Two-period, stochastic, supply-chain models with recourse for naval surface warfare

Abstract

We model the minimum-cost procurement and allocation of anti-ship cruise missiles to naval combat ships as a two-period stochastic integer program. Discrete scenarios in two periods define "demands" for missiles (i.e., targets and number of missiles required to kill those targets), which must be met with sufficiently high probabilities. After the former combat period, ships may replenish their inventories from a depot if desired and if the available depot inventory suffices. A force commander optimizes ship-to-target assignments to meet demands. The basic model solves slowly, so we add constraints to enforce reasonable operational directives, and add valid inequalities. These improvements reduce the solution time by 95% for the test case. Instances with up to six ships and five scenarios in each period then solve in less than one hour on a 2 GHz personal computer.