Determining the Appropriate Crop Rotation Plan in a Farm Scale Using Fuzzy Goal Programming Model

Introduction One of the important subject in the field of agricultural programming is reaching to a pattern or appropriate crop rotation to plant. Existing constraints, including the amount of available resources, and different goals, makes the decision to optimize the use of resources and production factors a complicated task. Therefore, applying mathematical models can be a grate help in this field. The goal of this study is to determine the appropriate patterns of crop cultivation in a farm in the North Khorasan province. Materials and Methods Implem enting fuzzy goal programming (FGP) model based on different scenarios was employed to achieve our goals. According to results ,represented process , constraints and problem goals, four plant patterns are offered based on eight proposed scenarios for crop products in this farm or this study. These proposed cultivation pattern can help to make better decision for determination the appropriate rotation of crops in different conditions and different goals by decision makers. Results Discussion Finally, proposed cultivation patterns were prioritized according to maximum amount of reaching the desired level of total goals. Based on maximum level of reaching goals, different scenarios consisted of income, cost, production resources, income-cost, income-production resources, cost-production resources, income-cost-production resources with equal weights, and income-cost-production resources with different weights have been prioritized and four cropping pattern have been detected. In first pattern, three scenario consisted of scenario 1 (income), scenario 4 (income-cost) and scenario 5 (income-production resources) have combined. The second pattern have made scenario 2 (cost). In third pattern, scenario 3 (production resources), scenario 6 (cost-production resources) and scenario 7 (income-cost-production resources with equal weights) have combined. The scenario 8 (income-cost-production resources with different weights) have considered as fourth pattern, too. For each pattern, the level of reaching goals have been differentiated. In order to determine the appropriate pattern of cropping Euclidean distance have been used. The main difference between outputs of these patterns in pursuit of favorable culture could be due to labor, urea, and income, so the highest aspiration to achieve the desired level of labor have been to cultivation patterns 2 and 3. The desired level of urea fertilizer have been 3, and the highest aspirations and achieve the desired level of income of cropping pattern have been 1. Overall, the appropriate pattern of crop have selected based on the minimum Euclidean distance among of four patterns. In conclusion, Pattern 4 based on scenario 8 (income-cost-production resources with different weights) with minimum swing of desired level of goals have selected as appropriate pattern. Patterns 2, 3 and 1 situated in next priorities. Conclusion In agriculture planning, sometimes, conflict between objectives occurs. Goal programming is a technique to achieve proper patterns in agricultural planning, by considering different objectives. Due to high uncertainty about the number of desired level of objectives, goal programming model results may be desirable to have or not to conform actual conditions. To resolve this problem, fuzzy goal programming can be utilized where in addition to consider the appropriate level of ideals, fluctuations can be defined for each of them. In this study, fuzzy goal programming models were applied. The proposed method of this study can help farmers to make decision to detect crop patterns. Therefore they can approach to the right decisions based on limited, available resources and importance of goals. Therefore, decision makers can select the appropriate pattern for cropping according to their priority for each goal

A Heuristic Procedure for the Capacitated m-Ring-Star Problem

In this paper we propose a heuristic method to solve the Capacitated m-Ring-Star Problem which has many practical applications in communication networks. The problem consists of finding m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be \u201callocated\u201d to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than the capacity Q given as an input parameter. The objective is to minimize the total visiting and allocation costs. The problem is a generalization of the Traveling Salesman Problem, hence it is NP-hard. In the proposed heuristic, after the construction phase, a series of different local search procedures are applied iteratively. This method incorporates some random aspects by perturbing the current solution through a \u201cshaking\u201d procedure which is applied whenever the algorithm remains in a local optimum for a given number of iterations. Computational experiments on the benchmark instances of the literature show that the proposed heuristic is able to obtain, within a short computing time, most of the optimal solutions and can improve some of the best known results

Variable Neighborhood Search for the Cost Constrained Minimum Label Spanning Tree and Label Constrained Minimum Spanning Tree Problems

Given an undirected graph whose edges are labeled or colored, edge weights indicating the cost of an edge, and a positive budget B, the goal of the Cost Constrained Minimum Label Spanning Tree (CCMLST) Problem is to find a spanning tree that uses the minimum number of labels while ensuring its cost does not exceed B. The Label Constrained Minimum Spanning Tree (LCMST) Problem is closely related to the CCMLST problem. Here, we are given a threshold K on the number of labels. The goal is to find a minimum weight spanning tree that uses at most K distinct labels. Both of these problems are motivated from the design of telecommunication networks and are known to be NP-complete. In this paper, we present a Variable Neighborhood Search (VNS) algorithm for the CCMLST problem. The VNS algorithm uses neighborhoods defined on the labels. We also adapt the VNS algorithm to the LCMST problem. We then test the VNS algorithm on existing data sets as well as a large-scale dataset based on TSPLIB instances ranging in size from 500 to 1000 nodes. The computational results show the effectiveness of the proposed algorithms

The Generalized Covering Salesman Problem

Mathematical models and metaheuristis algorithms are proposed for the solution of the Generalized Covering Salesman Problem. Computational results on benchmark instances from the literature show the effectiveness of the proposed approaches