The General Model Sample Clauses

The General Model. For an inventory system with stationary demand and a stationary stocking policy, the long-run fill rate can be calculated by computing the expected units satisfied per period (or per replenish- ment cycle) and dividing this by the average demand. In a finite horizon setting, the achieved fill rate is a random variable. Xxxx et al. (2003) and Xxxxxxxx and Xxxx (2005) investigate the behav- ior of the expectation of the achieved fill rate over a finite horizon; however, a supplier facing a service-level agreement may be interested in the probability of meeting the specified target serv- ice level, rather than the expectation. Xxxxxx (2005) investigates the distribution of the fill rate achieved over a finite horizon, including the probability of meeting a specified target. It is worth noting that in all those papers, as well as this one, the form of the inventory policy is restricted to be a stationary, order-up-to policy. Such a policy is not necessarily optimal for a supplier facing a finite-horizon SLA, however, stationary policies are easy to implement and common in prac- xxxx. To focus on the implications of the service-level agreement, we choose a simple, periodic review inventory system with no ordering cost and zero lead time (next period delivery). Over a T period horizon, the supplier faces demands Di, i = 1,…,T . At the end of each period the sup- plier incurs a holding cost h per unit held in inventory and a shortage cost p per unit for un- filled orders. In addition to those costs, the supplier receives a bonus if her fill rate over the T - period horizon meets or exceeds the threshold fill rate, a0 . Since we will be making comparisons across different review horizon lengths, we will refer to the bonus amount in per-period terms. Let B denote the per-period bonus amount, implying a bonus of B × T for the T -period hori- zon. To clarify, the supplier gets the entire bonus of B × T if she achieves the target fill rate and zero otherwise. Let S represent the supplier’s order-up-to stocking level over the T -period horizon. The units of demand satisfied in any period t is then min( Dt , S ) . The supplier’s cost function has two components. First, in each period there is the familiar expected holding and shortage costs: G (S ) = pE( D – S )+ + hE(S – D )+. t t t We assume throughout our experiments that the demands are independent and identically- distributed across periods; thus we can drop the subscript t from Gt and represent the expected holdin...