Question

Question:The bathtub theory of operations management is being promoted as the next breakthrough for global competitiveness. The factory is a bathtub with 50 gallons of capacity. The drain is the outlet to the market and can output three gallons per hour when wide open. The faucet is the raw material input and can let material in at a rate of four gallons per hour. Now, to test your comprehension of the intricacies of operations (assume the bathtub is empty, to begin with):

1. Draw a diagram of the factory and determine the maximum rate at which the market can be served if all valves are set to maximum. What happens to the system over time?
2. Suppose that, instead of a faucet, a five-gallon container is used for filling the bathtub (assume a full container is next to the tub, to begin with); it takes two hours to refill the container and return it to the bathtub. What happens to the system over time?

Short answer

Answer

Technically bottlenecks can be defined as a point in any process where the workflow is somehow delayed or breakdown. In simple terms, when we talk about a bottleneck in any calculation then it is the comparison between two numeric values, and the lowest number is considered the bottleneck.

In this question, both parts i.e. ‘A’ and ‘B’ will be solved using the bottleneck concept.

Step-by-step solution

Step 1:(a) Maximum rate of output

Step 1:(a) Maximum rate of output

The maximum rate of output will be limited by the value of the bottleneck, which is either faucet or the drain.

Here, the faucethas a higher value i.e. 4 gallons per hour than the drainwhich has the value of 3 gallons per hour. So drain is the bottleneckof the system with a value of 3 gallons per hour.

(b) Maximum rate of output as the situation

Step 2: (b) Maximum rate of output as the situation

One 5-gallon container will be added to the tub every two hours, so the hourly input rate will be:

= Number of containers/ Hours

= 5/2 = 2.5 gallons per hour.

The drain will still drain at 3 gallons per hour, so here the bottleneckis the container with the average output rate of 2.5 gallons per hour