Capacity Decision with Time Series

A manufacturing company is building a new facility where the company's product will be manufactured over the next 15 years. The company must decide how much capacity to build now in the face of uncertainty of future demand. Each year the company will produce to demand unless demand is greater than capacity, in which case the excess demand will be lost. The unit price of the product will remain constant in all years. The plant cost is $6 million plus a random multiple of capacity. The unit production cost is a linearly decreasing function capacity with a random intercept. Also, the unit operating cost is random. The model assumes that each of these unit costs remains constant through time, but it could be modified easily to let them change through time.

The company has 15 years of historical demand data for this product. To generate future data, @RISK's Time Series Fit tool is used on the historical data. Several processes, including MA1, AR1, and MA2, provide similar fits to the historical data, and because of the small amount of historical data, it is difficult to know which of these processes is best for generating future data. (In fact, there is so little historical data that the Auto Detect feature refuses to perform automatic detection. Because of the general upward trend, it is a good idea to check the Detrend option.) Therefore, one of the goals of this example is to try different time series processes for the future data, run RISKOptimizer on each, and see how much difference the time series process makes in terms on the results.

RISKOptimizer is set up to maximize the 10th percentile of the NPV of annual profits, assuming that the building cost is incurred at the beginning of year 1, and all other costs and revenues occur at the ends of the respective years. The current time series in column F is from the best-fitting process, MA1. If you run RISKOptimizer one or times (each with different random numbers), you should get fairly similar optimal solutions, but they won't be identical. Then if you substitute the best AR1 or the best MA2 process for MA1 in column F and run RISKOptimizer, you should get fairly similar results to MA1. In each case, the optimal capacity and 10th percentile of NPV should be in the neighborhood of 860,000 and $1.7 million, respectively. So it doesn't seem to matter too much which time series process is used as long as it is reasonable. But all of these time series processes are so variable that RISKOptimizer can give different results on different runs. For example, we got optimal capacities as low as 844,000 and as high as 870,000 on different RISKOptimizer runs, and these were both from the same AR1 process.

Note: The Industrial edition is required to use the Time Series and RISKOptimizer features of @RISK.

Capacity Decision with Time Series

A manufacturing company is building a new facility where the company's product will be manufactured over the next 15 years. The company must decide how much capacity to build now in the face of uncertainty of future demand. Each year the company will produce to demand unless demand is greater than capacity, in which case the excess demand will be lost. The unit price of the product will remain constant in all years. The plant cost is $6 million plus a random multiple of capacity. The unit production cost is a linearly decreasing function capacity with a random intercept. Also, the unit operating cost is random. The model assumes that each of these unit costs remains constant through time, but it could be modified easily to let them change through time.

The company has 15 years of historical demand data for this product. To generate future data, @RISK's Time Series Fit tool is used on the historical data. Several processes, including MA1, AR1, and MA2, provide similar fits to the historical data, and because of the small amount of historical data, it is difficult to know which of these processes is best for generating future data. (In fact, there is so little historical data that the Auto Detect feature refuses to perform automatic detection. Because of the general upward trend, it is a good idea to check the Detrend option.) Therefore, one of the goals of this example is to try different time series processes for the future data, run RISKOptimizer on each, and see how much difference the time series process makes in terms on the results.

RISKOptimizer is set up to maximize the 10th percentile of the NPV of annual profits, assuming that the building cost is incurred at the beginning of year 1, and all other costs and revenues occur at the ends of the respective years. The current time series in column F is from the best-fitting process, MA1. If you run RISKOptimizer one or times (each with different random numbers), you should get fairly similar optimal solutions, but they won't be identical. Then if you substitute the best AR1 or the best MA2 process for MA1 in column F and run RISKOptimizer, you should get fairly similar results to MA1. In each case, the optimal capacity and 10th percentile of NPV should be in the neighborhood of 860,000 and $1.7 million, respectively. So it doesn't seem to matter too much which time series process is used as long as it is reasonable. But all of these time series processes are so variable that RISKOptimizer can give different results on different runs. For example, we got optimal capacities as low as 844,000 and as high as 870,000 on different RISKOptimizer runs, and these were both from the same AR1 process.

Note: The Industrial edition is required to use the Time Series and RISKOptimizer features of @RISK.

Decision and InputsCapacity 900,000Cost to build #NAME?Unit production cost #NAME?Unit operating cost #NAME?Unit price $10.00Discount rate 10%

Historical data Simulation modelYear Demand Year Demand Units sold Revenue-14 526,000 1 #NAME? #NAME? #NAME?-13 548,000 2 #NAME? #NAME? #NAME?-12 624,000 3 #NAME? #NAME? #NAME?-11 527,000 4 #NAME? #NAME? #NAME?-10 539,000 5 #NAME? #NAME? #NAME?-9 568,000 6 #NAME? #NAME? #NAME?-8 641,000 7 #NAME? #NAME? #NAME?-7 612,000 8 #NAME? #NAME? #NAME?-6 568,000 9 #NAME? #NAME? #NAME?-5 580,000 10 #NAME? #NAME? #NAME?-4 630,000 11 #NAME? #NAME? #NAME?-3 657,000 12 #NAME? #NAME? #NAME?-2 667,000 13 #NAME? #NAME? #NAME?-1 713,000 14 #NAME? #NAME? #NAME?0 810,000 15 #NAME? #NAME? #NAME?

Prod Cost Oper Cost Profit#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?#NAME? #NAME? #NAME?

NPV #NAME?