CASE STUDIES CHOOSING A MANUFACTURING PROCESS AJS, Ltd. is a manufacturing company that performs contract work for a wide variety of firms. It primarily manufactures and assembles metal items, and so most of its equipment is designed for precision machining tasks. The executives of AJS currently are trying to decide between two processes for manufacturing a product. Their main criterion for measuring the value of a manufacturing process is net present value (NPV). The contractor will pay AJS $8 per unit. AJS is using a three-year horizon for its evaluation (the current year and the next 2 years). Process 1 Under the first process, AJS's current machinery is used to make the product. The following inputs are used: Demand Demand for each of the three years is unknown. These three quantities are modeled as discrete random variables denoted DO, D1, and D2 with the following probability distributions: Dy P(Dy) D, P(D,) D, P(D,) 11K 0.2 8K 0.2 4K 0.1 16K 0.6 19K 0.4 21K 0.5 21K 0.2 27K 0.4 37K 0.4 Variable Cost Variable cost per unit changes each year, depending on the costs for materials and labor. Let Vo, V1, and V), represent the three variable costs. The uncertainty surrounding each variable is represented by a normal distribution with mean $4 and standard deviation $0.40. Machine Failure Each year, AJS's machines fail occasionally, but obviously it is impossible to predict when or how many failures will occur during the year. Each time a machine fails, it costs the firm $8,000. Let Zo, Z1, and Z, represent the number of machine failures in each of the 3 years, and assume that each is a Poisson random variable with parameter A = 4. Fixed Cost Each year a fixed cost of $12,000 is incurred. Process 2 The second process involves scrapping the current equipment (it has no salvage value) and purchasing new equipment at a cost of $60,000. Assume that the firm pays cash for the new machine, and ignore tax effects. Demand Because of the new machine, the final product is slightly altered and improved, and consequently demand is likely to be higher than before, although more uncertain. The new demand distributions are: D, PDo) Dy PDy) D, PD,) 14K 0.3 12K 0.36 9K 0.4 19K 0.4 23K 0.36 26K 0.1 24K 0.3 31K 0.28 42K 0.5 Variable Cost Variable cost still changes each year, but this time Vj, V1, and V; are each judged to be normal with mean $3.50 and standard deviation $1.00. Machine Failures With the new equipment, failures are less likely, occurring each year according to a Poisson distribution with parameter A = 3. They also tend to be less serious, costing only $6,000. Fixed Cost The fixed cost of $12,000 is unchanged. Questions 1. Draw an influence diagram for this decision problem. Do you think it would be feasible to solve this problem with an influence diagram? Explain. 2. Write out the formula for the NPV for both processes previously described. Use the variable names as specified, and assume a 10% interest rate. 3. For Process 1, construct a model and perform 1,000 simulation trials. Estimate the mean and standard deviation of NPV for this process. Print a histogram of the results, and estimate the probability of a negative NPV occurring. Repeat Question 3 for Process 2. 5. Compare the distribution of NPV for each of the two alternatives. Which process would be better for AJS? Why? Source: This case was provided by Tom McWilliams. b