The present article deals with a backorder Economic Order Quantity (EOQ) model for natural leisure/closing time system where the demand rate depends upon the total shortage period and the seasonal effect. A cost minim...
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The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in ...
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The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The Shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one node to another often gives the best way to route message between the nodes. This paper presents an O(n 2 ) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs. The space complexity of this algorithm is of O(n 2 ). This problem has been solved by constructing n breadth-first search (BFS) trees with each of the n vertices as root. As the lower bound of time complexity for computing the all pairs shortest paths is known to be of O(n 2 ), this proposed algorithm is optimal.
This article focuses on an imperfect production inventory model considering product reliability and reworking of imperfect items in three-layer supply chain under fuzzy rough environment. In the model, the supplier re...
This article focuses on an imperfect production inventory model considering product reliability and reworking of imperfect items in three-layer supply chain under fuzzy rough environment. In the model, the supplier receives the raw materials, all are not of perfect quality, in a lot and delivers the items of superior quality to the manufacturer and the inferior quality items are sold at a reduced price in a single batch by the end of the cent percent screening process. The manufacturer produces a mixture of perfect and imperfect quality items. A portion of the imperfect items is transformed into perfect quality items after rework. Another portion of imperfect items, termed as `less perfect quality items', is sold at a reduced price to the retailer, and the portion which cannot be either transformed to the perfect quality items or sold at a reduce price is being rejected. Here, retailer purchases both the perfect and imperfect quality items from the manufacturer to sell the items to the customers through his/her respective showrooms of finite capacities. A secondary warehouse of infinite capacity is hired by the retailer on rental basis to store the excess quantity of perfect quality items. This model considers the impact of business strategies such as optimal order size of raw materials, production rate, and unit production cost in different sectors in a collaborating marketing system that can be used in the industry, like textile, footwear, and electronics goods. An analytical method has been used to optimize the production rate and raw material order size for maximization of the average profit of the integrated model. Finally, a numerical example is given to illustrate the model.
In this paper, we developed and investigated some four-dimensional profit maximization transportation problems considering damageablity and substitutability, where the parameters are of a type-2 normal uncertain varia...
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The aim of this article is to present a fuzzy programming approach to a singlesink, fixed-charge, multiobjective, multi-index stochastic transportation problem (SSMISTP). This article focuses on the minimization of th...
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Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...
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Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
In this paper, a new concept of bifuzzy bi-matrix game is introduced where all elements of the payoff matrices are characterized by bifuzzy variables. The uncertainties of entries of payoff matrices (bifuzzy variables...
In this paper, a new concept of bifuzzy bi-matrix game is introduced where all elements of the payoff matrices are characterized by bifuzzy variables. The uncertainties of entries of payoff matrices (bifuzzy variables) are measured by bifuzzy measure known as Chance measure. Combining the bifuzzy set theory and bi-matrix game theory, the solution concept of bifuzzy bi-matrix game theory is introduced. The quadratic programming problem plays the major role to solve bifuzzy bi-matrix game. In order to show the applicability and feasibility of our proposed method, a real-life bi-matrix game problem is considered and solved.
A solution of m×n rectangular fuzzy game with payoff as imprecise numbers instead of crisp real numbers namely interval and triangular fuzzy numbers is considered here. Solution of such fuzzy games with pure stra...
A solution of m×n rectangular fuzzy game with payoff as imprecise numbers instead of crisp real numbers namely interval and triangular fuzzy numbers is considered here. Solution of such fuzzy games with pure strategies and the algebraic method to solve 2×2 fuzzy game without saddle point by using mixed strategies is also discussed. Here the m×n payoff matrix is reduced to 2×2 payoff matrix by dominance method. In this paper, we discuss a saddle point solution from an uncertain payoff matrix. Moreover solution method for fuzzy games has also been developed. Numerical example is provided to illustrate the method.
An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference betw...
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An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.
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