Question

A production process consists of two resources. One resource consists of one machine that is used to make 3 different parts. Those parts are needed to make the one product. The parts are labeled, A, B and C. To make a product requires 3 A parts, 2 B parts and 1 C part. Switching production from one type of part to another requires 2.5 minutes. Once setup to make a part, the machine works at the rate of 8 A parts per minute, 5 B parts per minute, and 2 C parts per minute.The second resources is an assembly process with 4 workers. The processing time at assembly is 4.5 minutes.Demand for this product occurs at the rate of 42 per hour.

How many part As should be made in a production cycle to minimize inventory without constraining the flow rate through the process? A non-integer answer is acceptable.

Answer 1

DemandDrate = 42 per hour

Total time required of resource 1 to meet demand rate = 42*(3/8+2/5+1/2)

= 53.55 minutes (excluding setup time). This is less than 60 minutes. Therefore, this resource can satisfy the Demand rate using appropriate batch size.

Capacity of assembly resource = 4*60/4.5 = 53.33 per hour. This is more than Demand rate. Therefore, assembly is not bottleneck.

With a batch size of Q (final product), cycle time including setup time required of resource 1 = Q*(3/8+2/5+1/2)+2.5*3 = 1.275Q+7.5 minutes

Desired cycle time as per demand rate = Q*60/42

To minimize inventory, 1.275Q+7.5 = 1.4286Q

Q = 7.5/(1.4286-1.275)

= 48.84

Number of As to be made in a production cycle = 48.84*3 = 146.52