A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process

The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels

An inventory control project in a major Danish company using compound renewal demand models

We describe the development of a framework to compute the optimal inventory policy for a large spare-parts’ distribution centre operation in the RA division of the Danfoss Group in Denmark. The RA division distributes spare parts worldwide for cooling and A/C systems. The warehouse logistics operation is highly automated. However, the procedures for estimating demands and the policies for the inventory control system that were in use at the beginning of the project did not fully match the sophisticated technological standard of the physical system. During the initial phase of the project development we focused on the fitting of suitable demand distributions for spare parts and on the estimation of demand parameters. Demand distributions were chosen from a class of compound renewal distributions. In the next phase, we designed models and algorithmic procedures for determining suitable inventory control variables based on the fitted demand distributions and a service level requirement stated in terms of an order fill rate. Finally, we validated the results of our models against the procedures that had been in use in the company. It was concluded that the new procedures were considerably more consistent with the actual demand processes and with the stated objectives for the distribution centre. We also initiated the implementation and integration of the new procedures into the company’s inventory management systemBase-stock policy; compound distribution; fill rate; inventory control; logistics; stochastic processes

Survival after prolonged resuscitation with 99 defibrillations due to Torsade De Pointes cardiac electrical storm: a case report

A 48-year-old previously healthy woman suffered witnessed cardiac arrest in hospital. She achieved return of spontaneous circulation and was transferred to the intensive care unit. During the following 3 hours, she suffered a cardiac electrical storm with 98 episodes of Torsade de Pointes ventricular tachycardia rapidly degenerating to ventricular fibrillation. She was converted with a total of 99 defibrillations. There was no response to the use of any recommended anti arrhythmic drugs. However, the use of bretylium surprisingly stabilized her heart rhythm and facilitated placing of a temporary pacemaker. Overdrive pacing prevented further arrhythmias and was life saving. A number of beneficial factors may have contributed to the good neurological outcome. Further investigations gave no explanation for her cardiac electrical storm