Inventory systems with multi-class demands under continuous review : policies and algorithms
Date of Issue2012
School of Mechanical and Aerospace Engineering
As the after-market service industry’s prospects grow, it is becoming imperative for the OEMs to satisfy their customer’s varying service requirements and do so economically. Differentiating the demand into different classes according to their service requirement and using inventory rationing to fulfill the demand is one technique to accomplish this. In military materials management, when the same spare part is requisitioned from various divisions, an inventory control policy that prioritizes the request for fulfillment is needed so that the division with the most mission-critical needs obtain the part first. Critical level inventory rationing, where the lower class demand is either backordered or not satisfied after on hand inventory reaches a pre-determined critical level (called rationing level), is the most cost effective inventory policy used for this type of problems. Since the revenue generated from aftermarket service and sales of spare parts is huge, firms are more concerned to solve this type of problems with an objective of minimizing the inventory cost and maximizing the service level imparted to different customer classes. In the first part of the dissertation, inventory rationing policies are considered for ‘n’ customer classes, and a model is developed to find the optimal policy parameters, assuming deterministic demand. A general penalty cost structure including delay cost and stock out is considered in developing this model; which has not been considered in the other studies. It is assumed that demands are backordered from a customer class after its run-out time. Run-out time of a customer class is defined as the time after which demand from that class is rejected and satisfied when next replenishment arrives. The total inventory cost to be minimized consists of inventory carrying cost, ordering cost and penalty cost. An algorithm is developed to determine the optimal cycle time and consequently, the run-out time for each customer class. Finally some numerical examples are provided to demonstrate the effectiveness of the algorithm. The part second part analyses an inventory system with multiple customer classes and considered rationing polices. Under the assumption of Poisson demand, a model is developed and the expression for expected cost is derived. Apart from developing an algorithm to solve the multiple-class problem, the impact of collapsing an n-class model into a 2-class or 3-class model (by aggregating several classes together) is investigated, numerically. In most of the cases, an aggregated 2-class or 3-class model achieves most of the benefits of rationing with a cost that is only marginally higher than an n-class model. The final part of this dissertation reports a new class of two-bin policy where two separate bins are kept for the two classes. When demand arrives from a class, it is satisfied from the bin designated for it, if inventory is available. The higher class can use the lower class’s bin when its own stock runs out but not vice versa. Demand follows a Poisson process and is differentiated by the penalty cost of not satisfying that class’ demand. The policy reserves some stock for both the classes, but the higher class is given more priority by allowing it to use the lower class’ stock. The exact expression for the expected cost of a policy as well as search algorithm for determining the optimal policy is developed. Although critical level inventory rationing provides an inventory policy with a lower cost, its shortcoming is in respect to the service levels it provides to the different classes. Numerical results show that this policy provides a much higher service level to the lower class, compared to inventory rationing, at a slightly higher cost, for most of the cases. It was also found that the proposed policy outperforms the critical level rationing policy when the holding cost is low and lead time is relatively higher.