09 QM Lecture Note C

# 09 QM Lecture Note C - Optimization GG Hegde Readings from...

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1 Optimization: GG Hegde Readings from the text: Ch.1, Ch.2 skip section 2.10 Ch.3 skip sections 3.10, 3.12, 3.13, 3.14 Ch.4 skip sections 4.7,4.8 Ch.6 skip sections 6.16, 6.17 Ex.1: “Mobile Phones production” How many basic models and how many premium models to produce? Mobile phones need to be assembled by software engineer S and tested by Quality control manager Q. Refer to the data below. Models : Basic(B) Premium(P) Resources : Software engineer S 20 min/unit 5 min/unit (2,400 min available ) QC manager Q 15 min 30 min (2,400 min available ) Selling price/unit: \$45 \$60 Total Labor Time/unit: 35 min 35 min Market (Demand): 100 units 50units Total Revenue=

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2 a) Can you satisfy the demand Check whether we can satisfy the demand B=100 P=50 Required Available S 100*20=2000 50*5=250 2250 min 2400 min Q 100*15=1500 50*30=1500 3000 min 2400 min b)Which is your preferred product? B: \$45/15 min of Q = \$3 per min of Q P: \$60/30 min of Q =\$2 per min of Q Prefer B. c)B=100 units, P= Leftover time of Q/ 30 min = (2400- 100*15 min)/30= 30 units Thus, best production plan: B=100 units, P= 30 units, Total revenue= \$6300
3 Formulate the problem as an LP LP formulation Decision Variables : B= # of units of Basic models to be produced, P= # of units of Premium models to be produced. Goal: Optimal production plan Objective Function : Max Total Revenue: Max 45 B + 60 P Constraints: Engineer S: 20 B + 5 P <= 2400 Manager Q: 15 B + 30 P <= 2400 Demand for B: B <= 100 Demand for P: P <= 50

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4 Computer Solution: E xcel Layout. This is what you type in Excel: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 AB C D E F G Ex.1-Mobile Phone BP # to be Produced 1 1 Obj: Rev 45 60 =SUMPRODUCT(B4:C4,\$B\$3:\$C\$3) Max Rev Software Engineer S 20 5 =SUMPRODUCT(B5:C5,\$B\$3:\$C\$3) <= 2400 minutes QC Manager Q 15 30 =SUMPRODUCT(B6:C6,\$B\$3:\$C\$3) <= 2400 minutes Market for B 1 =SUMPRODUCT(B7:C7,\$B\$3:\$C\$3) <= 100 units Market for P 1 =SUMPRODUCT(B8:C8,\$B\$3:\$C\$3) <= 50 units LP: max 45B+60P 20B+5P<=2400min 15B+30P<=2400min B<=100 P<=50 This is what you see in Excel: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C D E F G Ex.1-Mobile Phone # to be Produced 1 1 Obj: Rev \$45 \$60 105 Max Rev Software Engineer S 20 5 25 <= 2400 minutes QC Manager Q 15 30 45 <= 2400 minutes Market for B 1 1 <= 100 units Market for P 1 1 <= 50 units LP: max 45B+60P 20B+5P<=2400min 15B+30P<=2400min B<=100 P<=50
5 Solver Dialog Box

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6 Computer Output: Answer Report 6 7 8 9 10 11 12 13 14 15 16 17 18 AB C D E F G Target Cell (Max) Cell Name Original Value Final Value \$D\$4 Rev 105 6300 Adjustable Cells Cell Name Original Value Final Value \$B\$3 # to be Produced B 1 100 \$C\$3 # to be Produced P 1 30 Constraints Cell Name Cell Value Formula Status Slack \$D\$5 Software Engineer S 2150 \$D\$5<=\$F\$5 Not Binding 250 \$D\$6 QC Manager Q 2400 \$D\$6<=\$F\$6 Binding 0 \$D\$7 Market for B 100 \$D\$7<=\$F\$7 Binding 0 \$D\$8 Market for P 30 \$D\$8<=\$F\$8 Not Binding 20 Optimal values of decision variables: B= 100, P= 30, Optimal Objective Function Value(OFV)= Total Rev= \$ 6300 Max Total Revenue: Max 45 B + 60 P C o n s t r a i n t s : S L A C K Engineer S: 20 B + 5 P <= 2400 Manager Q: 15 B + 30 P <= 2400 Demand for B: B <= 100 Demand for P: P <= 50
7 “Sensitivity” Analysis: Now we will illustrate how each of the numbers in the Sensitivity report is computed.

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## This note was uploaded on 08/10/2011 for the course BUSQOM 0050 taught by Professor Glowackia during the Spring '08 term at Pittsburgh.

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09 QM Lecture Note C - Optimization GG Hegde Readings from...

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