H20 Water Supply Company with
Demonstration Model

Problem Definition:
H2O is a local water supply and delivery company. It owns a fleet of 30 tanker trucks for delivering water to customer. There are 3 sizes of the truck tanks: size A is 12 cubic meters, size B is 18 cubic meters, and size C is 28 cubic meters. Currently, there are 9 trucks with tanks of size C, 12 trucks with tanks of size B, and 9 trucks of size A.

To place order, a customer must come in person to the H2O office. He should first pay for the size of tank he wants to order, receive a copy of the receipt, proceed to the water station operator and hand him the receipt copy, and wait in the waiting area until a tanker truck of the required size is filled with water at any of the available pumps. Currently, there are 7 pumps installed at H2O. When the truck is ready, the customer name is called and he leaves the station escorted by his truck. After the truck empties its water tank at the customer's location, it returns immediately to the station and becomes ready for new orders. Problems water reported in this system when no trucks of the size requested by a customer are available. In this case, the customer would have to wait until at least one truck of the size desired returns and is filled with water again. These delays can, often, be very long and it is common that customers either get frustrated and leave after getting their money back, or closing lime comes before any truck of the requested size has arrived.

Goal:
Given past operational data, H2O management would like to determine how many trucks of each tank size it should maintain in order to reduce the average delay time before a customer's order is satisfied (Davg) to less than 15 minutes, given the current number of installed pumps. It is also desired to know the required number of pumping stations to maintain in order to reduce (Davg) below 15 minutes given the current number of trucks in the company's fleet. The management would then decide whether is cheaper its goal of limiting (Davg) by buying more trucks or by installing more pumps.

Assumptions:

• Customer interarrival times are exponentially distributed with 10 minutes between 2pm and 8pm, and with mean 20 minutes between 8am, (opening time) and 2pm and between 8pm and 10pm (closing time)
• Truck filling times are exponentially distributed with means: 10 minutes, 12 minutes, 20 minutes for tank sizes A, B and C, respectively
• Truck delivery time is normally distributed with mean 35 minutes and standard deviation 2
• The order processing time is uniformly distributed from 3 minutes to 5 minutes. Assume a FIFO queue is formed in case of congestion
• Ignore fueling and maintenance operation of trucks and pumps
• The probability that a customer will request a size A tank = 0.3, the probability that a customer will request a size B tank = 0.4, and the probability that a customer will request a size C tank = 0.3
• Increasing the number of trucks will follow the same ratio that the probability that a customer request a size. That means 0.3 for truck A, 0.4 for truck B, and 0.3 for truck

Demonstration Model (H2O.spm)

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H2O Water Supply Company Demonstration Model file (H2O.spm)

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