Deliveries in an inventory/routing problem using stochastic dynamic programming

An industrial gases tanker vehicle visits n customers on a tour, with a pos sible (n+1)st customer added at the end. The amount of needed product at ea ch customer is a known random process, typically a Wiener process. The obje ctive is to adjust dynamically the amount of product provided on scene to e ach customer so as to minimize total expected costs, comprising costs of ea rliness, lateness, product shortfall, and returning to the depot nonempty. Earliness costs are computed by invocation of an annualized incremental cos t argument. Amounts of product delivered to each customer are not known unt il the driver is on scene at the customer location, at which point the cust omer is either restocked to capacity or left with some residual empty capac ity, the policy determined by stochastic dynamic programming. The methodolo gy has applications beyond industrial gases.