1. Wally’s Widget Warehouse takes orders from 7 AM to 7 PM. The manager wants to analyze the process and has provided the process flow diagram shown below (with capacity rates at each step). There are three steps required to ship a customer order. The first step is to take the order from a customer (one customer places one order). The second step is to pick the order for the customer, and then they have to pack the order ready for shipping. There are three workers taking care of these three steps. Wally promises that every order placed today gets shipped tomorrow. That means that the picking and packing operations must finish all orders before they go. Wally wants to figure out the following: a. What is the current maximum output of the process per day assuming that no one works overtime? b. What is the process time of the order picker? c. If orders arrive every 1.5 minutes, what is the process utilization? d. How long will the picking and packing operations have to work if we have a day where the order taker works at his maximum capacity? (Hint: how many orders have arrived?) e. Wally is not satisfied with the number you give in (a); he wants the maximum output per day to become larger. There are workers recently hired. Where do you send them to? Why?
2. Gracias Restaurant is a newly open in downtown Miami. The restaurant has 50 tables at which it can serve customers. The flow unit through Gracias is a “party”, which is a group of one or more people who arrive, get seated at a table, eat and depart. On average, a party takes 60 minutes to eat dinner, and then another 20 minutes to eat dessert. (We will use the term “dessert” to refer to any after-dinner item, such as sweets, coffee, other drinks, and so on.) The average party generates a contribution margin (revenue minus variable cost) of $80 on dinner, and $20 on dessert. a. If all parties have both dinner and dessert, what is the capacity rate of the entire restaurant? b. At what rate (dollars per hour gained) is margin generated by the restaurant if it is operating at full capacity?
3. Auto pistons at the South Florida plant are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as shown in the spreadsheet. Hint: you may need Table S6.1 in the textbook. a. If the population (process) standard deviation is 0.5, what are the Upper Control Limit and Lower Control Limit for sample means using 3-sigma? b. Without the knowledge of the population stadard deviation, find the Upper Control Limit and Lower Control Limit of sample means using 3-sigma. c. Find the Upper Control Limit and Lower Control Limit for the range using 3-sigma
4. Five data entry operators work at the data processing department of the Georgia Bank. Each day for 30 days, the number of defective records in a sample of 250 records typed by these operators has been noted, as shown in the spreadsheet. a. Establish the 99.73% upper and lower control limits for a p-chart. b. When we apply the control limits, what would we do if we saw a day’s sample (250 records) has 1 defective record?