The finite horizon nonstationary stochastic inventory problem: Near-myopic bounds, heuristics, testing

Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They have been shown in the literature to be optimal when demand ‘is increasing over time’, and to provide upper bounds for the stationary finite horizon problem (and in some other situations). Some results are also known, given special salvaging assumptions, about lower bounds on the optimal policy which are near-myopic. Here analogous but stronger bounds are derived for the general finite horizon problem, without such special assumptions. The best upper bound is an extension of the heuristic used by industry for some years for end of season (EOS) problems; the lower bound is an extension of earlier analytic methods. Four heuristics were tested against the optimal obtained by stochastic dynamic programming for 969 varying problems. The simplest heuristic is the myopic heuristic itself: it is good especially for moderately varying problems without heavy end of season salvage costs and averages only 2.75% in cost over the optimal. However, the best of the heuristics exceeds the optimal in cost by an average of only 0.02%, at about 0.5% of the computational cost of dynamic programming.