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# Probabilistic Forecast Analysis Of A Manufacturing Process

Profitability projections in a manufacturing environment are directly tied to how the sales forecast fits with the capability of the operation. When a company has a large portfolio of products with very different operational production rates, the manufacturing capacity of the plant will be significantly impacted by the product mix to be produced. This in turn will have a radical effect on the output of the plant and the allocation of the fixed cost of production. In this case we present an example where a company is trying to decide how best to balance the sales of certain families of products to maximize revenue, maintain a diverse product line and properly price each individual product based on the impact to the manufacturing schedule and fixed cost allocation.

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### Probabilistic Forecast Analysis Of A Manufacturing Process

1. 1. Jose A. Briones, Ph.D.SpyroTek Performance Solutions, LLCPalisade’s Risk Analysis Conference, October 2009
2. 2.  Introduction Model description Financial modeling inputs Scenario modeling Results analysis
3. 3.  Profitability projections in a manufacturing environment are directly tied to how the sales forecast fits with the capability of the operation. When a company has a large portfolio of products with very different operational production rates, the manufacturing capacity of the plant will be significantly impacted by the product mix to be produced. This in turn will have a radical effect on the output of the plant and the allocation of the fixed cost of production. There is a need to integrate the financial model with the production forecast and production capabilities
4. 4.  In this case we present an example where a company is trying to meet the following objectives  Balance sales and production of certain families of products to maximize profit  Maintain a diverse product line  Properly price each individual product based on the impact to the manufacturing schedule and fixed cost allocation
5. 5.  Model uses @Risk probabilistic decision analysis software  Monte Carlo simulation  Risk and opportunity analysis Designed for complex projects with high levels of uncertainty  Inputs contain high number of variables, either technical or financial with a high degree of uncertainty, assumptions and dependencies ▪ New product development assessment ▪ Capital spending decisions ▪ Value chain analysis ▪ Production and sales forecasting analysis Eliminates use of “one at a time” cases  Analyzes thousands of cases simultaneously  Generates a range of outcomes  Outcome charts are analyzed to make decisions on direction
6. 6.  Input values are entered in range format – Width and shape of range are critical inputs  Definition of the input ranges is the most critical step  Do not start with the typical value, start with the range, define the shape of the function (10%, 50%, 90% probability). There are multiple choices for the shape of the input range:  Triangular: Most common for initial assumptions  Normal distribution: Used when more accurate input data is available  PERT: When data is in form of probabilities  Gamma distribution: Good to model pricing distributions in B-B cases
7. 7.  Multiline product portfolio  4 Product families – A, B, C, D  A, C and D are existing products  B is a new product family that is meant to replace product A ▪ B has higher margins than A but lower production rates ▪ C and D have higher margins than B but even lower production rates
8. 8.  4 Production lines – 1, 2, 3, 4  Products A and B can be made in all production lines ▪ Products A and B have different production rates  Products C and D can only be made in lines 3 and 4 ▪ Products C and D have different production rates  Post-treatment facility after production lines limits total production rate
9. 9. Product Family A Line 1 125 Kg/hr/lineProduct Family B Line 2 87.5 Kg/hr/line Post-Treatment FacilityProduct Family C Line 3 350 Kg/hr 62.5 Kg/hr/lineProduct Family D Line 4 37.5 Kg/hr/line
10. 10.  Manufacturing facility was being upgraded and debottlenecked.  Production rates for all products were expected to change as the project progresses throughout the year. Variable margins are different for all product families and cannot be known with absolute certainty Sales forecast is not exact, has variability Fixed costs billed in foreign exchange
11. 11.  Business manager wants to forecast total business profitability and profit by product under 2 scenarios: 1. Maintain forecast for Product C and D fixed and evaluate if Product A should be discontinued and replaced by better performing Product B 2. Maximize sales of Product C, maintain D forecast fixed, again evaluate Product B vs. A
12. 12. Typical Range Range Min MaxProduction Target of product C, Kg/mo 15,000 10,000 20,000Production Target of product D, Kg/mo 10,000 5,000 15,000Production Rate of Product A, lines 1 and 2, Kg/hr 250 240 260Production Rate of Product B, lines 1 and 2, Kg/hr 175 165 200Rate of Production product C, lines 3 and 4 Kg/hr 125 90 140Rate of Production product D, lines 3 and 4 Kg/hr 75 60 80Maximum Production Rate 4 lines running, Kg/hr 350 330 370Var Margin Product A US\$/kg \$2.50 \$2.30 \$2.70Var Margin Product B US\$/kg \$2.75 \$2.60 \$3.00Var Margin Product C US\$/kg \$4.00 \$3.50 \$4.50Var Margin Product D US\$/kg \$5.00 \$4.50 \$5.50Plant fixed cost Euros/month 500,000 € 450,000 € 550,000 €Selling & Admin costs Euros/month 50,000 € 45,000 € 55,000 €Projected fixed cost savings Euros/month 75,000 € 65,000 € 90,000 €US Dollar/ Euro Exchange Rate 0.8 0.7 0.95
13. 13.  Plant will be run at full capacity to maximize profit. Production capacity of products A or B is dependent on the free time left after meeting production targets for C and D.
14. 14.  Common method of dividing total fixed cost by the total production is not acceptable when products have widely different production rates. In order to calculate profitability by product, we need to allocate fixed costs based on projected run time for each product family This allows us to make the right decisions as to which product to promote or stop promoting.  Do not subsidize slow running products.
15. 15.  Calculate % manufacturing time used to meet forecast of C & D Calculate % manufacturing time available to manufacture A or B Calculate maximum production of A or B subject to treatment line constraints Estimate total profitability and gross profit by product Run sensitivity analysis
16. 16. % of treatment line time devoted to A or B, C & D 0.772 0.829 % of treatment line time 5.0% devoted to A + B Grades / % of treatment line time 0. Column devoted to Product C / 100.0% Column60 Minimum 0.7431 Maximum 0.8577 Minimum 0.054950 Mean 0.8027 Maximum 0.1432 Std Dev 0.0176 Mean 0.0941 Values 1000 Std Dev 0.015540 D % of treatment line time30 devoted to Product D / Column20 Minimum 0.0854 C A or B Maximum Mean 0.1304 0.103110 Std Dev 0.00761 Values 10000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 9 20% of Production time is allocated to C & D Values 1000
17. 17. Total theoretical capacity, Product A plus Products C & D, kg/yr 2.699 2.906 5.0% 90.0% 5.0% Total theoretical capacity, 92.3% 7.7% 0.0% Product A plus Products C & 7 D, kg/yr 6 Minimum 2633085.3298 A Maximum 3018607.7688 5 Mean 2803346.2034 Val ues x 10 ^ -6 B Std Dev 63912.9226 4 Values 1000 3 Total theoretical capacity, Product B plus products C & 2 D, kg/yr 1 Minimum 2357095.8177 Maximum 2788160.2845 0 Mean 2604929.4916 Std Dev 65567.7702 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 Values 1000 Values in MillionsSubstituting Product A with Product B Results in Lower Total Plant Capacity
18. 18. Profitability, Product A vs. Product B US\$/yr 0.000 1.450 17.3% 75.9% 6.8% 11.3% 75.8% 12.9% Profitability, Product A Case 8 US\$/yr / Column 7 A Minimum -1219775.4188 Maximum 2289688.1319 6 Mean 596061.7364 A BValues x 10 ^ -7 Std Dev 598929.0090 5 Values 1000 4 Profitability, Product B Case 3 US\$/yr / Column 2 Minimum -1091259.4015 1 Maximum 2484366.8328 Mean 752663.4930 0 Std Dev 597144.6785 Values 1000 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 Values in MillionsProduct B has a lower probability of losses than product A
19. 19. Fixed cost US\$/kg Products A, B, C, D 5.45 7.40 Fixed cost US\$/kg Product Fixed cost US\$/kg Product 5.0% 90.0% 5.0% D B 99.8% 0.2% 0.0% Minimum \$4.9476 Minimum \$2.0664 2.5 Maximum \$8.3905 Maximum \$3.1881 Mean \$6.3397 Mean \$2.5700 Std Dev \$0.6112 Std Dev \$0.1997 2.0 B Values 1000 Values 1000 1.5 Fixed cost US\$/kg Product C A Minimum \$2.8058 1.0 Maximum \$5.5362 C D Mean \$3.8559 Std Dev \$0.4473 0.5 Values 1000 0.0 Fixed cost US\$/kg Product A 1 2 3 4 5 6 7 8 9 Values in \$ Minimum \$1.8656 Maximum \$2.9132 Mean \$2.3665Slower production rates result in much higher Std Dev \$0.1899fixed costs for Products C and D Values 1000
20. 20. Gross Profit Products A, B, C, D US\$/Kg -0.22 0.48 Profit Product A US\$/Kg / 5.0% 5.0% Column 2.9% 12.1% Minimum -\$0.5836 2.5 Maximum \$0.7011 Mean \$0.1335 Std Dev \$0.2097 2.0 Values 1000 A 1.5 Profit Product B US\$/Kg / B Column 1.0 Minimum -\$0.4348 Maximum \$0.8052 D C Mean \$0.2133 0.5 Std Dev \$0.2216 Values 1000 0.0 Profit Product C US\$/Kg / -5 -4 -3 -2 -1 0 1 2 Values in \$ Profit Product D US\$/Kg / Minimum -\$1.5576Product D has a Negative Gross Maximum \$1.4447 Mean \$0.1441Profit Due to Long Production Minimum -\$4.5032 Std Dev \$0.4867 Maximum -\$0.7534Cycles Mean -\$2.3397 Values 1000 Std Dev \$0.6452
21. 21. % of treatment line time devoted to A/B, C & D Grades 0.448 0.575 % of treatment line time 5.0% 90.0% 5.0% devoted to A + B Grades / Column 100.0% 0.0% 0.0%60 Minimum 0.3699 D Maximum 0.608050 Mean 0.5203 Std Dev 0.0384 Values 500040 % of treatment line time30 devoted to Product D / Column20 Minimum 0.0849 C A or B Maximum 0.1304 Mean 0.103210 Std Dev 0.00770 Values 5000 0 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 % of treatment line time devoted to Product C / Column Minimum 0.2963 Maximum 0.5094 ~50% of time devoted to C & D Mean 0.3766 Std Dev 0.0374 Values 5000
22. 22. Total theoretical capacity, Product A vs. B plus Products C & D, kg/yr 2.700 2.906 5.0% 90.0% 5.0% Total theoretical capacity, 100.0% 0.0% 0.0% Product A plus Products C & 7 D, kg/yr A Minimum 2596788.1735 6 Maximum 3001093.4875 5 Mean 2803246.3861 Val ues x 10 ^ -6 Std Dev 62557.3764 4 Values 5000 B 3 Total theoretical capacity, Product B plus products C & 2 D, kg/yr 1 Minimum 1942146.1959 Maximum 2697819.5994 0 Mean 2362657.7945 Std Dev 120704.1615 2.6 2.8 3.0 3.2 1.8 2.0 2.2 2.4 Values 5000 Values in MillionsProduction of B v.s A results in a more significant loss of capacity compared to Scenario 1
23. 23. Profitability, Product A vs B Case US\$/yr 0.00 1.45 1.2% 51.1% 47.7% 13.2% 72.0% 14.8% Profitability, Product A Case 7 US\$/yr / Column 6 Minimum -852160.3638 B A Maximum 3287264.9694 5 Mean 1405082.2802 V al u e s x 1 0 ^ - 7 Std Dev 608985.6034 4 Values 5000 3 Profitability, Product B Case US\$/yr / Column 2 Minimum -2021651.9911 Maximum 3250368.3280 1 Mean 735213.2672 Std Dev 665321.2558 0 Values 5000 -3 -2 -1 0 1 2 3 Values in Millions 4Production of A has less than 2% probability of losses, 48% probability of profit >1.5 MM \$
24. 24. Fixed cost US\$/kg Products A, B, C & D 5.40 7.43 Fixed cost US\$/kg Product Fixed cost US\$/kg Product 5.0% 90.0% 5.0% D / Column B. / Column 99.8% 0.2% 0.0% Minimum \$4.6730 Minimum \$1.8782 2.0 Maximum \$8.7315 Maximum \$3.2967 1.8 Mean \$6.3410 Mean \$2.5241 A Std Dev \$0.6228 Std Dev \$0.2136 1.6 Values 5000 Values 5000 1.4 B 1.2 Fixed cost US\$/kg Product C / Column 1.0 0.8 C D Minimum \$2.6522 Maximum \$5.8660 0.6 Mean \$3.8579 Std Dev \$0.4645 0.4 Values 5000 0.2 0.0 Fixed cost US\$/kg Product A / Column 1 2 3 4 5 6 7 8 9 Values in \$ Minimum \$1.2306 Maximum \$2.6219 Mean \$1.9559 Std Dev \$0.2068 Values 5000Fixed Cost of Product A drops in this scenario
25. 25. Profit Products A, B C & D US\$/Kg 0.00 0.91 Profit Product D US\$/Kg / Profit Product A US\$/Kg / Column Column 0.7% 94.3% 5.0% 13.2% 86.7% 0.1% Minimum -\$0.1944 Minimum -\$4.84111.8 Maximum \$1.2512 Maximum -\$0.3715 Mean \$0.5441 Mean -\$2.34101.61.4 B A Std Dev \$0.2233 Std Dev Values \$0.6569 5000 Values 50001.2 Profit Product B US\$/Kg /1.0 Column0.8 Minimum -\$0.63660.6 D C Maximum \$1.0344 Mean \$0.25930.4 Std Dev \$0.2276 Values 50000.20.0 Profit Product C US\$/Kg / -5 -4 -3 -2 -1 0 1 2 Column Values in \$ Minimum -\$2.0249 Maximum \$1.5637 Mean \$0.1421 Std Dev \$0.5091 Values 5000Profit of Product A increases in this scenario
26. 26. Scenario 1 - A Scenario 1 - B Scenario 2 - A Scenario 2 - B% time devoted 20% 20% 48% 48%to C & DProduction of C 0.2 MM kg/yr 0.2 MM kg/yr 0.7 MM kg/yr 0.7 MM kg/yrTotal Plant 2.8 MM kg/yr 2.6 MM kg/yr 2.8 MM kg/yr 2.4 MM kg/yrCapacityProfitability 0.6 MM\$/yr 0.75 MM\$/yr 1.4 MM \$/yr 0.7 MM \$/yrProbability of 17% 11% 1% 13%Losses Scenario 2 with sales of Product A has the best probability for higher profits
27. 27. Scenario 1 – Scenario 1 – Scenario 2 – Scenario 2 – Fixed Cost/Kg Gross Profit/Kg Fixed Cost/Kg Gross Profit/KgProduct A \$2.37 \$0.13 \$1.96 \$0.54Product B \$2.57 \$0.21 \$2.52 \$0.26Product C \$3.86 \$0.14 \$3.85 \$0.14Product D \$6.34 -\$2.34 \$6.34 -\$2.34 Fixed cost for Product A drops in Scenario 2, gross profit increases Product D has negative gross profit under both scenarios
28. 28. Profitability, Product A Case US\$/yr / Column Regression Coefficients US Dollar/ Euro Exchange Rate 0.73 Plant fixed cost Euros/month -0.51 Var Margin Product A US\$/kg 0.34 Maximum Production Rate 4 lines running, kg/hr 0.22 Projected fixed cost savings Euros/month 0.13 Operational Efficiency 0.10 Days of the week operating 0.07 Production of product C, Kg/mo 0.06 Var Margin Product C US\$/kg 0.06 Selling & Admin costs Euros/month -0.05 Rate of Production product D, Kg/mo 0.05 Var Margin Product D US\$/kg 0.04Production Rate of Product A, lines 1 and 2, kg/hr 0.03 Hours/day operating 0.02 Production of product D, Kg/mo 0.01 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Coefficient Value Maximum Production Rate for the 4 lines is a critical factor for profitability of A
29. 29.  Product D was discontinued Emphasis was placed on Product C sales Product B sales were not emphasized but sold based on market demands Product A had been overpriced relative to fixed costs.  Findings allowed pricing flexibility and an increase in market share
30. 30.  Jose A. Briones, Ph.D. SpyroTek Performance Solutions, Irving, TX Brioneja@Spyrotek.com (469) 737-0421
31. 31. Theoretical capacity Products A & B Kg/mo 154.4 172.8 5.0% 90.0% 5.0% 100.0% 0.0% 0.0% Theoretical capacity Product 8 A Kg/mo / Column 7 Minimum 143825.4377 Maximum 182165.7345 6 Mean 163603.8872Val ues x 10 ^ -5 Std Dev 5589.9594 5 Values 5000 4 Theoretical capacity Product 3 B kg/mo / Column 2 Minimum 89846.9886 1 Maximum 157539.8296 Mean 126888.1712 0 Std Dev 10465.5035 Values 5000 140 150 160 170 180 190 80 90 100 110 120 130 Values in Thousands
32. 32.  Lines 3 and 4 fully devoted to Products C and D Production of product C & D, Kg/mo Comparison with Triang(55000,60000,65000) 56.6 63.4 Production of product C, 5.0% 5.0% Kg/mo / Column 5.0% 5.0% Minimum 55075.19590.0010 Maximum 64901.14420.0009 Mean 59999.97730.0008 Std Dev 2041.4514 Values 50000.00070.0006 Triang(55000,60000,65000)0.00050.0004 Minimum 55000.00000.0003 Maximum 65000.0000 Mean 60000.00000.0002 Std Dev 2041.24150.00010.0000 Production of product D, 0 10 20 30 40 50 60 70 Kg/mo / Column Values in Thousands Minimum 9008.7846 Maximum 10992.7913 Mean 10000.0010 Std Dev 408.2882Production of C goes from 15 M to 60 M Kg/mo Values 5000

Profitability projections in a manufacturing environment are directly tied to how the sales forecast fits with the capability of the operation. When a company has a large portfolio of products with very different operational production rates, the manufacturing capacity of the plant will be significantly impacted by the product mix to be produced. This in turn will have a radical effect on the output of the plant and the allocation of the fixed cost of production. In this case we present an example where a company is trying to decide how best to balance the sales of certain families of products to maximize revenue, maintain a diverse product line and properly price each individual product based on the impact to the manufacturing schedule and fixed cost allocation.

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