The value of flexibility in robust location-transportation problem


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Facility location decisions play a critical role in transportation planning. In fact, it has recently become essential to study how such commitment integrate with the delivery of goods on an underlying transportation network problems especially when there are reasons to be uncertain about what are going to be those needs. In this research, we study a capacitated fixed-charge location-transportation problem in which, while the location and capacity of each facility need to be determined immediately, the determination of final production and distribution of products can be delayed until actual orders are received. In contexts where little is known about future demand, robust optimization, namely using a budgeted uncertainty set, becomes a natural method to employ in order to identify meaningful decisions. Unfortunately, it is well known that these types of two-stage robust problems are computationally intractable. To overcome this difficulty, we propose a set of conservative tractable approximations to the problem that each exploits to a different extent the idea of reducing the flexibility of the delayed decisions. While all of these approximations will outperform previous approximation models that have been proposed for this problem, each of them will have the potential to reach a different level of compromise between efficiency of resolution and quality of the solution. We will also demonstrate that full flexibility is often unnecessary to reach nearly, or even exact, optimal robust locations and capacities for the facilities. We illustrate our findings with an extensive numerical study where we evaluate the effect of the amount of uncertainty on the performance and structure of each approximate solutions that can be obtained.

, 24 pages

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