Optimal lot sizing for products sold under free-repair warranty

Repairable items sold under a free-repair warranty (FRW) policy are examined. In the literature, the lot-size problem is treated as a quality-control problem and not as an inventory problem for a continuous-type deteriorating production system, in which there is a shift from an in-control state to an out-of-control state and it is assumed that the system has a geometric survival distribution. Consequently, smaller lots result in a reduction in warranty cost per item, but such a reduction is achieved at the expense of an increased manufacturing cost per item. In order to control such a production system economically under an FRW, tradeoffs between manufacturing cost and warranty cost must be analyzed. In this paper, analytical results are extended to a discrete general shift distribution, to provide an optimal lot size so that the long run total cost of the setup, inventory holding, and warranty is minimized. Different conditions for optimality, properties and bounds on the optimal lot size are provided. A numerical example is given to see the adequacy of using the geometric distribution when the actual distribution is discrete Weibull.