Resource Allocation for Contingency Planning: An Inexact Bundle Method for Stochastic Optimization

Abstract

Resource contingency planning aims to mitigate the effects of unexpected disruptions in supply chains. While these failures occur infrequently, they often have disastrous consequences. This paper formulates the resource allocation problem in contingency planning as a two-stage stochastic optimization problem with a risk-averse recourse function. Furthermore, the paper proposes a novel computationally tractable solution approach. The proposed algorithm relies on an inexact bundle method with subgradient approximations through a scenario reduction mechanism. We prove that our scenario reduction and function approximations satisfy the requirements of the oracle in the inexact bundle method, ensuring convergence to an optimal solution. The practical performance of the developed inexact bundle method under risk aversion is investigated for our resource allocation problem. We create a library of test problems and obtain their optimal values by applying the exact bundle method. The computed solutions from the developed inexact bundle method are compared against these optimal values, under different risk measures. Our analysis indicates that our inexact bundle method significantly reduces the computational time of solving the resource allocation problem in comparison to the exact bundle method, and is capable of achieving a high percentage of optimality within a much shorter time.