A Continuous Review Inventory System with Bulk Demand and Markov Dependent Replenishment Quantities

Abstract

The paper deals with a continuous review bulk demand (positive-integer valued) (s, S) inventory system where the interarrival times of demands are independent and identically distributed random variables. We assume that the successive quantities demallded lie between a and b (0<a⩽b; s-b+l⩾0) with p_k, k=a, a+l, ... ,b-1, b as the probability that k items are demanded by an arriving unit. The maximum capacity of the system is S units and as soon as the inventory level falls to the set A= {s- b + 1, s- b + 2, ... , s -1, s}, order is placed for a quantity S- i if the ordering level is i, i ε A. Our model assumes that the quantity replenished forms a Markov chain defined over thestatespace E={c, c + l, ... , S - s} with c⩾b. Lead time is zero and no shortage is permitted. The distribution of the on band inventory at arbitrary time point and also the limiting distributions are obtained. A numerical illustration associated with the model is also provided.