One of the key issues for investors is the issue of creating an optimal stock portfolio. In the issue of choosing an portfolio, the decision maker faces different and sometimes conflicting goals such as rate of return, liquidity, dividend, and risk. In portfolio optimization, the main issue is the optimal choice of assets and securities that can be made with a certain amount of capital, but on the one hand, the uncertainties associated with each share, and, on the other hand, the multiplicity of the optimal portfolio selection model, on the complexity of the problem increases. In this paper, the portfolio optimization under uncertainty has been studied. A randomized approach to converting uncertainty into a state of definiteness and agreeing to plan for a single objective is used in combination. Information about 20 pharmaceutical companies from the Tehran Stock Exchange has been used and the validity of the model has been investigated. The results show that the stock portfolio offered has a high performance.

Supplier selection is one of the influential decisions for effectiveness of purchasing and manufacturing policies under competitive conditions of the market. Regarding the fact that decision makers (DMs) consider conflicting criteria for selecting suppliers, multiple-criteria PROGRAMMING is a promising approach to solve the problem. This paper develops a nadir COMPROMISE PROGRAMMING (NCP) model for decision-making under uncertainty on the selection of suppliers within the framework of binary PROGRAMMING. Depending on the condition of uncertainty, three statuses are taken into consideration and a solution approach is proposed for each status. A pure deterministic NCP model is presented for solving the problem in white condition (certainty of data) and a solution approach resulted from combination of NCP and stochastic PROGRAMMING is introduced to solve the model in black (uncertainty of data) situation. The paper also proposes a NCP model under certainty and uncertainty for solving problem under grey (a combination of certainty and uncertainty of data) conditions. The proposed approaches are illustrated for a real problem in steel industry with multiple objectives. Also, a simulation approach has been designed in order to examine the results obtained and also verifies capabilities of the proposed model.

In this study, agricultural sustainability of selected townships of Fars province evaluated using model of agricultural sustainability and COMPROMISE PROGRAMMING method. In this regard, data were collected from various sources such as Fars province Agricultural Organization and Fars Regional Water Authority in 2006. Townships of the province were classified into three groups, namely, sustainable (Kazerun, Lamerd, Mamasani and Abadeh), relatively sustainable (Lar, Eghlid, Firozabad, Fasa, Darab and Arsenjan) and unsustainable (Marvdasht, Estahban, Shiraz and Jahrom). Results indicated that townships in sustainable group had groundwater balance, more diversity in crops and lands with more organic substance. Furthermore, high nitrate concentration in groundwater, negative balance of groundwater, inefficient irrigation system, and over utilization of pesticides and chemical fertilizers were remarkable features of unsustainable group.

Supplier selection is naturally a complex multi-objective problem including both quantitative and qualitative factors. This paper deals with this issue from a new view point. A quantity discount situation, which plays a role of motivator for buyer, is considered. Moreover, in order to find a reasonable COMPROMISE solution for this problem, at first a multi-objective modeling is presented. Then a proposed fuzzy COMPROMISE PROGRAMMING is utilized to determine marginal utility function for each criterion. Also, group decision makers’ preferences have taken into account and the weight of each criterion has been measured by forming pair-wise comparison matrixes. Finally the proposed approach is conducted for a numerical example and its efficacy and efficiency are verified via this section. The results indicate that the proposed method expedites the generation of COMPROMISE solution.

Flood protection must be taken into account in almost all development projects. Owing to the fact that hazards associated with flooding (such as disruption of services, health impacts, famine and disease), the new approaches in flood risk management are needed. Therefore, it is essential that the selection of flood management option by cost-benefit viewpoint to be shifted to the selection of flood management option by considering the economic, technical, social, and environmental aspects. Due to the complexity of these challenges, water resources planners require a holistic, adaptive, incremental, and sustainable decision-making process, where multiple non-commensurate, competing, and often conflicting objectives (criteria) must be addressed and reconciled. During the past several decades, multi criteria decision making (MCDM), by its philosophical underpinning and the theory, methodology, and practice that have been developed on the basis of its holistic philosophy, has served as a harmonizing agent in technology, society, and policy. Thus, formidability of this method in addressing the flood management alternatives challenges is undeniable fact. In this paper, there are seven flood management measures in Gorganrood Watershed flood management project, including: conservation of natural condition, Golestan Reservoir management, levee construction, diversions-canal construction, flood forecasting and warning system and flood insurance. Prioritization of the alternatives is in demand of evaluation criteria. Each alternative would be prioritized based upon proposed MCDMs to investigate the most conclusive alternative. The flood management project is ranked based on eleven criteria, including: expected average number of casualties, recovery rate, gradual rate, expected annual damage, safety feeling, employment rate, public participation, landscape protection, wildlife habitat conservation, water quality conservation and technical feasibility and performance. These criteria have been classified into four main groups as social, economic, environmental and technical features. COMPROMISE PROGRAMMING model (CP) is employed to rank these seven alternatives which are compared with simple additive weighted model (SAW). SAW is known to be common method, which is accepted in many researches due to its simplicity. In this method, alternatives are assessed with respect to each criterion, whilst CP defines the best solution as the one in the set of efficient solutions whose point is at the least distance from an ideal point and the aim is to obtain a solution that is as close as possible to some ideal alternative. The results show that by increasing the value of P parameter, the CP model emphasizes on the importance of recovery rate, expected average number of casualties and safety feeling, which categorized in economic, social and technical feasibility, respectively. This result is obtained by assessing the changes in criteria weights while the P parameter increase from P=1 to P=¥. In the proposed model, integration of a flood warning system and flood insurance was chosen as the most conclusive alternative for flood hazard mitigation. This alternative is a combination of a pre and post disaster action. In contrast, SAW model is unable to highlight or discriminate between the criteria. One of the criticisms over MCDM states that different techniques may yield different results when applied to the same problem. An analyst looks for a solution that is closest to the ideal, in which alternatives are evaluated according to all established criteria. Therefore, it is necessary to compare the MCDMs plus assessment of subjectivity with sensitivity analysis of input data. In this study, sensitivity analysis was performed to examine the response of alternatives when the criteria weights changed to its minimum and maximum values. The results show that the CP model has less sensitivity to changes in criteria weights. Due to considering the ideal solution distance, CP model has more sensitivity to economic and technical criteria in comparison with environmental and social criteria. Although SAW model has less sensitivity to changes in criteria weights, it makes no priority between criteria even in sensitivity analysis. It is observed that the change of the MCDM methods produces differences in the final ranking of the alternatives. The discrepancy that appears between the rankings obtained by different MCDM methods, highly depended on the difference in their mathematical modeling while solving a decision problem. Thus, the main focus must lie on the selection of the most appropriate MCDM method to be adopted, not to mention that proper structuring of the decision problem, considering the relevant criteria and decision alternatives are imperative facts on this issue.

Because of the significant impact of water on economic development, social stability and ecological balance, the allocation of water resources has become a worldwide issue. In this paper, a multi-objective planning model consist of two objective functions was developed for water allocation to maximize the productivity of economical benefit and the equity of water allocation in Sefidroud basin located in Iran. A COMPROMISE PROGRAMMING method was applied to trade off both the objective functions. The different weights of the objective functions and the definitions of TDS, DSA and DSB schemes were investigated in terms of equity, economical benefit productivity and equity establishment. The results showed that TDS is the best scheme for balancing the target functions. With the except of TDS, surface water allocation and economical benefit do not follow a particular pattern in other weights of target functions, so that decision makers are confused to choose the best weights of the objective functions. Shannon Entropy theory is a suitable solution for selecting the best weights of the objective functions. The results obtained by applying the Shannon Entropy theory showed that the best weights of the objective functions for the productivity of economical benefit and water allocation equity according to the decision maker’ s priority were 0. 35 and 0. 65, respectively. Generally, the results of this study showed that if decision maker’ s priorities were not clear, Shannon Entropy theory and COMPROMISE PROGRAMMING method could be used to determine the weights of each objective functions in order to make a balance among the objective functions.

Introduction: Rational planning and optimization of agriculture are essential because of water and land constraints، the need to increase economic profit and to reduce the negative impacts of fertilizers and pesticides. To this end، decision-makers and planners need to acquire knowledge and information on the quantity، quality، type، and distribution and cultivation area of agricultural products. Therefore، for planning and management of local and regional agriculture، we need to know the distribution of agricultural crops and their planting pattern. Over the years، experts have researched the proper cultivation area for major crops. In this regard، optimization of land allocation in agricultural sector is very important. The agricultural economy will have sustainable growth if the cropping pattern is determined based on the environmental potential and climatic conditions of each region. It is necessary that environmental conditions، soil type، water resources، technology and other parameters be considered to achieve the optimal cultivation pattern. Due to the variety of ecological and climatic conditions of Golestan Province of Iran، a relatively fertile land، availability of resources including surface water، adequate rainfall in parts of the province and human resources، relatively ideal conditions exist for agricultural development in the region. However، the agricultural status of this region is now unfavorable because of the lack of attention to the factors affecting the agricultural income such as product type، economic efficiency، crop performance، cultivation costs، required water for cultivation and other factors. Therefore، it is essential that rational management and planning be implemented to mitigate these problems and to increase the economic efficiency of the agricultural sector in the province. Accordingly، the main objective of this study is to optimize land allocation for grow crops and garden products based on the initial scenario of Jihad agricultural organization، current status and the environmental scenario to achieve economic goals and to identify capacities for various agricultural activities in this region. To this end، we analyzed agricultural scenarios based on COMPROMISE mathematical PROGRAMMING using multi criteria analysis tool (MCAT). Materials & methods: The study area is Golestan Province in the north east of Iran located between 52◦ 51' and 56◦ 21' E and 36◦ 24' and 38◦ 7' N. The climate، latitude، topography، water resources، and the natural vegetation of the region is diverse. The total area of the agricultural land in the province is about 679678 hectares and the irrigated cultivation is practiced in about 377866 hectares. The results of the land use planning of Golestan Province showed that about 316326 hectares of irrigated land have suitable ecological capacity to grow crops and garden products. Accordingly، in this study we carried out land planning to determine the optimal area for cultivation of irrigated crops and garden products in accordance with the proposed scenario of Jihad agricultural organization of the Province، the current status scenario and the environmental scenario. First، a comparison matrix was formed based on the 36 proposed products and 12 optimization factors for the agricultural land allocation. The matrix was completed based on experts’ opinions and scientific information in relation to the crops and garden products. Also، the optimization criteria were weighted using Analytical Hierarchy Process (AHP) method using Expert Choice software. Due to differences in economic performance and strategic importance of the crops، we defined a prioritization factor for both positive and negative ideal values for each of the criteria. Next، data analysis was implemented based on the COMPROMISE mathematical PROGRAMMING using the MCAT software for land allocation for each of the products. The three scenarios including current (business as usual)، organizational (the proposed Jihad agricultural organization) and the environmental option were assessed for performance of agricultural products. Results & discussion: The necessary data and information were collected and prepared using reports of the Jihad agricultural organization and the ongoing land use planning project of the Golestan Province (Salmanmahiny et al.، 2013). After data analysis، weights assigned to the criteria shown in the Table 1. In addition، the results of land allocation to each of the agricultural crops are shown in the Table 2. In the end، the performance of all products was assessed on the basis of the criteria illustrated in the Table 3. The results showed that water consumption with a weight of 0. 261 is the most important criterion among the considered criteria because of its important role in agriculture. Also، the results illustrated that the production of clover، barley، wheat and canola with 12. 37، 6. 91، 6. 81 and 6. 08 percent of the total area of the irrigated land have priority for cultivation، whereas according to scenario of Jihad Agriculture Organization most of the province's irrigated land should be allocated to wheat، soybeans and cotton. In comparison، the environmental scenario indicated that water consumption، the need for machinery، fertilizer and chemical pesticides can be decreased، whereas، the employment، benefit to cost ratio، quantity of dry matter، share in household basket and performance ratio of agricultural products can be increased at the same time. Conclusion: The results of this study clarified that the profitability and economic efficiency in the agricultural condition of Golestan Province can be increased by implementation of the environmental scenario. Moreover، this study shows that officials، managers، experts and farmers of the province can learn to reach an informed decision when optimizing the cultivation of each product using the results of the employed decision support system. Certainly، it would be useful to improve the agricultural condition of this region through considering the local conditions.

The existence of various objectives in agricultural activities makes optimal inputs allocation more difficult. Therefore, it is necessary to apply approaches to approximate the objectives to desirable points, simultaneously. In this paper, it was explicated the way of applying multi objective PROGRAMMING (MOP) and COMPROMISE PROGRAMMING (CP) in order to make a farm planning in Mashhad plain. It was considered two objectives: maximizing gross margin (GM) and minimizing irrigation water. Efficient sets and the best COMPROMISE solutions were obtained by MOP and CP respectively. Results showed that, in COMPROMISE solutions GM of small (less than 3 hectare) and medium (between 3 and 8 hectare) farms are increased and irrigation water decreased. Cropping pattern was the same in the model and representative of large farms (more than 8 hectare). According to finds, there is a scope for more efficient use of inputs by increasing size of farms through decreasing the number of farm lands.

Neutrosophic set theory plays an important role in dealing with the impreciseness and inconsistency in data encountered in solving real-life problems. The current paper focuses on the neutrosophic fuzzy multiobjective linear PROGRAMMING problem (NFMOLPP), where the coefficients of the objective functions, constraints, and right-hand side parameters are single-valued trapezoidal neutrosophic numbers (NNs). From the viewpoint of complexity of the problem, a ranking function of NNs is proposed to convert the problem into equivalent MOLPPs with crisp parameters. Then suitable membership functions for each objective are formulated using their lowest and highest value. With the aim of linear PROGRAMMING techniques, a COMPROMISE optimal solution of NFMOLPP is obtained. The main advantage of the proposed approach is that it obtains a COMPROMISE solution by optimizing truth-membership, indeterminacy-membership, and falsity-membership functions, simultaneously. Finally, a transportation problem is introduced as an application to illustrate the utility and practicality of the approach.

In traditional portfolio selection model coefficients often are certain and deterministic, but in real world these coefficients are probabilistic. So decision maker cannot estimate them exactly. Financial optimization is one of the most attractive areas in decision under uncertainty. In the portfolio selection problem the Decision Maker considers simultaneously conflicting objectives such as rate of return, liquidity, Dividend and risk. Multi-objective PROGRAMMING techniques such as goal PROGRAMMING and COMPROMISE PROGRAMMING are used to choose the portfolio best satisfying the Decision Maker’s aspirations and preferences; additionally Multi Criteria Decision Making (MCDM) Techniques for dealing with portfolio selection have been used. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained COMPROMISE PROGRAMMING model is based on COMPROMISE PROGRAMMING and chance constrained PROGRAMMING models as a deterministic transformation to multi-objective stochastic PROGRAMMING portfolio model. To determine the share of industry investment planning MCDM were used. The result of the planning model for portfolio selection in Tehran Stock Exchange is shown.