Iranian Journal Of Operations Research
Volume:6 Issue: 1, Winter and Spring 2015

This paper presents a new mathematical model for a bi-objective job shop scheduling problem with sequence-dependent setup times that minimizes the weighted mean completion time and the weighted mean tardiness time. For solving this multi-objective model, we develop a fuzzy multi-objective linear programming (FMOLP) model. In this problem, a proposed FMOLP method is applied with respect to the overall acceptable degree of the decision maker (DM) satisfaction. Finally, a numerical example demonstrates the feasibility of applying the proposed model to job shop scheduling with set up times problem. The proposed model yields a compromised solution and the decision maker’s overall levels of satisfaction.

This paper proposes a robust model for optimizing collaborative reverse supply chains. The primary idea is to develop a collaborative framework that can achieve the best solutions in the uncertain environment. Firstly, we model the exact problem in the form of a mixed integer nonlinear programming. To regard uncertainty, the robust optimization is employed that searches for an optimum answer with nearly all possible deviations in mind. In order to allow the decision maker to vary the protection level, we used the "budget of uncertainty" approach. To solve the np-hard problem, we suggest a hybrid heuristic algorithm combining dynamic programming, ant colony optimization and tabu search. To confirm the performance of the algorithm, two validity tests are done firstly by comparing with the previously solved problems and next by solving a sample problem with more than 900 combinations of parameters and comparing the results with the nominal case. In conclusion, the results of different combinations and prices of robustness are compared and some directions for future researches are suggested finally.

Here, we propose a fuzzy analytic hierarchy process (FAHP) method to evaluate the alternatives of enterprise resource planning (ERP) system. The fuzzy AHP approach allows the users get values more accurately to model the vagueness which changes according subjective ideas in the decision-making environment for ERP system selection problem. Therefore, fuzzy AHP method is used to obtain firm decisions and noticeable solutions. The criteria are determined and then compared according to their importance. The methodology also gives some suggestions about successful ERP selections. The proposed methodology can be used for other sectors with some changes. Fuzzy group decision-making can be used for this purpose. We show how effective fuzzy AHP is as a decision-making tool in system selection problem. It is seen that fuzzy AHP is a useful decision-making methodology to make more precise selection-decisions that may help the company to achieve a competitive edge in a complex environment. Fuzzy AHP approach incorporates quantitative data of the criteria, which have to be evaluated by qualitative measures. The proposed selection methodology is flexible to incorporate new or extra criteria or decisions for the evaluation process. Besides, this methodology provides the opportunity to a project team to decompose complicated selection problem into smaller parts. Thus, the project team can understand the relationships among different criteria and easily assign its own ideas to the hierarchical structure. Also, a case study is presented to demonstrate the feasibility of the framework.

ýIt is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problemý. ýIn this paperý, ýwe first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxationsý. ýFor each of these relaxationsý, ýdifferent rounding algorithm is exploited to produce a near-optimal dominating setý. ýFeasibility of the generated solutions and efficiency of the algorithms are analyzed as wellý.

The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start algorithm that in each iteration constructs a randomized greedy solution and applies local search to it. Path-relinking stores elite solutions and to find better solutions explores the paths between different solutions. Experimental results show the performance of our algorithm on many benchmark problems compared to the other algorithms.

In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and show that the constraint qualification are necessary and suficient conditions for the Karush- Kuhn-Tucker(KKT) multipliers set to be nonempty and bounded.