Supply centers allocation under budget restrictions minimizing the longest delivery time (original) (raw)

Let G = (V, E) be a connected directed graph expressing a distribution network. The elements of D G k' represent demand centers, while S c V contains the candidate supply centers. To each node x ES, we associate a weight w(x) which corresponds to the cost of installing a supply center at node x. To every arc (x, y) E E we associate a weight a(x, y) which indicates the required time to reach node y directly from node x. The purpose of this paper is the determination of the subsets of S under a given budget restriction, so to minimize the longest delivery time of facilities to the demand nodes of D.

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Solving the Allocation of Customers to Potential Distribution Centers in Supply Chain Networks by GA, KA, SA

The 10th International Conference of Iranian Operation Research Society, 2017

This paper studies the two main parties of the supply chain networks; distribution centers (DCs) and costumers. The allocation problem of these parties is one of the main issues in the supply chain. There are two core types of cost for this problem; opening cost assumed for opening a potential DC plus dispatching cost per unit from DC to the costumers. The model chooses some potential places as distribution centers to supply the requirements of all costumers. In order to solve such NP-hard and basic problems, three algorithms are used. The Taguchi experimental design method utilized to find the best parameters for each algorithm. The aim of efficiency evaluation of proposed algorithms is several test problems that are employed and are compared to the computational results of each algorithm. Eventually, we examine the impacts of the rise in the problem size on the performance of our algorithms.

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Facility Location with Tree Topology and Radial Distance Constraints

Complexity

Let Gd=V,Ed be an input disk graph with a set of facility nodes V and a set of edges Ed connecting facilities in V. In this paper, we minimize the total connection cost distances between a set of customers and a subset of facility nodes S⊆V and among facilities in S, subject to the condition that nodes in S simultaneously form a spanning tree and an independent set according to graphs G¯d and Gd, respectively, where G¯d is the complement of Gd. Four compact polynomial formulations are proposed based on classical and set covering p-Median formulations. However, the tree to be formed with S is modelled with Miller–Tucker–Zemlin (MTZ) and path orienteering constraints. Example domains where the proposed models can be applied include complex wireless and wired network communications, warehouse facility location, electrical power systems, water supply networks, and transportation networks, to name a few. The proposed models are further strengthened with clique valid inequalities which ca...

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M.: Optimizing budget allocation in graphs

2016

In a classical facility location problem we consider a graph G with fixed weights on the edges of G. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We consider a new model for facility location problems, where the weights on the graph edges are not fixed, but rather should be assigned. The goal is to find the valid assignment for which the resulting weighted graph optimizes the facility location objective function. We present algorithms for finding the optimal budget allocation for the center point problem and for the me-dian point problem on trees. Our algorithms work in linear time, both for the case that a candidate vertex is given as part of the input, and for the case where find-ing a vertex that optimizes the solution is part of the problem. We also present an O(log2(n)) approximation algorithm for the center point problem over general met-ric spaces. 1

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Distribution Network Configuration Considering Inventory Cost

Inter-city distribution network structure is considered as one of which determine the quantity of economic activities in each city. In the field of operations research, several types of optimal facility location problem and algorithms for them have been proposed. Such problems typically minimize the logistic cost with given inter-city transportation cost and facility location cost. But, when we take inventory to coop with fluctuating demands into account, facility size becomes different for each location reflecting the level of uncertainty of demand there. As observed in many developed countries, customers require more variety of commercial goods, and we must prepare more number of commercial goods. Moreover, life length of each product becomes shorter. Without highly organized management, large inventory for many products yield large risk of depreciation of commercial value as well as large cost for floor space for stocking. Considering those, inventory cost should be explicitly co...

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