Prepositioning emergency supplies under uncertainty: a parametric optimization method

ABSTRACT

Prepositioning of emergency supplies is an effective method for increasing preparedness for disasters and has received much attention in recent years. In this article, the prepositioning problem is studied by a robust parametric optimization method. The transportation cost, supply, demand and capacity are unknown prior to the extraordinary event, which are represented as fuzzy parameters with variable possibility distributions. The variable possibility distributions are obtained through the credibility critical value reduction method for type-2 fuzzy variables. The prepositioning problem is formulated as a fuzzy value-at-risk model to achieve a minimum total cost incurred in the whole process. The key difficulty in solving the proposed optimization model is to evaluate the quantile of the fuzzy function in the objective and the credibility in the constraints. The objective function and constraints can be turned into their equivalent parametric forms through chance constrained programming under the different confidence levels. Taking advantage of the structural characteristics of the equivalent optimization model, a parameter-based domain decomposition method is developed to divide the original optimization problem into six mixed-integer parametric submodels, which can be solved by standard optimization solvers. Finally, to explore the viability of the developed model and the solution approach, some computational experiments are performed on realistic scale case problems. The computational results reported in the numerical example show the credibility and superiority of the proposed parametric optimization method.

Keywords:

• Emergency supplies
• parametric optimization
• risk measure
• variable possibility distribution
• domain decomposition method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported partially by the National Natural Science Foundation of China [Nos. 61374184 & 61374082], the Youth Natural Science Foundation of Hebei Province [No. A2016204057] and the China Scholarship Council [No. 201606365008].