QUANTITATIVE ANALYSIS-OPERATIONS MANAGEMENT CASE STUDY

Visit the site: Wheaton Sanitary District. This tour of a wastewater treatment plant is an example of a high-volume, public project. How is capacity defined at a wastewater treatment plant? Throughout the year, the demand on capacity can vary significantly. How do they meet peak demand? Provide a quantitative analysis from the available information. What are the constraints involved in changing the capacity of a facility like this?

***Weekly Module Notes***:

Theory of Constraints The aim of theory of constraints (TOC) is to help firms continually achieve their goals. According to this philosophy, every firm, at each point in time, has at least one constraint, or bottleneck, that limits the firm’s performance with respect to its goal. Consider the following simple example of a laundry system with one washer, one dryer, and one person who folds the dried clothes: If one were to continuously send one load after another into this laundry system, what is the capacity of the system in minutes per load? Answer: 60 minutes per load If this answer seems confusing, it might help to think of the system as follows: Now, if the goal of the system is to achieve a capacity of 30 minutes per load (or 2 loads per hour), what step is the bottleneck in this system? Answer: Dryer. Perhaps, replacing the current dryer with a faster one will eliminate this bottleneck. Identifying and eliminating bottlenecks is what TOC is all about. A more formal example in operations management follows: 2 The manager of a bank is attempting to identify the bottleneck in a loan application process. Each loan application arrives at Step 1 (20 min), where it is evaluated for completeness. At Step 2 (30 min), the application is categorized into one of the different classes, with respect to the amount of loan requested, and other criteria. Step 3, credit checking (25 min), and Step 4, data entry process (45 min), are done simultaneously. At Step 5, the loan is either approved or rejected (10 min). Which of the 5 steps is the most significant bottleneck? How many loans can the bank process in an 8-hour weekday? The most significant bottleneck is the step that takes the largest time. Here, Step 3 and Step 4 can be viewed as one step because Step 5 cannot be done unless and until both Step 3 and Step 4 are finished. The total time for a loan application here = 20 + 30 + Max (25, 45) + 10 = 20 + 30 + 45 + 10 = 105 min The most important bottleneck is clearly Step 4. If you reduce Step 4 by 20 min, the total time for a loan application will be 20 + 30 + Max (25, 25) + 10 = 85 min. The capacity of the bank currently is 45 minutes per loan (recall the laundry system example). In an 8-hour weekday, the bank’s daily capacity is (8 hours * 60 min per hour) / 45 min per loan = 10.7 loans per day, on average. Taguchi Loss Function Taguchi loss function (TLF) is a formula given by Genichi Taguchi to evaluate the “loss” (regret) incurred by a firm for deviating from the target value. QSO 600 Module Nine 3 Consider the following example: Joe is packing french fries at a fast-food restaurant. The target weight for each bag of fries is 7 oz. However, there is a tolerance of ± 2 oz. In other words, the restaurant considers no loss (regret) incurred for any bag that weighs between 5 oz. and 9 oz. This is the traditional view of quality loss. Using the traditional view of quality loss, there is no loss to the company if the measurement lies between the lower specification (5 oz) and the upper specification (7 oz). There is a loss to the company as soon as the measurement falls more than the upper specification or less than the lower specification. But, imagine a situation where almost every bag weighs less than 9 oz, but very close to 9 oz (say, 8.99 oz). What is the problem here? The customers are paying for 7 oz, and the restaurant is consistently selling them more than what they are paying for. This means that even though the traditional view of quality says that there is no loss, there is a loss. Now, imagine a situation where almost every bag weighs over 5 oz, but very close to 5 oz (say, 5.01 oz). What is the problem here? Even though it might seem like the restaurant is gaining because it is selling the customers less than what they are paying for, eventually, it will lose its customers because they will be dissatisfied. This means that even though the traditional view of quality says that there is no loss, there is a loss. After discovering the drawbacks of the traditional view of quality, Taguchi proposed a quality loss function that is depicted by the following figure. It illustrates the loss incurred by the 4 QSO 600 Module Nine company as soon as the measurement deviates from the target value. And the farther the measurement is from the target, the higher the loss. The following formula is called the Taguchi Loss Function (TLF): Expected loss per unit produced by the company = where A is the loss incurred for just crossing either the lower specification or the upper specification. Typically, it is considered to be the cost incurred by the customer to get the product repaired. This concept is further clarified in the following example.  is the tolerance limit x is the measurements in the sample taken n is the sample size m is the target value The following example illustrates how the formula is applied. Customer tolerances for the diameter of a product are 1.5 – 0.02 and 1.5 + 0.02 meters. For a product that just exceeds these limits, the cost to the customer for getting it fixed is $50. Ten products are randomly selected and their diameters, in meters, are measured as follows: 1.53, 1.49, 1.50, 1.49, 1.48, 1.52, 1.54, 1.53, 1.51, and 1.52. Find the expected Taguchi loss incurred by the company per unit. A = $50 Even though the customer is incurring this cost, Taguchi suggests that the company considers this cost as its own because it risks the possibility of losing several potential future 5 sales from this customer. = 0.02 meter m = 1.5 meters n = 10 Expected loss per unit: 6

Reference Russell, R. S., and Taylor, B. W. (2009). Operations and supply chain management. (6th ed.). Wiley.