311_Session6

311_Session6 - Operations Management Session 6: Linear...

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Session 6 Operations Management 1 Operations Management Session 6:  Linear Programming
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Session 6 Operations Management 2 Reminders HW #2 Due Now. Bring laptops for Wednesday’s class!!!
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Session 6 Operations Management 3 Previous Class Capacity planning for Shouldice hospital How to best expand capacity?   Uneven schedules? New floor? Saturday surgeries? Open a franchise unit? How did we know that the given uneven schedule  maximized capacity (the number of patients that  could be admitted each week)?
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Session 6 Operations Management 4 Today’s Class Understand what a Linear Program is. Understand how to solve small LP’s graphically. See how to model the Shouldice hospital patient  admittance problem as an LP.
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Session 6 Operations Management 5 What to produce? A computer manufacturer produces 2 types of  computers HS (High Speed) and LS (Low Speed).  The profit margin for HS computer is $100 per unit  and for LS computer is $75 per unit.  One assembling machine is used for both models.  The machine operates 600 minutes a day. A HS  unit needs 30 minutes, and A LS unit needs 10  minutes. 
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Session 6 Operations Management 6 What to produce? One testing machine is also used for both models. The machine operates 600 minutes a day. A HS unit needs 10 minutes and A LS unit needs  20 minutes. 
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Session 6 Operations Management 7 What to produce? We also need a packaging machine.  The machine operates 600 min a day.  Every single product needs 20 min for packing.  
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Session 6 Operations Management 8 Solve Graphically LS HS 40 30 15 20 5 5 100*HS+75*LS = C (5,5) C=3000 C=1500
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Session 6 Operations Management 9 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600
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Session 6 Operations Management 10 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600 10*HS+20*LS = 600 (24,12) 30
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Session 6 Operations Management 11 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600 10*HS+20*LS = 600 20*HS+20*LS = 600 (15,15) 30
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Session 6 Operations Management 12 What to produce? x = # LS to produce; y = # HS to produce Maximize profit:  100y + 75x Assembly machine constraint: 30y + 10x <= 600 Testing machine constraint: 10y + 20x <= 600 Packaging machine constraint: 20y + 20x <= 600
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Session 6 Operations Management 13 Another Production Example A toy company offers 2 different dolls: Beauty and  Beast.  The daily demand for each doll is 400  units. There are two types of machines. Everyday, M1  can make 10 units of Beauty and 2 units of Beast;   M2 can make 3 units of Beauty and 7 units of  Beast.
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Session 6 Operations Management 14 Another Production Example M1 costs $7 K and M2 costs $5 K.
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This note was uploaded on 04/30/2008 for the course BUAD 311 taught by Professor Vaitsos during the Spring '07 term at USC.

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311_Session6 - Operations Management Session 6: Linear...

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