Consider a production line with four single-machine station in series. Each has

Question

Consider a production line with four single-machine station in series. Each has processing times with mean 3 hours and standard deviation of 1.8 hours.

a) Suppose we run this line as a push system and release jobs into the line at a rate of 0.4 per hour with arrival variability given by Ca = 1.

What is the average WIP in the line?

b) Compute the throughput of this line if it is run as a CONWIP line with a WIP level equal to your answer in (a). Is the throughput higher or lower than 0.4? Explain this result.

Suppose the marginal profit is $70 per piece and the cost of WIP is $0.40 per piece per hour.

c) What is the profit from the push system if we set at 0.3?

d) What is the profit from the pull systems if we set at 15?

Explanation / Answer

Processing mean time(te) = 3 hr; SD = 1.8 hr; job rate (ra) = 0.4 per hr

Utilization of the server (u) = ra x te = 0.4/60 * 3 = .02

Time spend in the station (CT) = {(Ca) 2 + (Ce)2 /2} {u/1-u}*te + te

                                                 = {(1)2 + (1.8/3)2} {.02/.98} * 3 +3 = {0.68}{.02}*3+3 = .041+3 = 3.041

a. WIP = CT * TH = 3.041 * 3/60 = .0152 jobs

b. Throughput (TH) = 3/60 = 0.05 which is less than 0.4 (jobs arrival rate) Servicing rate is slower in this case.

c. marginal profit is $70 per pcs and WIP cost is $0.4 per pcs

Then profit from the push system is = 70*.4 -0.4*0.02 = $ 27 per

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