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Written Assignment #1 Submit your solutions to the following problems. Write your solutions clearly and neatly. Note 1: Show all your work to get credit! Problem 1 Chapter 4: Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 5 hours of each workday (Monday-Friday), 4 cashiers and 3 baggers serve approximately 29 customers per hour. A cashier and a bagger who require approximately 5 minutes at checkout and 4 minutes at bagging serve each customer. a) Calculate the utilization of cashiers and utilization of baggers. b) How many cashiers and baggers should Food Goblin Supermarket schedule if it requires a 10% capacity cushion? c) Assume that both baggers and cashiers are cross-trained to perform both activities so that they can serve customers independently. Customers are now both checked, and their groceries bagged by one individual. Further, assume that it takes 11 minutes for one individual to both cash out and bag each customer's groceries. Calculate the utilization of this new group of 7 cross-trained employees. d) How many cross-trained employees should Food Goblin Supermarket schedule if it requires a 10% capacity cushion? Problem 2 Chapter 4: Darren Mack owns the Gas n' Go convenience store and gas station. After hearing a marketing lecture, he realizes that it might be possible to draw more customers to his high-margin convenience store by selling his gasoline at a lower price. However, the Gas n' Go is unable to qualify for volume discounts on its gasoline purchases, and therefore cannot sell gasoline for profit if the price is lowered. Each new pump will cost $135,000 to install, but will increase customer traffic in the store by 14,000 customers per year. Also, because the Gas n' Go would be selling its gasoline at no profit, Darren plans on increasing the profit margin on convenience store items incrementally over the next five years. Assume a discount rate of 9 percent. The projected convenience store sales per customer and the projected profit margin for the next five years are as follows: Year Projected Convenience Store Sales Per Customer Projected Profit Margin 1 $6 15% 2 $7.50 20% 3 $10 25% 4 $13 30% 5 $14 35% a) What is the NPV of the next five years of cash flows if Darren had five new pumps installed now (Year 0)? b) If Darren required a payback period of four years, should he go ahead with the installation of the new pumps? Problem 3 Chapter 5: The following diagram describes a service process where customers go through either of two parallel three-step processes and then merge into a single line for the final step. The numbers in parentheses are the times in minutes for each step of the process. a) What is the capacity of the entire system? b) If you could increase the capacity of only one step through process improvement efforts, which step would you select and how much additional capacity would you strive for? What would the resulting capacity of the process be? Problem 4 Chapter 5: A company is setting up an assembly line to produce 90 units per hour. The table below identifies the work elements, times, and immediate predecessors. Work Element Time (Sec.) Immediate Predecessor(s) A 35 --- B 20 A C 30 B D 23 C E 28 D F 15 B G 17 F H 15 F I 12 G,H J 23 E,I a) What cycle time is required to satisfy the required output? b) What is the theoretical minimum number of stations? c) Use one of the heuristic decision rules described in Table 5.3 on page 194 to balance the assembly line so that it will produce 90 units per hour. Clearly state the decision rule you use, and the work elements assigned to each station. d) What is the efficiency of the line you found in part c?

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