Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations

© 2013 IEEE. Complementing missing information and priority vector are of significance important aspects in group decision making (GDM) with incomplete hesitant fuzzy linguistic preference relations (HFLPRs). In this paper, an integer programming model is developed based on additive consistency to estimate missing values of incomplete HFLPRs by using additive consistency. Once the missing values are complemented, a mixed 0-1 programming model is established to derive the priority vectors from complete HFLPRs, in which the underlying idea of the mixed 0-1 programming model is the probability sampling in statistics and minimum deviation between the priority vector and HFLPR. In addition, we also propose a new GDM approach for incomplete HFLPRs by integrating the integer programming model and the mixed 0-1 programming model. Finally, two case studies and comparative analysis detail the application of the proposed models

Application of the 0-1 Programming Model for Cost-Effective Regression Test

Abstract-This paper reports an application of the 0-1 programming model to the regression testing plan for an industrial software. The key idea is to formulate a testing plan as a 0-1 programming problem (Knapsack problem). The empirical study shows that the 0-1 programming method can produce a cost-effective testing plan in which all potential regressions are found at only 22% of the cost of running all test cases

Optimizing the Shunting Schedule of Electric Multiple Units Depot Using an Enhanced Particle Swarm Optimization Algorithm

The shunting schedule of electric multiple units depot (SSED) is one of the essential plans for high-speed train maintenance activities. This paper presents a 0-1 programming model to address the problem of determining an optimal SSED through automatic computing. The objective of the model is to minimize the number of shunting movements and the constraints include track occupation conflicts, shunting routes conflicts, time durations of maintenance processes, and shunting running time. An enhanced particle swarm optimization (EPSO) algorithm is proposed to solve the optimization problem. Finally, an empirical study from Shanghai South EMU Depot is carried out to illustrate the model and EPSO algorithm. The optimization results indicate that the proposed method is valid for the SSED problem and that the EPSO algorithm outperforms the traditional PSO algorithm on the aspect of optimality

Two-stage stochastic minimum s − t cut problems: Formulations, complexity and decomposition algorithms

We introduce the two‐stage stochastic minimum s − t cut problem. Based on a classical linear 0‐1 programming model for the deterministic minimum s − t cut problem, we provide a mathematical programming formulation for the proposed stochastic extension. We show that its constraint matrix loses the total unimodularity property, however, preserves it if the considered graph is a tree. This fact turns out to be not surprising as we prove that the considered problem is NP-hard in general, but admits a linear time solution algorithm when the graph is a tree. We exploit the special structure of the problem and propose a tailored Benders decomposition algorithm. We evaluate the computational efficiency of this algorithm by solving the Benders dual subproblems as max-flow problems. For many tested instances, we outperform a standard Benders decomposition by two orders of magnitude with the Benders decomposition exploiting the max-flow structure of the subproblems

The parking allocation problem for connected vehicles

International audienceIn this paper, we propose a parking allocation model that takes into account the basic constraints and objectives of a problem where parking lots are assigned to vehicles. We assume vehicles are connected and can exchange information with a central intelligence. Vehicle arrival times can be provided by a GPS device, and the estimated number of available parking slots, at each future time moment and for each parking lot is used as an input. Our initial model is static and may be viewed as a variant of the generalized assignment problem. However, the model can be rerun, and the algorithm can handle dynamic changes by frequently solving the static model, each time producing an updated solution. In practice this approach is feasible only if reliable quality solutions of the static model are obtained within a few seconds since the GPS can continuously provide new input regarding the vehicle’s positioning and its destinations. We propose a 0–1 programming model to compute exact solutions, together with a variable neighborhood search-based heuristic to obtain approximate solutions for larger instances. Computational results on randomly generated instances are provided to evaluate the performance of the proposed approaches

Combinatorial optimization model for railway engine assignment problem

This paper presents an experimental study for the Hungarian State Railway Company (M\'AV). The engine assignment problem was solved at M\'AV by their experts without using any explicit operations research tool. Furthermore, the operations research model was not known at the company. The goal of our project was to introduce and solve an operations research model for the engine assignment problem on real data sets. For the engine assignment problem we are using a combinatorial optimization model. At this stage of research the single type train that is pulled by a single type engine is modeled and solved for real data. There are two regions in Hungary where the methodology described in this paper can be used and M\'AV started to use it regularly. There is a need to generalize the model for multiple type trains and multiple type engines

Transportation of Raw Materials, Recondite Question in Manufacturing Enterprise

Based on the optimization theory, this paper studies the mathematical modeling problem related to the ordering and transportation of raw materials. The paper starts with reasonable assumptions, based on which the following factors are used as index: “average supply”, “order completion rate”, “average order value” and “standard deviation of supply” of each supplier, and the weight of each index is determined by using entropy weight method. On the premise of reasonable weight, the distance method of good-bad solutions (TOPSIS) is used to evaluate and rank each supplier, and finally, the most important supplier is selected. Then, a 0-1 programming model is established, in which “minimum order price” and “minimum loss” are taken as the objective functions, and the two-week inventory of the enterprise is combined with factors such as the loss rate of the forwarder, using MATLAB programming TOPSIS algorithm to solve the model to obtain the optimal ordering and transshipment plan. Considering the possibility that the enterprise needs low utilization of raw materials A and C, a bi-objective programming model is established to determine the weekly ordering and transshipment plan within the target weeks. On the other hand, when the number of suppliers is sufficient, the capacity of the forwarders limits the expansion of the capacity of the enterprise. Therefore, combined with the existing data, a linear programming model with the maximum production capacity as the objective function is established to obtain the maximum production capacity and formulate ordering and transshipment schemes. Finally, the solution process and results are summarized and analyzed