Forecast Probabilistic Analysis Of A Manufacturing Process

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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 …

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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  • 1. Jose A. Briones, Ph.D. SpyroTek Performance Solutions, LLC Palisade’s Risk Analysis Conference, October 2009
  • 2.
    • Introduction
    • Model description
    • Financial modeling inputs
    • Scenario modeling
    • Results analysis
  • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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. Line 1 Line 2 Line 3 Line 4 Product Family A Product Family B Product Family C Product Family D Post-Treatment Facility 350 Kg/hr 125 Kg/hr/line 87.5 Kg/hr/line 62.5 Kg/hr/line 37.5 Kg/hr/line
  • 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.
    • Business manager wants to forecast total business profitability and profit by product under 2 scenarios:
      • Maintain forecast for Product C and D fixed and evaluate if Product A should be discontinued and replaced by better performing Product B
      • Maximize sales of Product C, maintain D forecast fixed, again evaluate Product B vs. A
  • 12. Typical Range Range Min Max Production Target of product C, Kg/mo 15,000 10,000 20,000 Production Target of product D, Kg/mo 10,000 5,000 15,000 Production Rate of Product A, lines 1 and 2, Kg/hr 250 240 260 Production Rate of Product B, lines 1 and 2, Kg/hr 175 165 200 Rate of Production product C, lines 3 and 4 Kg/hr 125 90 140 Rate of Production product D, lines 3 and 4 Kg/hr 75 60 80 Maximum Production Rate 4 lines running, Kg/hr 350 330 370 Var Margin Product A US$/kg $2.50 $2.30 $2.70 Var Margin Product B US$/kg $2.75 $2.60 $3.00 Var Margin Product C US$/kg $4.00 $3.50 $4.50 Var Margin Product D US$/kg $5.00 $4.50 $5.50 Plant 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.
    • 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.
    • 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.
    • 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. 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 0 10 20 30 40 50 60 % of treatment line time devoted to A or B, C & D % of treatment line time devoted to A + B Grades / Column Minimum 0.7431 Maximum 0.8577 Mean 0.8027 Std Dev 0.0176 Values 1000 % of treatment line time devoted to Product D / Column Minimum 0.0854 Maximum 0.1304 Mean 0.1031 Std Dev 0.00761 Values 1000 % of treatment line time devoted to Product C / Column Minimum 0.0549 Maximum 0.1432 Mean 0.0941 Std Dev 0.0155 Values 1000 20% of Production time is allocated to C & D C D A or B 5.0% 100.0% 0.772 0.829
  • 17. 2 . 3 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 3 . 0 3 . 1 Values in Millions 0 1 2 3 4 5 6 7 V a l u e s x 1 0 ^ - 6 Total theoretical capacity, Product A plus Products C & D, kg/yr Total theoretical capacity, Product A plus Products C & D, kg/yr Minimum 2633085.3298 Maximum 3018607.7688 Mean 2803346.2034 Std Dev 63912.9226 Values 1000 Total theoretical capacity, Product B plus products C & D, kg/yr Minimum 2357095.8177 Maximum 2788160.2845 Mean 2604929.4916 Std Dev 65567.7702 Values 1000 Substituting Product A with Product B Results in Lower Total Plant Capacity A B 5.0% 90.0% 5.0% 92.3% 7.7% 0.0% 2.699 2.906
  • 18. - 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 Values in Millions 0 1 2 3 4 5 6 7 8 V a l u e s x 1 0 ^ - 7 Profitability, Product A vs. Product B US$/yr Profitability, Product A Case US$/yr / Column Minimum -1219775.4188 Maximum 2289688.1319 Mean 596061.7364 Std Dev 598929.0090 Values 1000 Profitability, Product B Case US$/yr / Column Minimum -1091259.4015 Maximum 2484366.8328 Mean 752663.4930 Std Dev 597144.6785 Values 1000 Product B has a lower probability of losses than product A A B A 17.3% 75.9% 6.8% 11.3% 75.8% 12.9% 0.000 1.450
  • 19. $0.1899 Values 1000 Fixed cost US$/kg Product B Minimum $2.0664 Maximum $3.1881 Mean $2.5700 Std Dev $0.1997 Values 1000 A B C D Slower production rates result in much higher fixed costs for Products C and D 5.0% 90.0% 5.0% 99.8% 0.2% 0.0% 5.45 7.40 1 2 3 4 5 6 7 8 9 Values in $ 0.0 0.5 1.0 1.5 2.0 2.5 Fixed cost US$/kg Products A, B, C, D Fixed cost US$/kg Product D Minimum $4.9476 Maximum $8.3905 Mean $6.3397 Std Dev $0.6112 Values 1000 Fixed cost US$/kg Product C Minimum $2.8058 Maximum $5.5362 Mean $3.8559 Std Dev $0.4473 Values 1000 Fixed cost US$/kg Product A Minimum $1.8656 Maximum $2.9132 Mean $2.3665 Std Dev
  • 20. Minimum -$1.5576 Maximum $1.4447 Mean $0.1441 Std Dev $0.4867 Values 1000 Profit Product D US$/Kg / Minimum -$4.5032 Maximum -$0.7534 Mean -$2.3397 Std Dev $0.6452 A B D C Product D has a Negative Gross Profit Due to Long Production Cycles 5.0% 5.0% 2.9% 12.1% -0.22 0.48 - 5 - 4 - 3 - 2 - 1 0 1 2 Values in $ 0.0 0.5 1.0 1.5 2.0 2.5 Gross Profit Products A, B, C, D US$/Kg Profit Product A US$/Kg / Column Minimum -$0.5836 Maximum $0.7011 Mean $0.1335 Std Dev $0.2097 Values 1000 Profit Product B US$/Kg / Column Minimum -$0.4348 Maximum $0.8052 Mean $0.2133 Std Dev $0.2216 Values 1000 Profit Product C US$/Kg /
  • 21. ~50% of time devoted to C & D A or B C D 5.0% 90.0% 5.0% 100.0% 0.0% 0.0% 0.448 0.575 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 10 20 30 40 50 60 % of treatment line time devoted to A/B, C & D Grades % of treatment line time devoted to A + B Grades / Column Minimum 0.3699 Maximum 0.6080 Mean 0.5203 Std Dev 0.0384 Values 5000 % of treatment line time devoted to Product D / Column Minimum 0.0849 Maximum 0.1304 Mean 0.1032 Std Dev 0.00770 Values 5000 % of treatment line time devoted to Product C / Column Minimum 0.2963 Maximum 0.5094 Mean 0.3766 Std Dev 0.0374 Values 5000
  • 22. Production of B v.s A results in a more significant loss of capacity compared to Scenario 1 A B 5.0% 90.0% 5.0% 100.0% 0.0% 0.0% 2.700 2.906 1 . 8 2 . 0 2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 3 . 2 Values in Millions 0 1 2 3 4 5 6 7 V a l u e s x 1 0 ^ - 6 Total theoretical capacity, Product A vs. B plus Products C & D, kg/yr Total theoretical capacity, Product A plus Products C & D, kg/yr Minimum 2596788.1735 Maximum 3001093.4875 Mean 2803246.3861 Std Dev 62557.3764 Values 5000 Total theoretical capacity, Product B plus products C & D, kg/yr Minimum 1942146.1959 Maximum 2697819.5994 Mean 2362657.7945 Std Dev 120704.1615 Values 5000
  • 23. Production of A has less than 2% probability of losses, 48% probability of profit >1.5 MM $ A B 1.2% 51.1% 47.7% 13.2% 72.0% 14.8% 0.00 1.45 - 3 - 2 - 1 0 1 2 3 4 Values in Millions 0 1 2 3 4 5 6 7 V a l u e s x 1 0 ^ - 7 Profitability, Product A vs B Case US$/yr Profitability, Product A Case US$/yr / Column Minimum -852160.3638 Maximum 3287264.9694 Mean 1405082.2802 Std Dev 608985.6034 Values 5000 Profitability, Product B Case US$/yr / Column Minimum -2021651.9911 Maximum 3250368.3280 Mean 735213.2672 Std Dev 665321.2558 Values 5000
  • 24. Values in $ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Fixed cost US$/kg Products A, B, C & D Fixed cost US$/kg Product D / Column Minimum $4.6730 Maximum $8.7315 Mean $6.3410 Std Dev $0.6228 Values 5000 Fixed cost US$/kg Product C / Column Minimum $2.6522 Maximum $5.8660 Mean $3.8579 Std Dev $0.4645 Values 5000 Fixed cost US$/kg Product A / Column Minimum $1.2306 Maximum $2.6219 Mean $1.9559 Std Dev $0.2068 Values 5000 Fixed cost US$/kg Product B. / Column Minimum $1.8782 Maximum $3.2967 Mean $2.5241 Std Dev $0.2136 Values 5000 Fixed Cost of Product A drops in this scenario A B D C 5.0% 90.0% 5.0% 99.8% 0.2% 0.0% 5.40 7.43 1 2 3 4 5 6 7 8 9
  • 25. Values in $ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Profit Products A, B C & D US$/Kg Profit Product A US$/Kg / Column Minimum -$0.1944 Maximum $1.2512 Mean $0.5441 Std Dev $0.2233 Values 5000 Profit Product B US$/Kg / Column Minimum -$0.6366 Maximum $1.0344 Mean $0.2593 Std Dev $0.2276 Values 5000 Profit Product C US$/Kg / Column Minimum -$2.0249 Maximum $1.5637 Mean $0.1421 Std Dev $0.5091 Values 5000 Profit Product D US$/Kg / Column Minimum -$4.8411 Maximum -$0.3715 Mean -$2.3410 Std Dev $0.6569 Values 5000 Profit of Product A increases in this scenario A B D C 0.7% 94.3% 5.0% 13.2% 86.7% 0.1% 0.00 0.91 - 5 - 4 - 3 - 2 - 1 0 1 2
  • 26. Scenario 2 with sales of Product A has the best probability for higher profits Scenario 1 - A Scenario 1 - B Scenario 2 - A Scenario 2 - B % time devoted to C & D 20% 20% 48% 48% Production of C 0.2 MM kg/yr 0.2 MM kg/yr 0.7 MM kg/yr 0.7 MM kg/yr Total Plant Capacity 2.8 MM kg/yr 2.6 MM kg/yr 2.8 MM kg/yr 2.4 MM kg/yr Profitability 0.6 MM$/yr 0.75 MM$/yr 1.4 MM $/yr 0.7 MM $/yr Probability of Losses 17% 11% 1% 13%
  • 27. Fixed cost for Product A drops in Scenario 2, gross profit increases Product D has negative gross profit under both scenarios Scenario 1 – Fixed Cost/Kg Scenario 1 – Gross Profit/Kg Scenario 2 – Fixed Cost/Kg Scenario 2 – Gross Profit/Kg Product A $2.37 $0.13 $1.96 $0.54 Product B $2.57 $0.21 $2.52 $0.26 Product C $3.86 $0.14 $3.85 $0.14 Product D $6.34 -$2.34 $6.34 -$2.34
  • 28. 0.73 -0.51 0.34 0.22 0.13 0.10 0.07 0.06 0.06 -0.05 0.05 0.04 0.03 0.02 0.01 - 0 . 6 - 0 . 4 - 0 . 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 Coefficient Value Production of product D, Kg/mo Hours/day operating Production Rate of Product A, lines 1 and 2, kg/hr Var Margin Product D US$/kg Rate of Production product D, Kg/mo Selling & Admin costs Euros/month Var Margin Product C US$/kg Production of product C, Kg/mo Days of the week operating Operational Efficiency Projected fixed cost savings Euros/month Maximum Production Rate 4 lines running, kg/hr Var Margin Product A US$/kg Plant fixed cost Euros/month US Dollar/ Euro Exchange Rate Profitability, Product A Case US$/yr / Column Regression Coefficients Maximum Production Rate for the 4 lines is a critical factor for profitability of A
  • 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.
    • Jose A. Briones, Ph.D.
    • SpyroTek Performance Solutions, Irving, TX
    • [email_address]
    • (469) 737-0421
  • 31.  
  • 32. 5.0% 90.0% 5.0% 100.0% 0.0% 0.0% 154.4 172.8 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 Values in Thousands 0 1 2 3 4 5 6 7 8 V a l u e s x 1 0 ^ - 5 Theoretical capacity Products A & B Kg/mo Theoretical capacity Product A Kg/mo / Column Minimum 143825.4377 Maximum 182165.7345 Mean 163603.8872 Std Dev 5589.9594 Values 5000 Theoretical capacity Product B kg/mo / Column Minimum 89846.9886 Maximum 157539.8296 Mean 126888.1712 Std Dev 10465.5035 Values 5000
  • 33.
    • Lines 3 and 4 fully devoted to Products C and D
    Production of C goes from 15 M to 60 M Kg/mo 5.0% 5.0% 5.0% 5.0% 56.6 63.4 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 Values in Thousands 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010 Production of product C & D, Kg/mo Comparison with Triang(55000,60000,65000) Production of product C, Kg/mo / Column Minimum 55075.1959 Maximum 64901.1442 Mean 59999.9773 Std Dev 2041.4514 Values 5000 Triang(55000,60000,65000) Minimum 55000.0000 Maximum 65000.0000 Mean 60000.0000 Std Dev 2041.2415 Production of product D, Kg/mo / Column Minimum 9008.7846 Maximum 10992.7913 Mean 10000.0010 Std Dev 408.2882 Values 5000