CPC, a chemical processing company, uses a special catalyst chemical in some of their processing; they keep the chemical in a large vat that holds up to 1,000 litres. Daily demand for the chemical averages 24.6 litres with a standard deviation of 11.1. The vat is equipped with a sensor that can alert an operator when the amount of chemical in the vat reaches a pre-determined reorder point, at which time an order is placed with the supplier who will use a tanker truck to deliver more chemical (they refill the vat directly from the tanker). The leadtime on a replenishment order is four days (assume no variability in lead time), and a typical order size is 500 litres.
In general, if the vat runs out of the chemical before the tanker arrives with replenishment, CPC can delay production without much problems, and thus they are thinking of setting the reorder point quite low (also because the chemical is expensive). Help them with the math:
At how many litres should the reorder point sensor be set if the goal is to ensure that there is less than a 5% chance of stocking out while waiting for the tanker to arrive (i.e. a 95% Cycle Service Level)?
At how many litres should the reorder point sensor be set if the goal is to ensure that there is less than a 10% chance of stocking out while waiting for the tanker to arrive?
At how many litres should the reorder point sensor be set if the goal is to ensure that there is less than a 15% chance of stocking out while waiting for the tanker to arrive?