Process Flow Analysis - Flow Shop

Twelve products are made with various routings through a flow shop consisting of 10 machines. The table shows operation times in the machines expressed in hours. Blank cells indicate that no processing is required. Machines are passed in numerical sequence.

 Product Machine A B C D E F G H I J K L 1 Mould 0.1 0.1 0.2 0.2 0.3 0.1 0.4 0.6 0.7 0.4 0.1 0.1 2 De-fraze 0.3 0.5 0.2 0.1 0.2 3 Barrel Polish 0.3 0.6 0.2 0.2 4 Test 0.4 0.1 0.3 5 Machine 0.4 0.2 0.2 0.3 0.4 6 Paint 0.2 0.2 0.2 0.2 0.2 0.2 0.6 7 Sub-assemble 0.1 0.3 0.2 0.3 0.1 0.1 8 Chemical Test 0.2 9 Dimensional insp. 0.1 0.3 0.1 0.2 0.5 0.4 0.2 0.2 10 Final insp. 0.4 0.4 0.2 0.3 0.3 0.2 0.2 0.4 0.1 0.2 0.3 0.3

Machine characteristics are shown in the table below. The cost added is the cost of the raw materials accumulated at each machine through which a product passes. The machine cost is the cost of operating a machine per week. The cost does not depend on the time used on the machines. Machines operate 40 hours per week.

 Machine 1 2 3 4 5 6 7 8 9 10 Machine Size (sq. m.) 2 3 4 5 4 3 2 3 4 1 Machine cost (\$/week) 50 30 40 30 100 80 60 20 70 40 Cost Added (\$) 10 1 2 1 3 1 2 2 1 1

Weekly sales and unit revenues for the products are in the table below with unit revenue

 Product A B C D E F G H I J K L Sales 100 200 50 300 80 40 120 200 250 100 120 180 Unit Revenue (\$) \$20 28 28 24 28 24 24 22 21 22 26 25

 a. Use the process flow add-in to determine the number of machines necessary to manufacture the amounts required to meet the projected sales. Provide enough capacity so that machines have an 80% utilization. Specify the number of machines required. b. Based on the economic data given above, what is the weekly profit for the system? c. Assume the order arrivals for the products are Poisson processes with expected values as in the sales table above. Assume processing times are exponentially distributions. Use a queuing analysis to estimate the queue delays at each machine. d. In addition to the machine space requirements allow at least 1.5 times the expected queue lengths (rounded up to the nearest integer) for waiting products. Assume that WIP in queues requires 0.4 sq. meters of space. Use the space requirements and the flow between machines for a facility layout analysis. Use a plant size that is 30 meters long by 10 meters wide. What is the total material flow per week for the best plant layout you can find?

Operations Management / Industrial Engineering
Internet
by Paul A. Jensen