Consider a CONWIP flow line with 3 stations in series (1 rightarrow 2 rightarrow

Question

Consider a CONWIP flow line with 3 stations in series (1 rightarrow 2 rightarrow 3); each station consists of a set of identical machines. The throughput capability (production rates) of stations 1, 2, and 3, are 3, 2, and 4 units per hour respectively, and the corresponding unit processing times are 2 hours, 2 hours, and 1 hour. Answer the following questions using the data specified. a) Calculate the bottleneck rate, the raw process time, and the critical WTP for this line. b) Can the critical WTP exceed the number of stations in a line? Can critical WTP exceed the number of machines in a line? Explain the logic behind your answers. c) How many identical machines are currently there at station 2? d) If WTP is managed so that it averages w = 6 units, compute the best case, worst case, and practical worst case throughput and the corresponding cycle times for the line. e) Based on the available information on the flow line, would you expect the actual line's throughput to be smaller or larger than your Practical Worst Case estimate?(Explain your reasoning-this question is asking you to examine if the assumptions behind the PWC calculations are satisfied by the line or not and if not what the impact of assumption violation is likely to be.) f) If you could not change the bottleneck rate and the raw process time for the line, what could you do to increase the practical worst case throughput to double the value that you obtained in your answer to part d above?

Explanation / Answer

(a) Bottleneck Rate (rb) = rate of workstation having maximum long-term utilisation = 2 units per hour of workstation 2.

Raw process time, T0 = Sum of average processing time of all workstations = 2+2+1 = 5 hours

Critical WIP, W0 = rb * T0 = 2*5 = 10 units

(b) Critical WIP can exceed the number of stations in a line, however for a balanced line, critical WIP is equal to the number of machines in line. otherwise it will be less than the number of machines in line. This is because critical WIP is calculated based on the bottleneck rate, which corresponds to the station with the maximum utilisation. which means there are other stations with less utilisation, and therefore the number of machines have to be more than the critical WIP.

(c) Number of identical machines at station 2 = throughput rate * unit processing time = 2 * 2 = 4 machines

(d) w = 6 units, W0 = 10 units. , w < W0, therefore

Best case: CTbest = T0 = 5 hours, THbest = w/T0 = 6/5 = 1.2 units per hour

Worst case: CTworst = w * T0 = 6*5 = 30, THworst = 1/T0 = 1/5 = 0.2

Practical Worst Case (PWC): CT(line)pwc = T0 + (w-1) / rb = 5 + (6-1)/2 = 7.5 , THpwc = [w/(w+W0 - )]rb = [6/(6+10-1)]*2 = 0.8

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