Iranian Journal of Operations Research

A goal programming approach for fuzzy flexible linear programming problems

Hadi Nasseri

We are concerned with solving Fuzzy Flexible Linear Programming (FFLP) problems. Even though, this model is very practical and is useful for many applications, but there are only a few methods for its situation. In most approaches proposed in the literature, the solution process needs at least, two phases where each phase needs to solve a linear programming problem. Here, we propose a method to solve the given problem in just one phase using only one problem. Furthermore, using our approach, sensitivity analysis of Fuzzy Flexible Linear Programming (FFLP) problem is simpler. For an illustration of our method, some numerical examples given. In particular, a practical problem is formulated and is solved by our method and several other methods and the obtained results are compared.

The problem of balancing allocation with regard to the efficiency of servers

Tahereh Sayar

One of the most reliable indicators of the evaluation of the same units is the use of mathematical programming based method called data envelopment analysis (DEA). DEA measures the efficiency score of a set of homogeneous decision making units (DMUs) based on observed input and output. The DEA method has been added to the literature by integrating Farrell's method in such a way that each evaluation unit has multiple inputs and multiple outputs. With the advancement and evolution of this approach, DEAis now one of the active areas of research in measuring performance and has been dramatically welcomed by world researchers. Charnes, Cooper, and Rhodes (CCR) [1] first proposed DEA method to evaluate the relative efficiency for not-for-profit organizations. So far, many studies and researches have been carried out in various associations and universities around the world about DEA and its applications. The simplicity of understanding and implementing the DEA method, along with its high precision and wide application in various political, cultural, social and economic fields has led many researchers to use this method to achieve their goals. So far, more than 50,000 articles, books, theses and more have been published on DEA theories and applications, calculations and issues.

Efficient Algorithm Based on Network Flows for Two-Depot Bus Scheduling Problem

M. Niksirat

In this paper bus scheduling problem under the constraints that the total number of buses needed to perform all trips is known in advance and the energy level of buses is limited, is considered. Each depot has a different time processing cost. The goal of this problem is to find a minimum cost feasible schedule for buses. A mathematical formulation of the problem is developed. When there are two depots, a polynomial time algorithm is developed for the problem and theoretical results about the complexity and correctness of the algorithm is presented. Also, several examples are introduced for illustrating validity of the algorithm.

DEA-Based Re-allocation Model with Constant the Efficiency and Improvement of Undesirable Factors. The Case Study in Tejarat Bank of Iran

S. Madadi

Resource allocation is a problem that commonly appears in organization with a centralized decision making (CDM), who controls the units. The aim of central decision making is to allocate resources in such a way that the organization get the most benefit. Some Data Envelopment Analysis (DEA) researchers presented DEA-based resource allocation models by paying attention to energy saving and environmental pollution reduction. In this paper, we expanded a resource allocation model for 25 branches of an Iranian Tejarat bank, so that determined how much decision making (DM) can save on energy and manpower hours, so that undesirable outputs like non-performing loans are significantly reduced in a way that achieve the minimum reduction of desirable outputs while unchanged the performance of each unit after re-allocation. The result of the implementation of the model shows that in total with a 10% and 23% reduction in staff and costs respectively can result in the 0.09% reduction of deposits and 56% of non-performing loans.

Assigning independent resources to fire stations to minimize the influence of the shortage

Reza Ghanbari

A new integer program is presented to model an independent resources assignment problem with resource shortages in the context of municipal fire service. When shortage in resources exists, a critical task for fire department's administrator in a city is to assign the available resources to the fire stations such that the effect of the shortage to cover (in providing service, in extinguishing fire and so on) is minimized. To solve the problem, we propose a polynomial time greedy algorithm.

A new Approach for Solving Linear Programming with Grey Variables Problem

Davood Darvishi

Linear programming problems with interval grey numbers have recently attracted some interest. In this paper, we study linear programs in which right hand sides are interval grey numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. Some methods have been developed for solving these problems. In this paper, we propose a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. A numerical example is provided to illustrate the proposed approach.