Reliable facility location design under disruptions

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Abstract

Distribution networks have been facing an increased exposure to risk of unpredicted disruptions causing significant economic forfeitures. At the same time, the existing literature features very few studies which examine the impact of facility fortification for improving network reliability. In this paper, we present two related models for design of reliable distribution networks: a reliable P-median problem (RPMP) and a reliable uncapacitated fixed-charge location problem (RUFL). Both models consider heterogenous facility failure probabilities, one layer of supplier backup, and facility fortification within a finite budget. Both RPMP and RUFL are formulated as nonlinear integer programming models and proved to be NP-hard. We develop Lagrangian relaxation-based (LR) solution algorithms and demonstrate their computational efficiency. We compare the effectiveness of the LR-based solutions to that of the solutions obtained by a myopic policy which aims to fortify most reliable facilities regardless of the demand topology. Finally, we discuss an alternative way to assess the effectiveness of the design solutions by using the rate of return on fortification investment.

Section snippets

Motivation

Distribution networks are referred to the entire chain of intermediaries and transportation logistics for distribution of goods and services from the suppliers to the consumers. Modern distribution networks are complex engineered systems due to their size, span, the nature of customer assignment, and the network flow. At the same time, more and more enterprises have been embracing the philosophy of lean manufacturing with an ever increasing reliance on consolidated suppliers, outsourcing, slim

Status of current literature

Most of the existing literature on design of distribution networks takes its roots in the classical P-median [33] and the uncapacitated fixed-charge location problems [21]. Both these problems seek to choose facility locations and assignments of customers to minimize the total transportation (and construction) cost. In both original models, all facilities are assumed to be perfectly reliable. However, as evidenced from the above examples, facilities can experience disruptions which can cause

The reliable P-median problem (RPMP)

The model extends the reliable P-median facility location problem introduced by Snyder [31] by considering heterogeneous facility failure probabilities and facility fortification. The model seeks to minimize the total expected transportation cost by optimally locating P facilities, allocating a finite fortification budget, and assigning the customers. We first formulate this problem as a nonlinear integer programming model and then develop a Lagrangian relaxation-based solution algorithm.

The reliable uncapacitated fixed-charge facility location model

The RUFL model can increase the network reliability of RPMP by relaxing the restriction on the number of open facilities. Our RUFL model extends the reliable fixed-charge facility location problem introduced by Snyder [31] by considering heterogeneous facility failure probabilities and facility fortification. The model seeks to minimize the sum of the total facility construction cost and the expected transportation cost by optimally selecting facility locations, allocating a finite

Experimental design

We tested the performance of both the RPMP and RUFL solution algorithms on four datasets [14], [15] containing 30, 49, 100, and 150 nodes, respectively. The last three datasets were adapted from [31] whereas the 30-node dataset was generated by arbitrarily selecting 30 nodes from the 49-node dataset. Demands hi were taken from [31]. The Euclidean distance between nodes i and j was used as the transportation cost dij. We let the sets I and J be equal. The failure probabilities qj were randomly

Conclusions

In this paper, we presented two related models for design of distribution networks exposed to risk of disruptions: a reliable P-median problem and a reliable uncapacitated fixed-charge location problem. Both models considered heterogenous facility failure probabilities and one layer of supplier backup. The facility failure probabilities were assumed to be independent and location specific. We considered facility fortification whereby the cost of fortification was assumed to be location

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    This work was supported by National Science Foundation Grant CMMI 0621030.

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