In this paper, a robust bi-level model is proposed to optimize decisions related to distribution and evacuation aid after earthquake. Usually in disastrous situation foreign countries help the affected country by sending relief commodities. In this problem, the foreign countries try to minimize their shipping costs and the affected country seeks to minimize its total costs which include inventory, operation, and transportation expenses. This situation is a game between different decision makers after a catastrophic disaster. To deal with this situation, a bi-level model is proposed in which the affected country is the leader and suppliers are the followers. To validate the proposed robust model, we consider Tehran probable earthquake in region 1 as a case study. Then the advantages of using bi-level modeling against considering just one player's point of view is provided. The sensitivity analysis of the experiments are presented to explore the effects of various parameters to show managerial insights that can guide DMs under a variety of conditions.

The purpose of this paper is to discuss the state of the art on models and methods for reliability optimization problems (ROPs) including reliability allocation, redundancy allocation and reliability-redundancy allocation. There are literally few surveys for reviewing the literature of the ROPs. Tillman et al. (1980) classified the related papers by system structure, problem type, and solution methods, separately. In another work, Tzafestas (1980) reviewed system reliability optimization models and the optimization techniques. Yearout (1986) reviewed the literature related to standby redundancy. Kuo (2000) studied the system reliability optimization based on system structure and solution methods. Kuo and Prasad (2004) overviewed system reliability optimization methods. Later, Kuo (2007) reviewed recent advances in optimal reliability allocation problems. The present study adds to the previous literature surveys and focuses mainly on papers after year 2000 but with a quick review on the previous works so that the readers become familiar with the existing approaches. This research investigates the literature from system structure, system performance, uncertainty state and solution approach standpoints, simultaneously.

In this paper, a new robust approach is presented to handle demand uncertainty in cell formation and layout design process. Unlike the scenario based approaches, which use predefined scenarios to represent data uncertainty, in this paper, an interval approach is implemented to address data uncertainty for the part demands, which is more realistic and practical. The objective is to minimize the total inter- and intra-cell material handling cost. The proposed model gives machine cells and determines inter-and intra-cell layouts in such a way that the decision maker can control the robustness of the layout against the level of conservatism. An illustrative example is solved by CPLEX 10 to demonstrate the performance of the proposed method. The results reveal that when the level of conservatism is changed the optimal layout can vary, significantly.

Emergency medical services (EMS) stations reduce mortality and irreparable damage from injuries through the timely treatment of patients. After performing the initial measures at the scene of the accident, if necessary, they transfer the patient to the hospital. In such cases, the goal is to save human lives. Thus, suggestions and solutions that can improve the performance of these centers are very welcome. One of the most important parameters in providing high-quality EMS is the timing of these services. Therefore, the location of these centers plays a key role in diminishing the response time to demand. In that regard, the location of these centers in cities, especially large and densely populated cities, is very important. In this study, in order to answer the mentioned questions, a linear mathematical model based on the maximum expected coverage model is presented. In this model, by considering the relative coverage conditions, the best locations in the city, as well as the coverage of demand points and distance traveled by the vehicles will be obtained. Furthermore, robust optimization (RO) is used to provide better situations for the operation of the model. Finally, according to the results, it is found that the proposed model has a better resolution time than nonlinear models and is also able to solve cases with high input data. The proposed model is implemented in District 10 of Tehran, Iran.

Job shop scheduling (JSS) problem has been one of the most interesting research issues
in the literature during the recent years. JSS problem has been studied in different forms
of deterministic, fuzzy, and stochastic at different depths. The idea of robust
optimization (ROP), on the other hand, has earned a particular value to become a
popular subject of the breakthrough for problem solving affairs amongst the researchers.
Based on the emerged opportunity for illustrating a new area of search, a robust JSS
problem is proposed as a challenge to this boundary of knowledge. The proposed
method is capable of handling the perturbation which exists amongst the processing
times. In fact, in many real world job scheduling problems, a small change in the
processing times, not only causes a non-optimal solution, but also the infeasibility of the
final solution may also occur. The proposed robust method could guarantee that, a small
deviation of the processing times does not affect the feasibility. The implementation of
the proposed method is illustrated using some numerical examples and the outcomes of
the investigation are discussed

Uncertainty plays an important role on many engineering problems and there is a growing interest in having reliable solutions especially for problems with sensitive parameters. The paper presents a robust optimization (RO) model for multi-objective operation of capacitated P-hub location problems (MCpHLP) under uncertainty set. There are, at least, two parameters in any P-hub problems, which are under uncertainty. The first one is associated with demand and the second one is the amount of time required to process commodities. We present a scenario based robust optimization technique, where these two items are considered under various scenario and a RO is implemented to find reliable solutions. The implementation of the proposed RO model is demonstrated for an example using weighting method.

Measuring the relative efficiency of similar units has been an important topic of research among many researchers. Data envelopment analysis has been one of the most important techniques for measuring the efficiency of different units. However, there are some limitations on using such technique and some people prefer to use other methods such as analytical hierarchy process to measure the relative efficiencies. Besides, uncertainty in the input data is another issue, which makes some misleading results. In this paper, we present an integrated robust DEA-AHP to measure the relative efficiency of similar units. The proposed model of this is believed to capable of presenting better results in terms of efficiency compared with exclusive usage of DEA or AHP. The implementation of the proposed model is demonstrated for a real-world case study of Airport industry and the results are analyzed.

One of the most important issues on educational systems is to measure the relative efficiency of similar units based on non-financial factors. Data envelopment analysis (DEA) has become popular among many who wish to rank educational systems using different factors such as the rate of educational success or the number of employees, etc. However, one of the main concerns on implementing DEA methods is the uncertainty involved in input/output parameters. In this paper, a robust data envelopment analysis (RDEA) is developed to measure the efficiency of high schools considering uncertainty on output parameters. We present an empirical study on a set of high schools located in Tehran, which is the capital city of Iran. The study uses uncertain data for input/output information and the results are compared with an existing parametric stochastic frontier analysis (SFA). The preliminary results indicate that the robust DEA approach is relatively a reliable method for efficiency estimating.

During the past two decades, there have been tremendous efforts on developing efficient
business excellence models to improve the quality of organizations. A typical business
excellence model proposes several alternatives with different budget and the primary objective
is to use the best ones. In this paper, we present a robust LINMAP method for measuring the
relative importance of various alternatives in an EFQM self assessment. The presented robust
model is capable of handling uncertainty as part of the problem formulation. The proposed
model of this paper is implemented for a case-study of energy sector in Iran with various
alternatives. The orderings of the alternatives are measured using data from multiple experts
through applying the proposed model of this paper.

During the past few years, there have tremendous efforts on improving the cost of logistics using varieties of Vehicle Routing Problem (VRP) models. In fact, the recent rise on fuel prices has motivated many to reduce the cost of transportation associated with their business through an improved implementation of VRP systems. We study a specific form of VRP where demand is supposed to be uncertain with unknown distribution. A Particle Swarm Optimization (PSO) is proposed to solve the VRP and the results are compared with other existing methods. The proposed approach is also used for real world case study of drug distribution and the preliminary results indicate that the method could reduce the unmet demand significantly.