Problem:
Many treatment facilities overbook customer demand to assure there is no shortage of capacity. Some customers have regular water and wastewater demand that is consistently scheduled in advance, while other customer demand may run from or to their treatment facility around other events that can influence demand (i.e. community event, holiday, etc.). The treatment facility estimates that their employee s capacity is 6,000 gallons per day (per 8 hour shift). Each employee costs $1.50 per gallon. If customer demand exceeds capacity, the treatment facility has to arrange for employees on-call to come in and operate a back-up system support the overload. This requires an added fee which results in a loss of $5 per gallon. Customer demand may not be regular or consistent. These issues are normally distributed with a mean of 200 gallons and a standard deviation of 50 gallons.