H2O Water Supply Company

Problem Definition

H2O is a local water supply and delivery company. It owns a fleet of 30 tanker trucks for delivering water to customers. 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. The customer pays for the size of tank he wants to order, receives a copy of the receipt, proceeds to the water station operator and hands him the receipt copy, and then waits 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’s 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 occur 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. It is common that customers get frustrated, get their money back and leave, or closing time comes before any truck of the requested size has arrived.


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


  • 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, and 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

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