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Review3_306

# Review3_306 - Simulation Exercise 8 Simulation Policy...

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Unformatted text preview: Simulation - Exercise 8 Simulation Policy variable: Number of machines (3 vs 4) Parameters: \$4 idle time cost per hour, \$6 lost \$4 goodwill cost per hour, 22 hours of machine time per day. time Endogenous variables: idle time, lost goodwill idle hours (hours carried over a day). hours Simulation - Exercise 8 Simulation Exogenous variables: # orders, hours per order per # of Orders 0 1 2 3 Prob. Prob. Range Range .10 0<=RN<.10 .30 .10<=RN<.40 .25 .40<=RN<.65 .35 .65<=RN<1.0 Simulation - Exercise 8 Simulation Hours per Order Prob. Range Prob. Range 10 .10 0<=RN<.10 15 .10 .10<=RN<.20 20 .10 .20<=RN<.30 25 .20 .30<=RN<.50 30 .25 .50<=RN<.75 35 .15 .75<=RN<.90 40 .10 .90<=RN<1.0 Simulation Exercise 8 Simulation Four Machines Order 1 Order 2 Order 3 Day R.N. for # of R.N. Hours R.N. Hours R.N. Hours # of orders orders 1 2 3 4 5 .45 .87 .24 .82 .88 2 3 1 3 3 .65 .64 .13 .67 .75 30 30 15 30 35 .95 .82 .20 .30 40 35 .64 30 20 .18 15 25 .62 30 simulation exercise 8 (cont.) simulation # of Machine # of Machine Cost of Cost of lost Cost Cost Hours Avail. Hours Req. Idletime Goodwill Idletime Goodwill \$4 \$4 \$6 88 88 88 88 88 70 95 22 65 90 \$72 18 \$72 18 \$264 66 \$264 66 \$92 23 \$92 23 - \$42 7 \$42 \$12 2 \$12 Total cost over 5 days Total \$482 Simulation Exercise 8 Simulation Three Machines Order 1 Order 2 Order 3 Day R.N. for # of R.N. Hours R.N. Hours R.N. Hours # of orders orders 1 2 3 4 5 .45 .87 .24 .82 .88 2 3 1 3 3 .65 .64 .13 .67 .75 30 30 15 30 35 .95 .82 .20 .30 40 35 .64 30 20 .18 15 25 .62 30 simulation exercise 8 (cont.) simulation # of Machine # of Machine Cost of Cost of lost Cost Cost Hours Avail. Hours Req. Idletime Goodwill Idletime Goodwill \$4 \$4 \$6 66 66 66 66 66 70 99 48 65 90 \$24 4 \$24 \$198 33 \$198 33 \$72 18 ­ \$72 18 \$4 1 \$4 \$144 24 \$144 24 Total cost over 5 days Total \$442 Select 3 Machines Exercise 7 - Initial Information Assume: Assume: Selling price (SP) = \$12 per unit Cost = \$5 per unit Fixed Cost = \$5,000,000 Development Cost = \$1,200,000 Demand is thought to be either 500,000; Demand 1,000,000; 2,000,000; or 5,000,000 1,000,000; How much should we produce??? Payoff Table Payoff Demand Produce 500 1,000 2,000 5,000 2,000 2,000 500 -1,500 -1,500 -1,500 -1,500 1,000 -4,000 2,000 2,000 -9,000 -3,000 9,000 9,000 5,000 -24,000 -18,000 -6,000 30,000 Payoff Table calculations Payoff For values on the diagonal : Condit. Payoff 500/500 = (SP - Cost) (Units sold) - Fixed Cost - Development cost (optional) Fixed = (12-5) (500) = \$3,500 - 5,000 = -\$1,500 (12-5) CP1000/1000 = (12 - 5)(1000) -5000 = -\$2,000 CP2000/2000 = (12 - 5)(2000) -5000 = \$9,000 CP5000/5000 = (12 - 5)(5000) -5000 = \$30,000 Payoff Table calculations For values above the diagonal : Conditional Payoff 500/1000 = (SP - Cost)(Units sold) - FC - DC(opt) (SP = (12-5)(500) - 5000 = -\$1500 CP500/2000 = (12-5)(500) - 5000 = -\$1500 CP CP1000/2000 = (12-5)(1000) - 5000 = \$2000 CP500/5000 = (12-5)(500) - 5000 = -\$1500 Payoff Table calculations For values below the diagonal : Conditional Payoff 1000/500 = (SP - Cost) (Units sold) - (Cost)(extra product.) - FC = (12-5)(500) - 5(500) -5000 = -\$4000 CP2000/1000=(12-5)(1000) -5(1000)-5000 = -\$3000 CP CP5000/1000= (12-5)(1000) -5(4000)-5000=-\$18000 CP5000/2000= (12-5)(2000) -5(3000)-5000 = -\$6000 CP2000/500= (12-5)(500) -5(1500) -5000 = - \$9000 Payoff Table Payoff Demand Produce 500 1,000 2,000 5,000 2,000 2,000 500 -1,500 -1,500 -1,500 -1,500 1,000 -4,000 2,000 2,000 -9,000 -3,000 9,000 9,000 5,000 -24,000 -18,000 -6,000 30,000 Payoff Table (with development cost included) included) Demand Produce 500 1,000 2,000 5,000 800 800 800 500 -2,700 -2,700 -2,700 -2,700 1,000 -5,200 2,000 -10,200 -4,200 7,800 7,800 5,000 -25,200 -19,200 -7,200 28,800 Payoff Table Payoff Demand Produce 500 1,000 2,000 5,000 2,000 2,000 500 -1,500 -1,500 -1,500 -1,500 1,000 -4,000 2,000 2,000 -9,000 -3,000 9,000 9,000 5,000 -24,000 -18,000 -6,000 30,000 Demand Stock Maximax Maximin (optimistic) (pessimistic) Payoff Table Payoff Equally Likely EMV 500 -1500 1000 2000 2000 9000 30,000*** 5000 ***Decision: Produce 5000 Demand Stock Maximax Maximin (optimistic) (pessimistic) Payoff Table Payoff Equally Likely EMV -1500 -1500*** 500 1000 2000 -4000 2000 9000 -9000 5000 30,000 -24,000 ***Decision: Produce 500 Demand Stock Maximax Maximin (optimistic) (pessimistic) Payoff Table Payoff Equally Likely EMV 500 -1500 -1500 -1500 1000 2000 -4000 500 9000 -9000 1500 *** 2000 5000 30,000 -24,000 -4500 ***Decision: Produce 2000 Decision Making EMV (Expected Monetary Value) : Sum of EMV Sum weighted payoffs associated with a particular act with EMV (A) = Σ [ CP (Act|State i)P(State i)] EMV )P(State i EMV (A) = Σ [ CP (Act|State i)P(State i)] EMV )P(State EMV(500) = .15(-1500) + .25(-1500) + EMV(500) .45(-1500) + .15(-1500) = -1500 -1500 EMV(1000) = .15(-4000) + .25(2000) + EMV(1000) .45(2000)+ .15(2000) = 1100 1100 EMV(2000) =.15(-9000) + .25(-3000) + EMV(2000) .45(9000) + .15(9000) = 3300 3300 EMV(5000) =.15(-24,000) + .25(-18,000) + EMV(5000) .45(-6000) + .15(30,000) = -6300 -6300 EMV Calculations EMV Payoff Table Payoff Demand Produce 500 1,000 2,000 5,000 2,000 2,000 500 -1,500 -1,500 -1,500 -1,500 1,000 -4,000 2,000 2,000 -9,000 -3,000 9,000 9,000 5,000 -24,000 -18,000 -6,000 30,000 Demand Stock Maximax Maximin (optimistic) (pessimistic) Payoff Table Payoff Equally Likely EMV 1100 3300*** 500 -1500 -1500 -1500 -1500 1000 2000 -4000 500 2000 9000 -9000 1500 5000 30,000 -24,000 -4500 -6300 ***Decision: Produce 2000 Value of Perfect Information Value EPPI- Expected Payoff w/ Perfect Information or or EPPP- Expected Payoff w/ Perfect Prediction or or EPUC- Expected Payoff Under Certainty Expected value of perfect information (cont.) (cont.) EPPI = Σ CP* (State i) P (State i) EPPI (State i = -1500 (.15) + 2000 (.25) + -1500 9000 (.45) + 30,000 (.15) = \$ 8,825 9000 This is the maximum we could expect to This make if we always knew ahead of time what the demand was going to be. Payoff Table Payoff Demand Produce 500 1,000 2,000 5,000 2,000 2,000 500 -1,500 -1,500 -1,500 -1,500 1,000 -4,000 2,000 2,000 -9,000 -3,000 9,000 9,000 5,000 -24,000 -18,000 -6,000 30,000 value of perfect information (cont.) value (cont.) EVPI Expected Value of Perfect Information Information EVPI is the expected value of having perfect EVPI expected value perfect information; i.e., it is the amount we could information i.e., make over and above what we could make over on our own without perfect information. on EVPI = EPPI - EMV* value of perfect information (cont.) (cont.) EVPI EVPI EVPI = EPPI - EMV* Expected Value of Perfect Information Information = 8825 - 3300 = \$5525 This is how much perfect information would This be worth to us. It’s also the maximum amount we would be willing to pay for perfect info. perfect Decision Tree Decision Make 500 D=500 (.15) -1500 D=500 -1500 D=1000 (.25) -1500 D=2000 (.45) -1500 -1500 D=5000 (.15) -1500 D=5000 -1500 Make 1000 D=500(.15) -4000 D=500(.15) -4000 D=1000 (.25) 2000 D=1000 2000 D=2000 (.45) 2000 D=2000 2000 D=5000 (.15) 2000 D=5000 2000 Decision Tree Decision Make 2000 D=500 (.15) -9000 D=500 -9000 D=1000 (.25) -3000 D=1000 D=2000 (.45) 9000 9000 D=5000 (.15) 9000 D=5000 9000 D=500 (.15) -24000 D=500 -24000 D=1000 (.25) -18000 D=1000 -18000 D=2000 (.45) -6000 D=2000 -6000 D=5000 (.15) 30000 D=5000 30000 Make 5000 Exercise 6 Exercise D = 900 u/yr. = 3 u/day Co = \$20/order Ch = \$2.50 .15 (50) + 2.50 = \$10.00 .15 Ci = .15 U = \$50/u D + C Q* * P = 6 cs./day TC = Co * h Q 2 L = 2 days days exercise 6 (cont.) exercise a) Q* = 2CoD = Ch 2 (20) (900) = 60 cs. 10 TC* = 2CoDCh = 2 (20) (900) (10) = \$600 (20) 900 n = D/Q = = 15 60 1 t= (300) = 20 days 15 exercise 6 (cont.) exercise Order Q* = 60 When R = 6 Units 60 -- 20 exercise 6 (cont.) exercise b) Q* = 2CoD Ch P P-D = 84.85 TC* = 2CoDCh ( 1- D/P ) = \$424.26 1900 900 n = D/Q = = 10.6 85 1 ~ t= (300) = 28 (300) 10.6 exercise 6 (cont.) exercise Order Q* = 85 When R = 0 85 -42 -14 Peak inv. level Q* 1- D P 28 exercise 6 (cont.) exercise d) Qd = 900 Ud = .98 (50) = \$49 Chd = .15 (49) + 2.50 = \$9.85 D Qd TC = Co + Chd = \$ 4,452.50 Qd 2 C. of Goods = 49 (900) = 44,100 \$48,552.50 No Discount TC* = \$600 C. of Goods = 900 (50) = \$45,000 Grand Total = \$45,600 Grand \$45,600 exercise 6 (cont.) exercise e) Cb = \$.50 Ch = \$10 2CoD Q*= Q*= Ch Ch+ Cb 2 (20) (900) 10 +.50 = 10 .50 Cb = 275 Cb TC* = 2CoDCh = \$130.93 C b+ C h Ch ~ 262 S* = Q* = Ch+ Cb exercise 6 (cont.) exercise Order Q* = 275 When S = 256 (L = 2) (L 13 -S* -256 --262 -Q* MRP MRP A: 1 2 3 4 5 6 7 8 Gross OH/SR 1500 Net POR 3000 4500 1500 4500 1500 4500 B: 2xA Gross OH/SR 1000 1000 Net POR x2 3000 9000 1000 9000 1000 9000 MRP MRP C: 2xA Gross OH/SR 1000 Net POR x2 3000 9000 D: 1xC Gross OH/SR 300 Net POR 2000 9000 3( 2000 9000 ) 2000 9000 1700 9000 2(1700 9000 ) 1 2 3 4 5 6 7 8 E: Gross Gross OH/SR 500 Net POR 3xC 2xD MRP MRP 3400 24000 27000 2900 24000 27000 2900 24000 27000 3000 18000 1000 18000 F: Gross Gross OH/SR 2000 OH/SR 2000 Net POR 1000 18000 1xB 1xC 1 2 3 4 5 6 7 8 MRP MRP G: 3xD Gross Gross OH/SR 6400 Net POR 5100 27000 25700 25700 H: Gross Gross OH/SR 2500 4000 OH/SR 2500 Net POR 3xB 3000 27000 23500 23500 1 2 3 4 5 6 7 8 ...
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