Stochastic dynamic programming heuristic for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1451" altimg="si16.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> policy parameters computation

This paper introduces a new stochastic dynamic program (SDP) based heuristic to compute the (R,s,S) policy parameters for non-stationary lot-sizing problem with backlogging of excessive demand, fixed order and review costs, linear holding penalty costs. Our model combines greedy relaxation that considers replenishment cycles independent modified version Scarf’s (s,S) SDP. A simple implementation requires prohibitive computational effort parameters. However, leveraging K-convexity property deploying memoisation techniques strongly reduce required. The resulting algorithm is considerably faster than state-of-the-art, extending its applicability by practitioners. An extensive study shows our approach computes optimal in more 97% analysed instances, 0.02% average optimality gap.