New Policies for Stochastic Inventory Control Models: Theoretical and Computational Results

Recently Levi, Pál, Roundy and Shmoys introduced a novel, Dual-Balancing policy for the classical singleitem, single-location inventory model with backlogged demands and dynamic forecasts of future demands that evolve as time advances. These models are usually computationally intractable due to the enormous size of the state space. The expected cost of the dual-balancing policy is guaranteed to be at most twice the optimal expected cost, but until now, no computational testing of the policy has been done. We propose two extended families of policies, based on cost-balancing techniques and myopic-like policies that generate lower and upper bounds on the optimal base-stock levels. We show that cost-balancing techniques combined together with these lower and upper bounds lead to improved policies. The expected cost of the new policies is also guaranteed to be at most twice the optimal expected cost. Nevertheless, empirically their performance is significantly better. Moreover, all of the new policies can be implemented efficiently in an on-line manner. We have conducted extensive testing of these policies, with demand forecasts that evolve according to the multiplicative MMFE model. The best of the new generation of policies are very robust. They are consistently better than the classical myopic policy over a broad set of important scenarios, and the improvement can get to up to 30 percent. The computational results demonstrate the effectiveness and computational practicality of the new policies in realistic scenarios.