Risk Management and Decision Analysis Examples
Chapter 8: Production Scheduling Risk
In Book 1: Novel Six Sigma Approaches to Risk Assessment and Management
ISBN: 9781522527039
Author: Vojo Bubevski
Abstract
The method is applied to Production Scheduling to manage the associated risk. DMAIC framework applies proven stochastic techniques as follows: 1. Define: Run stochastic optimisation to determine the optimal production schedules to minimise costs; 2. Measure: Simulate every determining optimal production schedule and calculate costs, risks, and Six Sigma metrics to measure against specified target limits; 3. Analyse: Analyse simulation results and identify and quantify the main contributors to the variability of the cost by using sensitivity analysis; 4. Improve: The optimal production schedules are ranked based on their costs and associated risk factors. The technically best optimal production schedule is recommended to the management for implementation; 5. Control: The Control stage is elaborated by reusing the data and presenting stochastic optimisation and simulation models for ongoing management of the optimal strategy. Some changes are applied to the data and models, however, to emulate the scenario of an implemented strategy.
Keywords: Production planning; Production scheduling; Six Sigma; DMAIC; Stochastic optimisation; Monte Carlo simulation.
The Results
Stochastic optimisation is used to resolve the optimal production schedules, i.e., plans. For this purpose, we minimise the Grand Total Costs (12), with constraints defined by (15), (16), (17), (18), and (19). For the optimisation, we need to specify trial values for the adjustable variables in the model including Regular Time Production per Month Vector (RTPpMV(i)) and Over Time Production per Month Vector (OTPpMV(i)). So, we specify zero for all these adjustable values.
The stochastic optimisation was run and determined two optimal schedules, the results per month which are presented in Table 3, Table 4, and Table 5.
Table 3: Optimal Production Schedule 1 Results per Mont
| Production |
Month 1 |
Month 2 |
Month 3 |
Month 4 |
Month 5 |
Month 6 |
| Regular Time |
754 |
764 |
775 |
784 |
645 |
728 |
| Over Time |
0 |
200 |
0 |
0 |
0 |
0 |
| Start Inventory |
400 |
154 |
518 |
493 |
-123 |
172 |
| End Inventory |
154 |
518 |
493 |
-123 |
172 |
0 |
| RT Prod. Costs |
$9,048 |
$9,168 |
$9,300 |
$9,408 |
$7,740 |
$8,736 |
| OT Prod. Costs |
0 |
$4,000 |
0 |
0 |
0 |
0 |
| Holding Costs |
$77 |
$259 |
$246.5 |
0 |
$86 |
0 |
| Penalty Costs |
0 |
0 |
0 |
$1,845 |
0 |
0 |
| Total Costs |
$9,125 |
$13,427 |
$9,546.5 |
$11,253 |
$7,862 |
$8,763 |
Table 4: Optimal Production Schedule 2 Results per Month
| Production |
Month 1 |
Month 2 |
Month 3 |
Month 4 |
Month 5 |
Month 6 |
| Regular Time |
900 |
900 |
900 |
900 |
751 |
867 |
| Over Time |
0 |
200 |
0 |
0 |
0 |
0 |
| Start Inventory |
400 |
300 |
800 |
900 |
400 |
801 |
| End Inventory |
300 |
800 |
900 |
400 |
801 |
768 |
| RT Prod. Costs |
$10,800 |
$10,800 |
$10,800 |
$10,800 |
$9,012 |
$10,404 |
| OT Prod. Costs |
0 |
$4,000 |
0 |
0 |
0 |
0 |
| Holding Costs |
$150 |
$400 |
$450 |
$200 |
$400.5 |
$384 |
| Penalty Costs |
0 |
0 |
0 |
0 |
0 |
0 |
| Total Costs |
$10,950 |
$15,200 |
$11,250 |
$11,000 |
$9,412.5 |
$10,788 |
Table 5: Optimal Production Schedules Total Results
| Production |
Schedule 1 |
Schedule 2 |
| Regular Time |
4,450 |
5,218 |
| Over Time |
200 |
200 |
| RT Prod. Cost |
$53,400.00 |
$62,616.00 |
| OT Prod. Cost |
$4,000.00 |
$4,000.00 |
| Holding Cost |
$668.50 |
$1,984.50 |
| Penalty Cost |
$1,845.00 |
0.00 |
| Total Cost |
$59,913.50 |
$68,600.50 |
Chapter 2: Analysing Profitability of New Products
In Book 4: Risk Management for Businesses with Stochastic Six Sigma DMAIC Method
ISBN: 978-620-2-67095-1
Author: Vojo Bubevski
Abstract
This chapter elaborates on how to estimate the average profitability of new products for businesses. The chapter considers the financial risk and applies the DMAIC stochastic method. The scenario is that a company wants to launch a new product on the market. When a company develops a new product, the profitability of the product is highly uncertain. A stochastic model is used to evaluate the variables involved in marketing the new product, such as market size, use of the product, competition, etc. Simulation is utilised to calculate the Net Present Value (NPV) of profits over a period of five years in order to assess the associated risks. The analysis of the simulation results helps the company’s management to decide whether to introduce the new product or not.
Keywords: Business Risk Management, Risk Assessment, Finance, Stochastic Model, Six Sigma DMAIC, Monte Carlo Simulation
The Results
The results of all the simulations are presented below for comparison. The results of the Profits Vector are presented in Table 14.
Table 14: Profits Vector Results in Comparison
| Profits Vector ($) for Five Years |
| Year |
1 |
2 |
3 |
4 |
5 |
| Sim #1 |
568,620 |
480,855 |
436,330 |
416,655 |
411,611 |
| Sim #2 |
668,752 |
549,976 |
491,914 |
467,014 |
460,203 |
| Sim #3 |
780,000 |
622,280 |
548,340 |
517,360 |
509,498 |
| Sim #4 |
902,947 |
697,090 |
605,065 |
568,154 |
558,621 |
| Sim #5 |
1,038,180 |
773,353 |
661,163 |
617,423 |
606,933 |
The summary trend of Profits Vectors per simulation has shown that the profit gradually increases from Sim #1 to Sim #5.
Chapter 1: Launching a New Product in Manufacturing
In Book 5: Risk & Decision Analysis in Risk Management for Businesses
ISBN: 978-620-2-79642-2
Author: Vojo Bubevski
Abstract
This chapter elaborates on the Risk Analysis of launching a new product considering financial aspects. The presented model is generic for the manufacturing industry. A manufacturer is launching a new product. The stochastic analysis is performed for 31 years starting with Year 0, i.e., the current year, to Year 30. There are 16 independent variables, i.e., inputs. To introduce the variability of the inputs, one of the inputs has a probability distribution applied, and the others are varied by using the function for variation. The associated variability parameters are empirical, which are averages of the historical data. Also, there are 11 dependent financial variables including Net Profit, which are calculated each year, i.e., from Year 0 to Year 30. Finally, the outputs of the stochastic analysis are Total Net Profit and Net Present Value. A simulation model is designed and run to calculate the variables for the analysis. What-If and Sensitivity Analysis are applied, which provide a comprehensive view of the probability of the outputs, and quantify the sensitivity of the outputs based on the variability of the associated inputs and financial variables. This risk analysis helps the management to decide whether to produce the new product.
Keywords: Risk & Decision Analysis, Manufacturing Industry, New Product Launch, Financial Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo simulation; Stochastic model.
The Results
The simulation is run and the results are presented below. The calculated Net Profit per Year results are presented in Table 2. The Net Profit is zero for Years 1 – 3 and for Years 17 – 30.
Table 2: Net Profit per Year Results
| Year |
0 |
4 |
5 |
6 |
7 |
| Net Profit ($) |
-270,000.0 |
142,500.0 |
160,576.9 |
180,799.3 |
203,417.5 |
| Year |
8 |
9 |
10 |
11 |
12 |
| Net Profit ($) |
228,711.3 |
256,992.4 |
288,609.0 |
323,949.4 |
363,447.0 |
| Year |
13 |
14 |
15 |
16 |
17 |
| Net Profit ($) |
338,139.6 |
314,425.5 |
292,201.5 |
311,370.9 |
0.00 |
The calculated Net Profit per Year graph for Years 0 –17 is presented in Figure 1 with value labels given in dollars ($). The calculated Net Profit per Year starts at -$270,000 in Year 0 and rises to zero in Year 1. It stays at zero to Year 3 and rises to $142,500 in Year 4. From Year 4 it approximately exponentially grows to a maximum of $363,447 in Year 12. Then it approximately exponentially reduces to a local minimum of $292,201 in Year 15. Subsequently, it rises to $311,371 in Year 16 and reduces to zero in Year 17. It stays at zero till Year 30. Note: The Mean results, which involve a probability distribution calculation, are lower than the calculated results, which do not use probability distributions. For example, the Mean for Year 0 is approximately -$333,333 compared to -$270,000 calculated above. Or, the maximum in Year 12 is calculated above to be $363,447, whereas the Mean is around $125,000.
Chapter 4: Analysing Profitability in Production
In Book 5: Risk & Decision Analysis in Risk Management for Businesses:
ISBN: 978-620-2-79642-2
Author: Vojo Bubevski
Abstract
This chapter presents a Risk Analysis of the profitability of an advanced technology company. The company operates five production plants, each located in a different part of the country. Each plant hires a different number of workers, pays different wages, and invests differently in training programs to improve productivity. The production and financial variables required for the analysis of each plant include Sale Price, Base Units Produced per Worker, Training Effectiveness Factor, Training Investment per Worker, Labour Cost per Worker, Number of Workers, Base Production Capacity, Efficiency Factor, Units Produced and Profit per Plant. Historical data is used to forecast some of the variables, and in order to consider the risk involved, probability distributions or variability functions are applied. The analysis calculates the Total Profit. What-If and Sensitivity Analyses are performed, which deliver a complete assessment of the output’s probability, and quantify the variability of the output based on changes in associated inputs. The risk analysis results provide management with comprehensive information for their decision-making.
Keywords: Risk & Decision Analysis, Production Industry, Profit, Financial Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo simulation; Stochastic model.
The Results
The calculated profit for each plant, i.e., the Profit per Plant variable, is as follows. The Profit per Plant is the following: i) $50,000,000 for Plant 1; ii) $175,000,000 for Plant 2; iii) $114,706,000 for Plant 3; iv) $356,000,000; and v) $720,000,000 for Plant 5.
The Profit per Plant Mean is not much greater than the calculated profit, which is given by the probability distribution. The Total Profit Mean is $1,415,724,400, which is only $18,400 greater than the calculated Total Profit of $1,415,706,000.
Chapter 4: Risk Analysis of Customer Loyalty with Incentive
In Book 8: Business Risk Analysis and Prediction
ISBN: 978-620-3-19675-7
Author: Vojo Bubevski (Independent Researcher)
Abstract
This chapter presents a Risk Analysis of an incentive to increase customer loyalty in the mobile phone market. A mobile phone provider currently has a specified market share and a number of its customers. Each of their customers spends a certain average amount, whit a given profit margin. Each year, each of the customers remains with the provider, and each of the competitors’ customers switches to them, with given probabilities. The model assumes an amount of one-time incentive when they make a switch. The advantage to the provider is that the probability of switching to them increases by a random percentage when the incentive is in effect. The simulation follows these customers through 30 years, with no incentive and with the incentive. The model utilises appropriate probability distributions to generate staying/switching behaviour. The model calculated outputs are Net Present Value (NPV) per Customer with No Incentive, NPV per Customer with Incentive, and Increase with Incentive. The simulation results show that the incentive is worth implementing.
Keywords: Risk Analysis, Marketing, Customer Loyalty, Incentive, Financial Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo simulation; Stochastic model.
The Results
The NPV per Customer No Incentive was calculated with Monte Carlo Simulation. The NPV Mean is $488.13 with a Standard Deviation of $0.62, i.e., 0.127%, which is a very low risk. The Six Sigma target parameters are TV = $488.00; LSL = $487.25; and USL = $488.75. The Six Sigma process capability metrics are: Cp = 0.4030; Cpk = 0.3312; and σ-L = 0.3914. There is a 5% probability that the Mean will be $487.11; a 90% probability that it will be in the range of $487.11 – $489.15; and a 5% probability that it will be above $489.15.
The NPV per Customer with Incentive was also calculated with Monte Carlo Simulation. The NPV Mean is $533.96 with a Standard Deviation of $29.77, i.e., 5.575%, which is a low risk. The Six Sigma target parameters are TV = $534.00; LSL = $490.00; and USL = $570.00. The Six Sigma process capability metrics are: Cp = 0.4478; Cpk = 0.4035; and σ-L = 0.5025. There is a 5% probability that the Mean will be below $483.41; a 90% probability that it will be in the range of $483.41 – $582.10; and a 5% probability that it will be above $582.10.
Chapter 5: Risk Analysis of Launching New Product
In Book 8: Business Risk Analysis and Prediction
ISBN: 978-620-3-19675-7
Author: Vojo Bubevski (Independent Researcher)
Abstract
This chapter elaborates on the Risk Analysis of launching a new product. The presented model is generic for the manufacturing industry considering the financial aspects. But it is interpreted here in the electric cars industry just as an example. A manufacturer is building a new model of an electric car. Assuming that the car will generate sales for the next five years, management has identified the essential factors that can influence the total revenue during that period. Several of these factors have probability distributions associated with them. A simulation model is designed and run to calculate the profit for the five years and the total revenue. What-If and Sensitivity Analysis are applied, which provide a comprehensive view of the probability of the outputs, i.e., profits and revenue, and quantify the sensitivity of the outputs on the changes of associated inputs. This risk analysis helps the management to decide whether to produce the new car model.Keywords: Risk Analysis, Manufacturing, New Product Launch, Financial Risk, What-If Analysis; Sensitivity Analysis; Monte Carlo simulation; Stochastic model.
The Results
The Profit per Year was calculated with Monte Carlo Simulation. The results are as follows: i): Profit in Year 1 is $6,091.2 MM; ii) Profit in Year 2 is $13,211.76 MM; iii) Profit in Year 3 is $13,958.75 MM; iv) Profit in Year 4 is $14,734.45 MM; and v) Profit in Year 5 is $15,587.81 MM.
The Profit per Year Mean is graphically presented in Figure 2 (i.e., the Summary Trend). The Mean results, which involve a probability distribution calculation, are equal to the calculated results, which also use the probability distribution for calculation. Importantly, however, the Summary Trend presents the Mean, 25% – 75% Variability, 5% – 95% Variability, and Simulation Path.
Chapter3: Decision Analysis of Purchasing StrategyIn Book 12: Operations Research Applications for Decision Analysis and Prediction
ISBN: 978-620-5-49772-2
Author: Vojo Bubevski
Abstract
This chapter presents a Decision Analysis of the purchasing strategy of a candy manufacturing company. The company knows that it will need a certain quantity of sugar in six months. The company has three options for purchasing this sugar: i) wait six months and purchase the sugar then, at the going price; ii) buy a futures contract for the required quantity of sugar now for a given price, which guarantees the delivery of the sugar in six months at a locked-in price equal to the current price per pound; or iii) buy a futures contract for one half of the sugar now at the current price and wait to purchase the other half at the going price in six months. There is considerable uncertainty in the price, which is reflected in the probability distributions applied. A decision tree is created and runs to aid the company’s decision in performing the necessary calculations. The results show that the difference in expected costs across the three alternatives is fairly small and the optimal decision is to wait and purchase all the sugar at the going price in six months. Thus, sensitivity analysis is performed to quantify the risks involved, which will support management to decide according to their risk appetite.
Keywords: Risk & Decision Analysis, Manufacturing Industry, Financial Risk, Sensitivity Analysis; Decision Tree; Monte Carlo Simulation; Stochastic model.
The Results
The Decision Tree resolved the Optimal Decision Tree. The optimal strategy is to wait and purchase all the sugar at the going price in six months. The ‘Purchase all in 6 months’ decision has a Path Probability of 1 (i.e., 100%) and a Path Value of $268,209.
Chapter 4: Decision Analysis for Bidding on a Contract
In Book 12: Operations Research Applications for Decision Analysis and Prediction
ISBN: 978-620-5-49772-2
Author: Vojo Bubevski (Independent Researcher)
Abstract
This chapter illustrates a Decision Analysis for a technology factory bidding on a contract. The company must decide whether to bid for a government contract to develop a piece of equipment and if the company decides to bid, it must decide how much to bid. The government will award the contract to the lowest bidder. However, there is a certain probability that there will not be any other bidders. If there are other bidders, there is a probability distribution for the lowest bid. There are four ranges of prices with given associated probabilities. The company estimates the cost of placing a bid at a particular amount and the cost of developing the equipment if it wins the contract. A decision tree is created and runs to calculate the probabilities and monetary values for making these decisions. The decision tree performs sensitivity analysis to quantify the effect of varying two of the inputs: (i) the cost to place a bid and (ii) the cost to fulfill the contract if the bid is won. Quantifying the risks involved will support management’s decision according to their risk appetite.
Keywords: Risk & Decision Analysis, Technology Industry, Bidding Strategies, Financial Risk, Sensitivity Analysis; Decision Tree; Stochastic model.
The Results
The Optimal Decision Tree resolved the optimal strategy.
Node 1: Bid with a Medium amount of $170,000 by paying a cost of $7,500.
Node 2: The Bid Amount Node Value is $2,900.
Node 3: The Medium Decision Indicator is TRUE and the Decision Value is $170,000. The Competing Bid Node Value is also $2,900.
Branch Yes: The Competing Bid Yes chance has an 80% probability with a value of zero. The Underbid Competitor Chance Node Value is $500.
Branch Yes from the Underbid Competitor Yes chance: The probability is 40% with a value of -$150,000. The Yes chance Path Probability is 32% and the Path Value is $12,500. For the Underbid Competitor No chance, the probability is 60% with a value of -$170,000. The No Chance Path Probability is 48% and the Path Value is -$7,500.
Branch No from the Competing Bid No chance: It has a 20% probability with a value of -$150,000. The No Chance Path Probability is 20% and the Path Value is $12,500.
