Question

PA 7-2 (Algo) A machine makes two components; call... A machine makes two components; call themn types A and B. It takes 550 seconds to switch production between the component types. During that time, no production occurs. When in production, each unit of A or B requires 0.5 second to be completed. The two components, A and B, are combined in an assembly process to make a final product; call it C. The assembly step can combine the two components into 1 unit every 4 seconds, or 15 units per minute. points 0204:12 Suppose the machine rotates between one batch of 2200 units of A and 2200 a. units of B. In that case, what is the capacity of the machine in component pairs per minute, where a component pair is one unit of A and one unit of B? component pairs per minute eBook Print References Suppose the machine rotates between one batch of 2200 units of A and 2200 units of B. What is the utilization of the machine? percent Suppose the machine rotates between one batch of 2200 units of A and 2200 U units of B. What is the average inventory of B components? units If the production schedule could be adjusted with the goal of minimizing d inventory in the process, how many units of A should be produced before switching to component B? Assume the same number of units of B would be produced as well. units

Answer 1

a.550 seconds set-up time for Unit A + (2200 components × 0.5 runtime for Unit A) + 550 seconds set-up time for Unit B + (2200 components × 0.5 runtime for Unit B) = 3300 seconds. 2200 component pairs/3300 seconds = 0.667 component pairs per second, or, 60 seconds per minute * 0.51 component pairs per second = 40.00 component pairs per minute.

b.Utilization = flow rate × processing time. Flow rate = 0.6667 assembled units per second. Processing time = 0.5 + 0.5 seconds. Utilization = 0.67*(0.5 + 0.5) = 67%

c.Average inventory = ½ × Maximum inventory

Maximum inventory = Batch × [1–(flow rate × processing time)] = 2200 × [1 - (0.67 × 0.5) ] = 1463

Average inventory = ½ × 1463 = 731.50

d.Batch size = [target capacity × total set-up time]/[1- (target capacity × processing time)]

Batch size = [ 0.67 × 2 × 550 ]/[1 - (0.67 × (0.5 + 0.5))] = 2233

Note: If the process is supply-constrained (i.e., the rate of demand is greater than the capacity of the bottleneck), then the target capacity is the capacity of the bottleneck