Abstract
We consider a production planning problem under uncertainty in which companies have to make product allocation decisions such that the risk of failing regulatory inspections of sites - and consequently losing revenue - is minimized. In the proposed decision model the regulatory authority is an adversary. The outcome of an inspection is a Bernoulli-distributed random variable whose parameter is a function of production decisions. Our goal is to optimize the conditional value-at-risk (CVaR) of the uncertain revenue. The dependence of the probability of inspection outcome scenarios on production decisions makes the CVaR optimization problem non-convex. We give a mixed-integer nonlinear formulation and devise a branch-and-bound (BnB) algorithm to solve it exactly. We then compare against a Stochastic Constraint Programming (SCP) approach which applies randomized local search. While the BnB guarantees optimality, it can only solve smaller instances in a reasonable time and the SCP approach outperforms it for larger instances.
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Kawas, B., Laumanns, M., Pratsini, E., Prestwich, S. (2011). Risk-Averse Production Planning. In: Brafman, R.I., Roberts, F.S., Tsoukià s, A. (eds) Algorithmic Decision Theory. ADT 2011. Lecture Notes in Computer Science(), vol 6992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24873-3_9
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DOI: https://doi.org/10.1007/978-3-642-24873-3_9
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