07 Jul University Of Texas OM 335 Exam 1
Question 1. (10 points) Consider the Fishing Fleet and Cannery exercise. Suppose that fish is caught and brought to the freezer daily according to the following pattern: (1) 100 tons/hr. between 8 a.m. and 10 a.m., (2) 150 tons/hr. between 10 a.m. and noon, (3) and 100 tons/hr. between 1 p.m. and 5 p.m. Note that there is no input between 12 noon and 1 p.m. The processing capacity of the cannery is: (1) 100 tons/hr. between 8 a.m. and noon, (2) 50 tons/hr. between noon and 2 p.m., and (3) 150 tons/hr. between 2 p.m. and 8 p.m.
(a) Assume that there is unlimited freezer space for unprocessed fish. (i) Draw an inventory buildup diagram that shows fish inventory in the freezer starting at 8 a.m. and ending at 8 p.m. Carefully label both vertical and horizontal axes. (2 points)
(ii) What is the average inventory of fish in the freezer during 8 a.m.-8 p.m.? (1 point)
(iii) What is the average waiting time of fish in the freezer (in minutes)? (1 point)
(iv) Consider a fish that enters the freezer between 8 a.m. and 12 noon. What is the average waiting time of such a fish in the freezer (in minutes)? (1 point)
(b) Assume that the freezer can hold at most 50 tons of unprocessed fish. As soon as the freezer fills up, the catch rate is reduced as necessary to make sure that there will be room in the freezer for the fish.
(i) Draw an inventory buildup diagram that shows fish inventory in the freezer starting at 8 a.m. and ending at 8 p.m. Carefully label both vertical and horizontal axes. (2 points)
(ii) What is the average inventory of fish in the freezer during the day (8 a.m.-8 p.m.)? (1 point)
(iii) What is the average waiting time of fish in the freezer (in minutes)? (1 point)
(iv) Consider a fish that enters the freezer between 10 a.m. and 12 noon. What is the average waiting time of such a fish in the freezer (in minutes)? (1 point)
Question 2. (10 points) Physical Examination on Hire – a chain of small clinics – has contracted with a consortium of HMOs to conduct physical examination of prospective health insurance clients. The table below lists the various tasks that need to be performed in a physical examination:
Task Task Description Duration (in minutes) 1 Blood pressure, weight, temperature, etc. 5 2 Medical history 8 3 Nurse’s checkup 7 4 Lab work 7 5 Doctor’s consultation 6 6 Final report 9
For any client: Task 6 has to follow every other task; Task 1 has to precede every other task; Task 5 has to follow Tasks 1-4; and no two tasks can be performed at the same time.
The current process is staffed with: 3 nurses, say A, B and C, with A performing tasks 1 and 2, B performing Tasks 3 and 4, and C performing Task 6; and 1 doctor, say D, who performs Task 5. All nurses are cross-trained to perform each other’s tasks. However, union rules prohibit assigning a nurse to more than four different tasks. Task 5 can only be performed by the doctor who will perform no other task. In drawing process flow diagrams for this problem please denote which employee is assigned to which task by writing the initial of the employee (A, B, …) on top of the task notation.
(a) Currently, each client progresses through the six tasks in the sequence 1-2-3-4-5-6. What is the system capacity (in clients/hour)? (1 point) Assuming adequate demand, what is the overall labor utilization (in percentage)? (1 point)
What would be the overall utilization of nurses (in percentage) if clients arrive at the rate of 3 per hour? (1 point)
(b) Suppose that a fourth nurse (say E) is now available to you. Redesign the process such that system capacity is maximized. Show the new process flow diagram. (2 points)
What is the system capacity (in clients/hour)? (1 point)
What is the rush order flow time (in minutes)? (1 point)
Suppose that one of the four nurses, say A, is unavailable. Redesign the process such that system capacity is maximized. Show the new process flow diagram. (2 points) What would be the system capacity now? (1 point)
Question 3. (20 points) Consider the Kristen’s Cookie Company (KCC) case when both you and your roommate are working. Suppose that the sequence of processing stages stays the same, but the duration of some of the process steps and labor assignment have changed. The required sequence of steps and their durations are as follows:
Mixing 6 minutes of labor time for 1 dozen cookies; 8 minutes of labor time for 2 dozens of the same type of cookies; 10 minutes of labor time for 3 dozens of the same type of cookies; Spooning 3 minutes of labor time per dozen cookies; Baking 12 minutes of oven time per dozen cookies (1 minute of labor time to set up and load the oven followed by 11 minutes of baking); Cooling 8 minutes; Packing 2 minutes of labor time per dozen cookies; Payment 2 minutes of labor time per order.
There is one other point of departure from the KCC case – your roommate will mix and accept payment; you will spoon, set up and load the oven, and pack. You will also unload the oven but we shall assume that this activity consumes negligible time and can be performed in the middle of doing something else. Assume as we did in class that once you start a process step (mixing/spooning a dozen/baking/packing a dozen/payment) you have to perform it without a break. Furthermore, assume that two identical ovens are available for your use.
Answer the following questions on the basis of the above information.
(a) Consider a particular day when each customer order is for one dozen cookies.
(i) List the resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of each. (2 points)
Identify the bottleneck. (1 point) Note down the steady-state system capacity (in dozens per hour). (1 point)
(ii) What is the steady-state utilization of the ovens (in percentage)? (1 point)
(b) Suppose that each customer order is for two dozen cookies of the same type.
(i) List the resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of each. (2 points) Identify the bottleneck. (1 point) Note down the steady-state system capacity (in dozens per hour). (1 point)
(ii) What is the steady-state utilization of labor (in percentage)? (1 point)
(iii) What is the rush order flow time (in minutes)? Explain. (2 points)
(iv) What is the cycle time (in minutes)? (1 point)
(c) Suppose that each customer order is for three dozen cookies of the same type.
(i) List the resources (You, Roommate, Ovens) and show the capacity (in dozens per hour) of each. (2 points) Identify the bottleneck. (1 point) Note down the steady-state system capacity (in dozens per hour). (1 point)
(ii) What will be the rush order flow time if your roommate is not working? Explain. (2 points)
(iii) What is the cycle time (in minutes)? (1 point)
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