Resource allocation for contingency planning: An inexact proximal bundle method for stochastic optimization

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. The solution method proposed relies on an inexact proximal bundle method with subgradient approximations through a scenario reduction mechanism. The paper extends the inexact oracle to a more general risk-averse setting, and proves that it meets 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 coherent risk measures. Our analyses indicate 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.