A single source transportation algorithm

In this paper, the scheduling problem of elective patients in the Orthopedic Department of the “Lozano Blesa” Hospital in Zaragoza is considered. This problem takes into account two contradictory objectives: obtain a given occupation rate of the Operation Room (OR) and respect as much as possible the preference order of the patients in the waiting list. Three different mathematical models are discussed: 1) Quadratic Assignment Problem (QAP); 2) a Mixed Integer Linear Programing (MILP) model; and 3) Generalized Assignment Problem (GAP). These models solve combinatorial problems with a high computational cost; for this reason, heuristic methods have been used to solve large instances. In particular, 1) a meta-heuristic Genetic Algorithm (GA) for the QAP; 2) a heuristic Steepest Descent Multiplier Adjustment Method (SDMAM) for the GAP; and 3) a heuristic iterative method for MILP. Finally, the models and the heuristics are compared according to the occupation rate and the preference order criteria.

In ordinary transportation problems, it is always supposed that the mileage from every source to every destination is a definite number. But in special conditions, such as transporting emergency materials when natural calamity occurs or transporting military supplies during wartime, carrying network may be destroyed, mileage from some sources to some destinations are no longer definite. It is uncertain, a grey number. In these conditions, transportation capacity is often poor; the problems of optimization become even more important. In this paper, we proposed a new method to find an optimalsolutionforgreytransportationproblemswheretransportationcost, supplyanddemandare interval grey numbers. Our method uses the concepts of center and width of grey numbers. One of the advantages of the proposed method compared to other methods that use grey number whitening is that the uncertainty in the input data is taken into account at the output of the method and it consists of five simple steps. The solution procedure is illustrated with a numerical example. Also, the new method can be served as an important tool for decision-makers when they are handling various types of logistic problems having uncertainty parameters such as grey numbers. Further, the proposed method is extended to fuzzy grey transportation problems.

Dynamic reserve site selection under contagion risk of deforestation

Supply Chain Optimization in Pulp Distribution Using a Rolling Horizon Solution Approach

This paper discusses objective-based clustering, represented by hard -means and fuzzy c -means (FCM) methods, from two perspectives. The first is the relationship between transportation problems and objective-based clustering. The transportation problem involves determining the amount of transportation from a supply location to a demand location to minimize the total transportation cost, given the respective supply and demand quantities and the respective transportation costs from the supply location to the demand location for given multiple supply and demand locations. In this study, we demonstrate a theoretical connection between transportation problems and objective-based clustering. The second is the proposal of a new clustering method that focuses on the first argument. First, by focusing on the transportation problem, we discuss the problem of defuzzification in methods that introduce fuzzy concepts, including FCM, that is mainstream in objective-based clustering, and propose an index to evaluate the clustering results from the perspective of defuzzification. Subsequently, we propose a new clustering algorithm based on this index. Moreover, we evaluate the performance of the proposed method using numerical examples.

A Supply Selection Method for better Feasible Solution of balanced transportation problem

The management of resources dedicated for the appraisal of critical product quality attributes is a matter of increasing importance in multistage manufacturing systems. An interesting quality planning problem lies in the operational implementation of a quality inspection policy to select specific locations and machines for inspection activities. In this research, a mathematical model is developed for solving the inspection allocation and assignment problems in a multistage manufacturing system. The multistage system here considered processes part types with distinctive machine visitation sequences, and inspections can be performed on one of the several inspection stations with possible inspection errors. The computational process shows that as the problem size increases the number of inspection allocation possibilities and the computer system memory required becomes prohibitively large. Thus, three heuristic solution methods have been developed and are found to be effective in arriving at a near optimal solution with considerable savings in computational effort when compared with the optimization method based on complete enumeration. The heuristic solution methods are further compared with each other to determine their relative strength and weakness. A computer simulation is conducted to evaluate the methods developed.

A new heuristic method is presented for the resolution of multiresource constrained conflicts in project scheduling. In attempting to find a minimal makespan solution, the algorithm employs a simple procedure to generate a feasible solution with no backtracking. A postanalysis phase then applies a hill-climbing search. The solution method is different from existing heuristic methods in that it repairs resource conflicts rather than constructs detailed schedules by dispatching activities. Resource-violating sets of activities are identified which must be prevented from concurrent execution because this would violate resource constraints. Repairs are made by imposing an arc to sequence two activities in such a resource violating set. Computational results are compared with those of existing heuristics for the minimal makespan problem.

Naturally decision makers try to maximize ratio of return/risk, return/cost, and time/cost of transportation problem under uncertain environment. In such cases fractional transportation problem (FTP) play perfect role in instead of ordinary transportation problem. Some limited methods for the solution of fractional transportation problem using exact or fuzzy parameters are available in literature, and existing methods cannot deal uncertain FTP properly having hesitation factors due to inexact information. Here, I introduce the concept of intuitionistic fuzzy expectation of trapezoidal intuitionistic fuzzy numbers, and some related theorems are presented. Further, I present the concept of trapezoidal intuitionistic fuzzy fractional transportation (TIFFTP) problem, and a methodology for the solution of TIFFTP problem based on expectation of trapezoidal intuitionistic fuzzy numbers. Finally, I illustrate the presented TIFFTP problem by using an example.

European freight railway operators are losing money with their single wagon load transportation activities. Closing down this business segment does not appear to be a valid option, since single wagon load transportation is connected with full train load business and intermodal traffic. This paper presents methods and techniques that were chosen to solve different problems of single wagon load transportation.

Transportation problem is an integral part of this competitive world. Minimizing transportation cost of a product from sources to destinations is the main objective of traditional transportation problems. In the present context single objective transportation problem fails to meet the managerial decision making requirements which demands the multi objective transportation problems. Many real life problems can be formulated as multi objective transportation problem, and their solution requires consideration of conflicting objectives. Naturally, these problems have a number of potentially Pareto-optimal solutions. Multi-objective transportation problem refers to a special class of vector minimum linear programming problem, which usually involves multiple, conflicting, and incommensurable objective functions. Solving these complexities, the decision maker has to develop a utility function. In this paper, we develop a utility function to attain the targeted goal for a multi objective transportation problem. This utility function is developed using fuzzy membership functions considering deviations of objective function from the goal value where deviation variable has chosen as fuzzy type. Moreover, fuzzy max-min operator has been included for taking limiting value of the objective functions. Performance of the utility function to achieve proper goal is evaluated and justified by solving numerical examples using fuzzy goal programming.

An exact algorithm for the general quadratic assignment problem

A Tabu search heuristic for the generalized assignment problem

An effective subgradient algorithm for the generalized assignment problem

The multilevel generalized assignment problem (MGAP) is a variation of the generalized assignment problem, in which agents can execute tasks at different efficiency levels with different costs. We present a branch-and-price algorithm that is the first exact algorithm for the MGAP. It is based on a decomposition into a master problem with set-partitioning constraints and a pricing subproblem that is a multiple-choice knapsack problem. We report on our computational experience with randomly generated instances with different numbers of agents, tasks, and levels; and with different correlations between cost and resource consumption for each agent-task-level assignment. Experimental results show that our algorithm is able to solve instances larger than those of the maximum size considered in the literature to proven optimality.