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# notfeb - University of Southern California Department of...

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University of Southern California Department of Industrial and Systems Engineering ISE 310L Production I; Facilities and Logistics Spring 2000 February Lecture Handouts (Part 1) Machine Requirement Planning Dr. Ardavan Asef-Vaziri

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Machine Requirement Planning Scrap Geometric Scrap Quality Scrap due to geometry -Ex. A rectangular sheet is used to create a circular component. -Ex. Roles of fabric to create shirt. Scrap due to quality: mistake in machining or assembly Ideal: zero quality scrap Better material Looser tolerances Factors reducing scrap Automated processes Quality at source ( More certified suppliers) Geometric scrap results in more material requirements Quality scrap results both in more material requirements and also machine requirements. Input / Output Analysis Notation P i Process i Process i I i O i = I i (1-P i ) P i I i
The above notation means the rate of quality scrap at process i is equal to P i , where P i is positive but much less than 1. We refer to P i as the rejection rate at process i. Therefore if I i is input to process i, and P i is the rejection rate at this process, then the output of process i is O i = I i –P i I i = I i (1-P i ) or I i = O i / (1-P i ) Ex. Suppose we need 134000 units of a part per year. 7 serial operations are required to produce this part. The production routing and the rejection rates are given below. Operation 1 2 3 4 5 6 7 Machine A B C D E F G Rejection rate (%) 4 5 2 3 2 0 0 What is the required input to operation 1 which results in 134,000 acceptable units out of operation 7? If the number of working hours is 2000/yr, then the required production of the final product is 134000/2000 = 67 output units per hour.. O 7 =67 I 7 = O 7 /(1- P 7 ) = 67/(1-0) =67 = O 6 O 6 = I 7 O i-1 = I i O i-1 = O i /(1- P i ) O 5 =67/(1-0) =67 O 4 = 67/(1-0.02) =68.3 O 3 = 68.3/(1-0.03) =70.5 O 2 = 70.5/(1-0.02) =72 O 1 =72/(1-0.05) =75.8 I 1 = O 1 /(1-P 1 ) =75.8/(1-0.04) = 78.9 Operation Machine Output Input

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1 A 75.8 78.9 2 B 72 75.8 3 C 70.5 72 4 D 68.3 70.5 5 E 67 68.3 6 F 67 67 7 G 67 67 What is the overall yield of the system? Yield = Out/In =O 7 / I 1 = 67/78.9 Overall yield is 85% Machine requirement planning To calculate required number of machines we need the following information. - volume of production (input to each operation).
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