DJN’s contractual conditions are as follows: it must satisfy the military’s demand for HQ89 every week of the year, i.e. 52 weeks. If DJN fails to meet weekly demand, it must pay a severe penalty of £50k per unit of HQ89 that it fails to supply.
For simplicity, let us assume that there is no backlog. Hence, charges, if they occur, only apply to the current week.
Each unit of HQ89 costs £95k to manufacture and sells for £150k.
The management of DJN is considering the following options in order to meet demand for the coming year:
(i) Option1: Maintain current manufacturing levels of 100 guaranteed units of HQ89 per week;
(ii) Option 2: Maintain current manufacturing levels of 100 units of HQ89 PLUS engage a sub-contractor so that the sub-contractor can supply up to 10 guaranteed extra unit of HQ89 per week to DJN. Such extra units would cost £100k;
(iii) Option 3: Speed up the manufacturing process so that DJN can manufacture 110 units of HQ89 a week at a reduced cost of £90k per unit. Unfortunately, speeding up the process reduces the quality of the manufacturing process so that there is now only a 95% chance that each manufactured unit has no defects and will function correctly. This means that there is a 5% chance each of the 110 units will fail. In this situation, the number of non-defective units of HQ89 that DJN will be able to manufacture each week can be predicted by a Binomial probability distribution with n = 110 and p = 0.95. If a unit is defective, then it cannot be repaired or used- it is scrapped. The cost of manufacturing each unit is the same whether the unit is defective or not. The Quality Control is very strict and they can detect the defective units with 100% accuracy.
The option that DJN chooses will not affect DJN’s contractual agreement with the military.
Assume the following:
(i) That the demand at the end of the current year will be 100, so that, for example, if the predicted change in weekly demand is +10%, then the predicted demand in the first week of the coming year will be 100 + 10%*100 = 110.
(ii) That, at the end of the current year, DJN has a residual stock of two HQ89 units so that if, for example, they manufacture 100 HQ89 units in the first week of the coming year, then they will be able to supply 102 HQ89 units in that week.
(iii) That demand figures are WHOLE numbers: If the predicted demand has fractional parts, e.g. 100.2, 100.5 or 100.6, then you must round the number up so that, for example, 100.2, 100.5 and 100.6 would all equal predicted demand of 101.
(iv) That whichever option DJN selects, the cost of storing the HQ89 units remains the same and therefore irrelevant to the decision.
You may make other reasonable assumptions.
Required:
(i) Simulate the problem using @risk.
(ii) Based on your model, write a report recommending to DJN on the optimal choice. Your recommendation must include a discussion of the merits and demerits of each of the three options DJN have considered.
Model Submission:
In case we need to check your model, you must submit the excel file containing your @risk model. Name the file using your student number as suffix, for example, as AtRisk_123456.xlsx
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