Iranian Journal of Operations Research

A Robust Modeling Of Inventory Routing In Collaborative Reverse Supply Chains

Yahia Zare Mehrjerdi

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.

Semidefinite relaxation for dominating set

Mehdi Djahangiri

‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exploited to produce a near-optimal dominating set‎. ‎Feasibility of the generated solutions and efficiency of the algorithms are analyzed as well‎.

A Metaheuristic Algorithm for the Minimum Routing Cost Spanning Tree Problem

Sattar Sattari

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.

Boundedness of KKT Multipliers in fractional programming problem using convexificators

Ali Ansari Ardali

‎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.