4 departure and arrival times. A fleet is a partition of the schedule into chains; each chain is a finite or infinite sequence of passages p1, p2, … having the property pn² = pn+i¹ and pn4 ≤ pn+i³. The fleet-size is the minimal possible dimension (i.e., the number of chains) of the fleets. The deficit function d(t, a) for a terminal a is the difference between the number of departures and arrivals occuring at a during the interval [O, t]. It is proved that the fleet-size is equal to ∑o max≥0 d(t, a). A general method for constructing all optimal fleets is described. A special case of periodic schedules is studied and it is proved that a periodic schedule can ba decomposed into an optical periodic fleet. Applications of the deficit function technique to practical scheduling when passages have tolerances for departure times are discussed. [ABSTRACT FROM AUTHOR]

This paper provides a framework for choosing modes of transportation (rail, highway, air, etc.) by taking into account the conflicting objectives of minimizing total transportation costs and average shipment times. An efficient algorithm using the operator theory of parametric programming is presented for determining the Pareto-optimal or efficient curve denoting the minimum attainable value for the second objective for differing values of the first objective. The algorithm also provides the optimal routes, modes of transportation, and the corresponding shipping amounts for every efficient point. [ABSTRACT FROM AUTHOR]

This paper discusses the General Routing Problem approach to solving large scale routing problems. The General Routing Problem on network G = (N; A) requires finding the minimum cost, cycle that visits every node in subset Q ⊆ N and that traverses every arc in a subset R ⊆ A. Utilizing special problem characteristics and the structure of real transportation networks, large reduction in effective problem size and complexity can often be made. This permits a very effective heuristic. to produce optimum and near optimum solutions `quickly. [ABSTRACT FROM AUTHOR]

For the solution of the multiple terminal delivery problem a formula for the actual savings is presented and a method of solution based on these actual savings is described. This method is simple both conceptually and computationally and gives results that appear to be `good.' [ABSTRACT FROM AUTHOR]

The problem of optimally assigning highway trailers to railcar hitches in intermodal transportation is studied. An integer-linear programming formulation is constructed. The problem is formulated using set covering. The resulting formulation is very small, and possesses in practice a tight linear programming relaxation. This allows it to be solved effectively by a general purpose branch-and-bound code. This formulation also provided the basis for the development of a Greedy Randomized Adaptive Search Procedure (GRASP). This heuristic is observed to be extremely fast. Empirically, it finds the optimal solution to all of the problem instances furnished over a two year period by Consolidated Rail Corporation. [ABSTRACT FROM AUTHOR]

We describe algorithms for optimal single facility location problems with forbidden regions and barriers to travel. The former are those where location is not permitted, but one can travel through them, e.g., a lake. The latter are the regions where neither location nor travel is permitted, e.g., large parks in a city. Using the convexity properties of the objective function, in the first case, we develop an algorithm for finding the optimal solution. The objective function in the barrier case is shown to be non-convex. We use the concept of visibility to create a network with the location point as the source and use Dijkstra's algorithm to compute the shortest distance to all the other demand points. Using simulated annealing we find an approximate optimal solution. Numerical examples illustrate the implementation of the algorithms. [ABSTRACT FROM AUTHOR]

We address the problem of scheduling the delivery of multiple items from a single supplier to a manufacturer. The items are packaged into containers, and the containers are shipped by truck. There is a fixed charge per truck shipment, and inventory holding costs are charged on end-of-period inventory. We seek to minimize the sum of transportation and inventory costs. The problem is a combination of a bin-packing problem (due to the presence of containers and finite-capacity trucks) and a multi-item joint replenishment problem. We present a heuristic solution procedure which starts with the optimal solution of the problem in which the integrality of the containers is relaxed. (A solution procedure for this relaxed problem appears in BEN - KHEDER and YANO[2]. We develop a method to modify this solution to account for the integrality of containers. This modification scheme involves sequentially considering each item and optimally scheduling the fractional containers in the relaxed solution. To solve this single-item problem, we devise a procedure that accounts for the availability of "free" remaining capacity of trucks that have been partially filled with other items. In a computational study, our heuristic is compared with a lower bound, with variations of our heuristic, and with simple rule-of-thumb policies. The results suggest that our heuristic performs very well, especially in problems where considering tradeoffs between inventory and transportation costs is important. [ABSTRACT FROM AUTHOR]

Location problems on a sphere can be solved easily by mathematical programming or geometrical methods i/it is known that all the demand points are located on a hemisphere. This paper presents an algorithm for determining whether m given demand points are on a hemisphere or not. In this algorithm, the great circle is rotated successively until the hemisphere which contains the m given demand points is found or it becomes known using our criteria that the m given demand points are not on a hemisphere. The convergence of this algorithm is proved, and two illustrative examples are presented. [ABSTRACT FROM AUTHOR]

It is known that the planar Weber location problem with lp distances has all its solutions in the convex hull of the demand points. For l1 and l∞ distances, additional conditions are known which reduce the set 0/possible optimal points to the intersection of that convex hull, the efficient set, and the points defined by a certain grid. In this paper, we determine the smallest set which includes at least one optimal point for every Weber problem based on a given set of demand points. It is shown that for 1 < p < ∞ a certain part of the convex hull is the smallest possible set, but for p = 1 or p = &infin the known conditions do not necessarily yield the correct set. Finally, we find the smallest possible set for p = 1 or p = ∞. [ABSTRACT FROM AUTHOR]

We show that an essential step in the PARTAN variant of the Frank—Wolfe algorithm for equilibrium assignment, the calculation of a minimal step length for maintaining feasibility, can be accomplished using either analytical formulas or simple rules. [ABSTRACT FROM AUTHOR]

This article attempts to solve a family of multi-depot vehicle routing and location-routing problems. The vehicle routing problem (VRP) is commonly defined as the problem of designing optimal delivery or collection routes from one or several depots to a set of geographically scattered customers, under a variety of side conditions. Location-routing problems (LRPs) are VRPs in which the optimal depot locations and route design must be decided simultaneously. Both the VRP and LRPs have been studied extensively in the last few years. Most studies related to this family of problems have been carried out in the context of the single depot VRP Graph transformations have been used by a number of authors to solve several TSP extensions. These transformations are such that every feasible solution to the original problem corresponds to one or more Hamiltonian circuits on a subgraph of the new graph. Any feasible solution on the transformed graph can be interpreted as a solution to the original problem on the original graph.

Numerous transportation applications as diverse as capital investment decision- making, vehicle fleet planning, and traffic light signal setting all involve some form of (discrete choice) network design. In this paper, we review some of the uses and limitations of integer programming-based approaches to network design, and describe several discrete and continuous choice models and algorithms. Our objectives are threefold--to provide a unifying view for synthesizing many network design models, to propose a unifying framework for deriving many network design algorithms, and to summarize computational experience in solving design problems. We also show that many of the most celebrated combinatorial problems that arise in transportation planning are specializations and variations of a generic design model. Consequently, the network design concepts described in this paper have great potential application in a wide range of problem settings. [ABSTRACT FROM AUTHOR]

In this paper we consider two network optimization problems which have the following characteristics: control parameters vary continuously and network users behave according to War-drop's first principle of traffic equilibrium ("user-optimization"). For each problem, we study an exact algorithm based on constraint accumulation and a heuristic algorithm previously proposed in the literature. [ABSTRACT FROM AUTHOR]