Stopped Myopic Policies in Some Inventory Models with Generalized Demand Processes

This paper considers single-item inventory systems with immediate delivery and no economies of scale. Bounds are provided on the value loss relative to optimal cost for restricting attention to the class of inventory stocking policies that behave myopically up to a specified stopping time. The stopping time may be random, and may depend on demand histories as well as information exogenous to the firm. The bounds are robust to the nature of the demand process faced after the stopping time, so are applicable when the statistics of demand after the stopping time are unknown. Stopping times that are large with high probability imply that near-term decisions are completely specified with high probability. The general bounding results allow one to consider demand processes that may otherwise be analytically intractable. It is shown that the class of demand models for which the assumption of additive i.i.d. shocks is appropriate is the same class admitting effective myopic stocking policies. The bounds also make rigorous the intuitive notion that myopic policies are least effective in systems with precipitous drops in demand coupled with an inability to recover cash invested in inventory. The option of selling inventory at discount is a reality in many real systems and enhances the attractiveness of the myopic stocking policy. In numerical examples, the myopic policy is shown to be an effective competitor in a range of systems for which optimal policies are not known. The results suggest that for systems with immediate delivery, no economies of scale, and no currently known optimal policy, the myopic stocking rule is a reasonable default policy to adopt.