The optimal production and advertising policies for an inventory control system of multi-item multiobjective problem under a single management are formulated as an optimal control problem with resource constraints und...
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In recent decades, global climate change has become one of the most critical environmental issues, leading to increased environmental and social concerns about the sustainability of logistics networks. This study prop...
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The k -tuple domination problem, for a fixed positive integer k , is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The case when k = 2 is cal...
The k -tuple domination problem, for a fixed positive integer k , is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The case when k = 2 is called 2-tuple domination problem or double domination problem. In this paper, the 2-tuple domination problem is studied on interval graphs from an algorithmic point of view, which takes O ( n 2 ) time, n is the total number of vertices of the interval graph.
Let G = ( V , E ) be a simple connected undirected graph. Each vertex v ∈ V has a cost c ( v ) and provides a positive coverage radius R ( v ). A distance d uv is associated with each edge { u , v } ∈ E, and d ( u ,...
Let G = ( V , E ) be a simple connected undirected graph. Each vertex v ∈ V has a cost c ( v ) and provides a positive coverage radius R ( v ). A distance d uv is associated with each edge { u , v } ∈ E, and d ( u , v ) is the shortest distance between every pair of vertices u , v ∈ V . A vertex v can cover all vertices that lie within the distance R ( v ), except the vertex itself. The conditional covering problem is to minimize the sum of the costs required to cover all the vertices in G . This problem is NP-complete for general graphs, even it remains NP-complete for chordal graphs. In this paper, an O ( n 2 ) time algorithm to solve a special case of the problem in a trapezoid graph is proposed, where n is the number of vertices of the graph. In this special
case, d uv = 1 for every edge { u , v } ∈ E , c ( v ) = c for every v ∈ V ( G ), and R ( v ) = R , an integer >1, for every v ∈ V ( G ). A new data structure on trapezoid graphs is used to solve the problem.
When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which the...
When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which they have to take a decision which is the best offer for them to make more profit. The retailers try to buy perfect-quality items at a reasonable price, and also they try to invest returns obtained by selling those items in such a manner that their business is not hampered. In this point of view, we consider an economic order quantity (EOQ) model for various types of time-dependent demand when delay in payment and price discount are permitted by suppliers to retailers. The models of various demand patterns are discussed analytically. Some numerical examples and graphical representations are considered to illustrate the model.
The bipolar fuzzy set and interval-valued bipolar fuzzy set efficiently analyse real-world problems where for each input of an object, there has counter information. This study's main objective is to lay a foundat...
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