Question

A company that produces steel foiled rolls haves the following manufacturing process: Raw ---> aceration material Hot ---> pickling rolled Cold rolled -> foiled Rolls An average of one foiled roll comes out from the section of hot rolled every 15 minutes (the time between the rolls that come out follows an exponential distribution) to the Pickling section. To transport the rolls, there is a forklift which transports an average of 6 rolls per hour (the transport time follows an exponential distribution), and deposits them in an acid bath. The longer it takes for a roll to be transported the thicker oxide layer is formed, which makes the Pickling operation more difficult and more expensive. The cost of pickling per roll is estimated to increase by S 1,000 per minute from the time the roll leaves the hot rolling section until it enters the acid bath. With the production of 2000 foiled rolls per month. Would it be justified to invest in another forklift which would cause an operation and investment expense equivalent to $ 200,000 per month? I think that this problem can be solved with queue theory So, if you use POM- QM for windows to solve it I will be fascinated, but if you prefer solve it by hand or any other method or software I will also be very thankful

Answer 1

Current arrival rate for every roll = 60/15 = L = 4 rolls per hour. Current transport rate = u = 6 rolls per hour with 1 forklift. p = average utilization = L/u = 0.66

Hence average time spent in line as per queuing theory is p*1/(u-L) = 1/3 hours = 20 minutes.

With an additional forklift, there are 2 servers now. Hence s = 2. The new utilization of the system now is p = L/(s*u) = 4/(2*6) = 33%. Effective service rate = 2*u = 12 per hour. Hence average time in queue = 1/24 hours = 2.5 minutes.

Hence reduction in Time waiting = 20 - 2.5 = 18.5 minutes. For each minute there is a $1000 savings in cost. Hence total savings = 18,500 per roll. For 2000 rolls a month the total savings is 37 MM which is much higher than the investment needed of 0.2 MM . Hence the investment is justified.