{
  "id": "1507.05125",
  "version": "v1",
  "published": "2015-07-17T22:15:31.000Z",
  "updated": "2015-07-17T22:15:31.000Z",
  "title": "On the Optimality of (s,S) Policies",
  "authors": [
    "Eugene A. Feinberg",
    "Mark E. Lewis"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper describes results on the existence of optimal policies and convergence properties of optimal actions for discounted and average-cost Markov Decision Processes with weakly continuous transition probabilities. It is possible that cost functions are unbounded and action sets are not compact. The results are applied to stochastic periodic-review inventory control problems, for which they imply the existence of stationary optimal policies and certain optimality properties. The optimality of $(s,S)$ policies is proved by using dynamic programming equations for discounted costs and the vanishing discount factor approach for average costs per unit time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-17T22:15:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90B15",
      "90C40"
    ],
    "keywords": [
      "optimality",
      "stochastic periodic-review inventory control problems",
      "average-cost markov decision processes",
      "vanishing discount factor approach",
      "stationary optimal policies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}