A renowned industrial engineering firm, headquartered in Pretoria, is considering implementing a new automated quality control system to enhance the inspection process in its manufacturing plants. This system is expected to operate for a few years before it is replaced by an upgraded version. However, there is uncertainty regarding the potential profitability and efficiency gains from this system, so an analysis is needed to determine whether to proceed with its implementation.Suppose the decision is made to move forward. In that case, the new system will first be tested in a pilot facility located in Pretoria to evaluate its effectiveness in identifying defects and improving product quality. If the pilot test indicates that the system will be successful, it will be deployed nationwide across the company's plants. The cost of developing and testing the system in the pilot facility is estimated to be R40 million. A total budget of R100 million has been allocatedfor the pilot and national implementation phases. A minimum of R5 million must be spent on testing in the pilot facility,with a maximum of R10 million allowed for this phase. The remaining R90 million to R95 million will be reserved for the national implementation. The system's performance in both the pilot facility and nationwide is assumed to be directly proportional to the investment in automation and quality control. However, marginal gains in performance are expected to decrease as the level of investment approaches a saturation point. Excluding the fixed cost of R40 million, the net savings from the pilot test are projected to be 50% of the investment. The outcome of the pilot test will fall into one of three categories: very successful, moderately successful, or unsuccessful. The probabilities of these outcomes are estimated to be 0.32, 0.30, and 0.38, respectively. If the outcome is verysuccessful, the expected net savings from the nationwide implementation would be approximately twice the investment. If the outcome is moderately successful, the corresponding net savings would be around 0.2 times the investment. The system would be abandoned if the outcome is unsuccessful, and no further implementation would occur.Use stochastic programming with recourse to formulate a model for this problem. Assuming the company proceeds with developing the system, solve the model to determine the optimal level of investment in the pilot facility and then determine the appropriate level of investment in the national implementation phase under each of the three possible outcomes.Finally, the expected value (statistically) of the total net savings from the system, including the fixed cost, is calculated.The company should proceed with the project only if the expected total net savings are positive.
A renowned industrial engineering firm, headquartered in Pretoria, is considering implementing a new automated quality control system to enhance the inspection process in its manufacturing plants. This system is expected to operate for a few years before it is replaced by an upgraded version. However, there is uncertainty regarding the potential profitability and efficiency gains from this system, so an analysis is needed to determine whether to proceed with its implementation.
Suppose the decision is made to move forward. In that case, the new system will first be tested in a pilot facility located in Pretoria to evaluate its effectiveness in identifying defects and improving product quality. If the pilot test indicates that the system will be successful, it will be deployed nationwide across the company's plants. The cost of developing and testing the system in the pilot facility is estimated to be R40 million. A total budget of R100 million has been allocated
for the pilot and national implementation phases. A minimum of R5 million must be spent on testing in the pilot facility,with a maximum of R10 million allowed for this phase. The remaining R90 million to R95 million will be reserved for the national implementation.
The system's performance in both the pilot facility and nationwide is assumed to be directly proportional to the investment in automation and quality control. However, marginal gains in performance are expected to decrease as the level of investment approaches a saturation point. Excluding the fixed cost of R40 million, the net savings from the pilot test are projected to be 50% of the investment. The outcome of the pilot test will fall into one of three categories: very successful, moderately successful, or unsuccessful.
The probabilities of these outcomes are estimated to be 0.32, 0.30, and 0.38, respectively. If the outcome is very
successful, the expected net savings from the nationwide implementation would be approximately twice the investment. If the outcome is moderately successful, the corresponding net savings would be around 0.2 times the investment. The system would be abandoned if the outcome is unsuccessful, and no further implementation would occur.
Use stochastic programming with recourse to formulate a model for this problem. Assuming the company proceeds with developing the system, solve the model to determine the optimal level of investment in the pilot facility and then determine the appropriate level of investment in the national implementation phase under each of the three possible outcomes.
Finally, the expected value (statistically) of the total net savings from the system, including the fixed cost, is calculated.
The company should proceed with the project only if the expected total net savings are positive.
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