Plastedor production decision report by sander kaus
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![Plastedor Production Decisions Report<br />This report analyses Plastedor production process decisions using an expected value criterion to find out the best outcome of probabilities and the best income in monetary terms. The income is valued through cash flow based accounting principles, leaving out costs carried out before the production (costs for experimenting). The accrual based accounting is left out in order to find out most effective cash flow based process. Related to the above said the experimenting costs of £1’000 per production run where excluded from the Process II and Process III setup costs. <br />The production decision and the sensitivity of related inputs are analysed through different perspectives. As the decision tree illustrates, the most important decision is whether to take the molecule chain-length test or not. Test taking is related to the accuracy of deciding the correct process and thus reflects higher economic benefit. The study of the test cost relation and the test reliability relation to the economic outcome are of great interest here. This report gives an analysis of the maximum affordable test cost. The synthesis of test accuracy up to ideal test standard (100% accurate test) provides a good outline of test accuracy and cost increase relation.<br />Further the report focuses on uncertainty related sensitivity study of Process III variable cost and on the likelihood of the minimum pressure exceeding 150 PSI in Process II followed by in depth testing of triangularly distributed probabilities for those two factors. The latter is basis for a critical discussion of the results based on probabilities and sensitivity analysis. The report will include arguments to the challenges related to uncertain and multidimensional risk factors. <br />Plastedor financial possibilities<br />Plastedor financial results are largely dependant on quality. As shown in the Table 1 the quality related profits are varying in severe extent in Process II and Process III.<br />Income price per pound (High Q, £)3Income price per pound (Standard Q, £)2,5PPS per month (pounds)100 000Extruding polypropylene resin (£ per pound)1Process IProcess IIProcess IIIVariable cost (£, per pound)0,650,750,85Setup cost per batch1 0002 5005 000Profit if high quality 122 500110 000Profit if standard quality84 00072 50060 000<br />Table 1: Plastedor processes profit calculus.<br />Although the cost of extracting the polypropylene resin varies between £I and £1.25 per pound, the calculus is made on the basis of £1 as the results of processes will differ equally if this cost is changed. The quality related profit distribution in Table 1 forms the basis for probability related calculus. It does not take into the consideration the test cost of £3’000 or the outcome of test results. <br />Plastedor decision tree<br />The primary decision is related to molecular weight test – test or no test. It is important since the test accuracy decreases uncertainty of the chain-length and therefore provides a better base for process decisions and corresponds to an increase in income (maximisation of the income). The test will provide a conditional probabilities table that notes if the raw material is heavy molecular weight (60% = 90%*50% + 30%*50%) or light molecular weight (40% = 10%*50% + 70%*50%) as follows:<br />Long ShortTotalHeavy90%30%60%Light10%70%40%P of short/long50%50%100%<br />Table 2: Molecular weight probabilities if taking the test<br />By using the above table, Bayes Theorem enables us to reverse the probabilities to outcomes of short or long chain probabilities variety in a test outcome of heavy or light molecular weight:<br />P [Heavy/Long]75,0% = 90%*50% / 60%P [Heavy/Short]25,0% = 30%*50% / 60%P [Light/Long]12,5% = 10%*50% / 40%P [Light/Short]87,5% = 70%*50% / 40%<br />Table 3: Raw material chain length probabilities after test results<br />If the test shows heavy molecular weight the most reasonable process to choose would be Process III with an average outcome of £97’500 = £110’000*75% + £60’000*25%. If the test shows light molecular weight, Process I would be the most profitable in this case with a certain result of £84’000. Taking into consideration the test cost of £3’000 and above calculated probabilities of heavy (60%) and light (40%) molecular weight the best average result with test taking would sum up to £89’100 = £97’500 * 60% + £84’000 * 40% - £3’000. If no test is taken, then Process II and Process III provide an identical result of £85’000. Because higher average income is attained by test taking, it is recommended.<br />The Plastedor decision tree for choosing the best manufacturing process is provided in Appendix 1.<br />The test cost sensitivity analysis<br />As analysed above, the best outcome if taking the given test with a cost of £3’000 has an income of £89’100 and the best outcome without test taking has an income of £85’000. The test with a cost of £3’000 offers increased accuracy and an average additional income of £4’100 = £89’100 – £85’000 compared to the best process outcome of not taking the test. This means that the maximum justifiable test cost with the given accuracy would be £7’100 = £4’100 + £3’000. If the test is more expensive than £7’100 the expected income is less than if taking no test. The relation is shown in the Chart 1.<br />Chart 1: Test cost relation to income<br />In case of 100% test accuracy (ideal test) the probabilities distribution is as follows:<br />Long ShortTotalHeavy100%0%50%Light0%100%50%P of short/long50%50%100%<br />P [Heavy/Long]100,0%P [Heavy/Short]0,0%P [Light/Long]0,0%P [Light/Short]100,0%<br />Table 4: Probabilities in case of ideal test.<br />The maximum income for a 100% accurate test would be 50/50 probability of outcomes of Process III and Process I: £ 97’000 = £110’000*50% + £84’000*50%. The maximum justifiable test cost for the 100% accuracy would be the difference between best outcome of the test taking and no test taking: £12’000 = £97’000 -£85’000. This means that a more reliable test should not cost more than £90 per 1% accuracy increase from the given test: £90 = (£12’000 – £3’000)*0.01. This logic is shown in the Chart 2.<br /> Chart 2: Test reliability increase relation from the given base (0) to the ideal test (1)<br />The uncertainties of Process II minimum pressure and Process III variable cost<br />If no test is taken the outcomes of Process II and Process III are equal at the level of £85’000:<br />Process II: £85’000 = (£122’500*50% + £72’500*50%)*50% + £72’500*50%<br />Process III: £85’000 = £110’000*50% + £60’000*50%<br />This means that a decrease in the probability of minimum pressure above 150 PSI will decrease the income for Process II and the Process III should be chosen. If the variable cost of Process III will increase the income of Process III will decline and Process II should be chosen. If the minimum pressure above 150 PSI probability will increase in Process II by 1% point the outcome will be: £85’250 = (£122’500*51% + £72’500*49%)*50% + £72’500*50%, thus meaning that 1% accuracy increase in PSI (from 50% to 50,5%) has an income effect of £125 = (£122’500 – £72’500)*50%*1%*50%. In Process III if the variable cost will decrease by 1% the outcome in profits will be: £850 = £100’000*£0.85*(100%-1%).<br />Taking the above said into consideration the impact of 1% decrease in Process III variable cost has 850/125 = 6.8 times higher effect on income than 1% increase in probability of minimum pressure above 150 PSI. The relation and impact to the income is shown in the Chart 3.<br />Chart 3: Impact of input changes in Processes II and III <br />The outcome of change in both parameters simultaneously is more complex. Chart 4 expresses the outcome of 100 changes in both parameters giving total 10000 outcomes. <br />The two factor interrelation is presented in the triangular area in the Chart 4. If the minimum pressure would exceed 150 PSI 100% (ideal outcome) the income for Process II would be maximised at the level of £97’500 = £122’500*100%*50% + £72’500*50%. The same income (£97’500) could be received with Process III if the variable cost equals to:<br />£0.725 = £0.85*(1 – ((£97’500 - £85’000) / (100’000*£0.85*1%))/100).<br />If the variable cost of Process III is less than £0.725, then Process II should be eliminated as it is less profitable even if 100% of needed minimum pressure (ideal outcome) is achieved (the linear flat plateau area in the chart related to change of Process III variable cost). <br />The related income area (triangular) of two processes<br />Chart 4: Sensitivity analysis of Process III variable costs change and Process II minimum pressure probability change of exceeding 150 PSI.<br />The optimal decision related to probabilities of Process II minimum pressure and Process III variable cost<br />As stated beforehand, if taking no test the best incomes are provided by Process II and Process III equally at the level of £85’000. Process I income is fixed at level of £84’000. Process I income is stable and not relevant to uncertainties. Process II and Process III incomes are average and depend on uncertainties as follows:<br />,[object Object]](https://image.slidesharecdn.com/plastedorproductiondecisionreportbysanderkaus-100622072310-phpapp02/85/Plastedor-production-decision-report-by-sander-kaus-1-320.jpg)
![Process III variable cost is most likely £0.85, but it could be as little as £0.55 or as large as £1.15 giving a roughly equilateral triangular probability distribution. As calculated beforehand a 1% point change (from 50% to 51%) in PSI accuracy costs £250. Based on latter and given probability distribution data the minimum income of Process II could be £80’000 = £85’000 – (50% - 30%)*100*£250 and the maximum income could be £93’750 = £85’000 + (85% - 50%)*100*£250. For Process III the minimum could be £55’000 = £85’000 – (£1.15 – £0.85)*100’000 and the maximum could be £115’000 = £85’000 + (£0.85-£0.55)*100’000.<br />Setting and running a 5’000 iterations simulation on above stated triangular distributions one could find income probability distribution of income for both processes. The results are presented in the Chart 5.<br />Chart 5: Process II and Process III income probability distribution compared to Process I income.<br />Chart 5 compares Process II and Process III probable outcomes with the outcome level of Process I (£84’000) as the stable one. Process II provides an average of 76.7% higher income than Process I and Process III gives in average 53.3% higher income than Process I. From that perspective Process II should have an advantage before other processes. But as stated before, it is an average outcome. The real outcome of each trial may vary in Process II from £80’000 to £93’750 and in Process III from £55’000 to £115’000. As the simulations results summary states the mean income of Process II is £86’250 and standard deviation of £2’842. Process III has the mean income of £85’000 and standard deviation of £12’249. Process III mean is equal to average outcome because of the equilateral triangular probability distribution. From the perspective of highest mean income and lowest standard deviation Process II should be chosen before Process III. <br />Choosing between Process I and Process II depends on risk aversion. Taking into consideration that the contract is only for 6 months, i.e. the sample size is only 6, there is high probability that within different 6-trials the average may vary to a very large degree. Because of the six possible trials the standard distribution of sample means cannot be used as the sample size is much less than 30 (Romero-Morales and Taylor, 2010). Still it is possible:<br />,[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Plastedor production decision report by sander kaus
- 3. to calculate the probability where 4 out of the 6 trials will give less income than £84’000 (median is less than £84’000);
- 5. Two outcomes are possible in each trial (more or less than £84’000)
- 6. The probabilities of the outcomes in each trial do not change
- 8. For Processes II and III the risk of hitting with all 6 trials lower than £84’000 is very marginal (0.02% and 1.04% respectively);
- 9. The risk that 4 trials (over half of the trials) will end up with less income than Process I is very low: 2.18% probability for Process II and 20.1% for Process III;
- 10. The 95% confidence interval of six trials average ranges for Processes II from £83’976 to £88’524 and for Process III from £75’199 to £94’801,
- 11. The range of Process II 95% confidence area is 4.3 = (£94’801 - £75’199)/(£88’542 - £83’976) times smaller than the area of Process III.Taking into consideration the above, Process II has better probabilities of providing higher income on average than Process III. Because of the smaller range in confidence area the risk of resulting in less average income if choosing Process II is lower than if choosing Process III. The risk of Process II resulting in 6 trials in less total (or average) income than Process I is very low and therefore the risk of choosing Process II as primary process is worth of risking.<br />Appendix 1: Plastedor decision tree <br />