Iranian Journal of Operations Research

A Benders' Decomposition Based Solution Method for Solving User Equilibrium Problem: Deterministic and Stochastic Cases

S Mahmoodi

The traffic assignment problem is one of the most important problems for analyzing and optimizing the transportation network to find optimal flows. This study presented a new formulation based on a generalized Benders' decomposition approach to solve its important part, i.e. user equilibrium problems, in deterministic and stochastic cases. The new approach decomposed the problem into a master problem and a sub problem. The first one was a nonlinear and the latter a linear programming problem. Iteratively, the master problem was solved and its outputs were used to solve the sub-problem in which to form appropriate cuts and add them to the master problem for solving it in the next iteration. Based on the convergence of Benders' decomposition, the iterative process was terminated in a finite number of steps. In this manner, some numerical examples were explained and compared with other methods.

Capacity Inverse Minimum Cost Flow Problem under the Weighted Hamming Distances

J Tayyebi

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capacity inverse problem under the bottleneck-type and the sum-type weighted Hamming distances. In the bottleneck-type case, the binary search technique is applied to present an algorithm for solving the problem in O(nm log n) time. In the sum-type case, it is shown that the inverse problem is strongly NP-hard even on bipartite networks

Availability Optimization of a Series Repairable System with Multiple k-out-of-n Subsystems

Ali A. Yahyatabar Arabi

An availability model is developed to optimize the availability of a series repairable system with multiple k-out-of-n subsystems in this paper. There are two types of decision variables that determine the system designer’s decision to allocate the number of repairmen and to allocate the number of redundant components in each subsystem in the presence of weight, volume and cost constraints. As per the nonlinear structure of the objective in the model, the model is located into the nonlinear programming category. A classical Particle Swarm Optimization (PSO) algorithm is proposed to solve seven various instances of the model. The aim of this study is to illustrate the model and to propose an applicable algorithm for the problem. The efficiency of the proposed PSO is illustrated by comparison with Simulated Annealing (SA) method.

Interdiction problem as a tool to identify an effective budget allocation to quality improvement plans

F Dehghanian

In the face of budgetary limitations in organizations, identifying critical facilities for investing in quality improvement plans could be a sensible approach. In this paper, hierarchical facilities with specified covering radius are considered. If disruption happens to a facility, its covering radius will be decreased. For this problem, a bi-objective mathematical formulation is proposed. Critical facilities are equivalent to the facilities which attacking them causes the most reduction in the quality of the system performance. Consequently, this problem is studied in the interdiction problem framework. To solve the multi-objective model the weighting-sum approaches are applied. The first interdictor's objective function helps decision makers to identify the vulnerability of the system. Moreover, the second objective function may assist in minimizing the cost of applied quality improvement plans.

Generation of a reduced first - level mixed integer programmimg problem

Godfrey Chagwiza

We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is developed. The proposed method of cuts generation, separation and strengthening is compared to the Gomory, linear branching and coordinated cutting plane methods. The computational results show that the proposed method is promising but becomes complicated as number of variables increases.