Abstract
This paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue point changes in a given definition set, the model can ensure the feasibility of each line. We propose a branch and price cutting algorithm, whose pricing problem is a robust resource-constrained shortest path problem. In addition, we take the Wenchuan Earthquake as an example to verify the practicability of the method. The robust model is simulated under different uncertainty levels and distributions and compared with the scheme obtained by the deterministic problem. The results show that the robust model can run successfully and maintain its robustness, and the robust model provides better protection against demand uncertainty. In addition, we find that cost is more sensitive to uncertainty level than protection level, and our proposed model also allows controlling the robustness level of the solution by adjusting the protection level. In all experiments, the cost of robustness is that the routing cost increases by an average of 13.87%.
Highlights
With the deterioration of the environment, natural disasters such as fire, earthquake, and tsunami are endangering people’s survival and development
We can conclude that there are various uncertainties in practical problems, and it is necessary to consider robust optimization methods to solve these problems. Their main methods are described by random programming, opportunity constraints, and other methods, or when using robust optimization, only one parameter is considered for an uncertain factor, and the use of two parameters to describe the demand uncertainty from different angles is not involved. erefore, this paper considers the variation of two parameters, that is, a cardinality constraint support to describe its demand uncertainty
We describe the impact of the maximum deviation hi on the demand and only change its value to describe the magnitude of the demand deviation, resulting in demand uncertainty
Summary
With the deterioration of the environment, natural disasters such as fire, earthquake, and tsunami are endangering people’s survival and development. Moreno et al [15] assumed that the demand, supply, and road capacity were uncertain and established a scenario based two-stage stochastic programming model with the goal of minimizing the cost of emergency logistics and the cost of unmet demand loss of victims at the disaster site From these literatures, we can conclude that there are various uncertainties in practical problems, and it is necessary to consider robust optimization methods to solve these problems. Contributions of is Paper (1) Two uncertain support sets are used to define demand uncertainty (2) A branch-price and cut algorithm is proposed to solve the proposed model (3) A real case (Wenchuan Earthquake) is used to verify the effectiveness and applicability of the algorithm e rest of the paper is organized as follows: Section 2 defines the robust emergency facility location-routing problem with uncertain demand, in which the uncertainty support is based on the cardinal constraint set.
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