PROBLEM : Machine Shop Grinders

Jake's Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on buying 1 or 2 more additional grinders. The grinding time required by a machine operator to sharpen cutting tool has an exponential distribution with mean grinding time equal to 1 minute. The machine operators arrive randomly to sharpen their tools at a mean rate of one every two minutes and the inter-arrival time is exponentially distributed.

The maintenance cost for a single grinder is estimated to be $1 per minute. The estimated cost of an operator being away from his/her machine for grinding his tools is $0.80 per minute (once an operator leaves for grinding, he/she does not come back until he/she grinds the tools and the time to go to the grinder is negligible).

Suppose that you are in the control of making decisions for buying additional grinders. You want to decide to buy 1 or 2 more additional grinders, or not to buy any more grinders. If you have more than one grinders, the machine operators will form a single line and the one in the front of the line will go to the next available grinder.

You can use the excel templates for calculating the measures of performance.

a) Calculate different measures of performance (L, Lc, W, WQ), when you do not buy any additional grinders. That is, when you have a single grinder. Also, calculate the cost per minute of the system with a single grinder.

b) Calculate different measures of performance (L, Lo, W, WQ), when you buy one additional grinder. That is, when you have two grinders. Also, calculate the cost per minute of the system with two grinders.

c) Calculate different measures of performance (L, Lc, W, WQ), when you buy two additional grinders. That is, when you have three grinders. Also, calculate the cost per minute of the system with three grinders.

d) Comparing costs per minute in parts a, b, and c, what is the decision you should make to minimize the cost per minute?