OIS 3660 Homework 1 Fall 2016 University Of Utah David Eccl

Ois 3660 Homework 1 Fall 20164 1university Of Utahdavid Eccles School

Ois 3660 Homework 1 Fall 20164 1university Of Utahdavid Eccles School

OIS 3660 Homework 1, Fall University of Utah David Eccles School of Business OIS 3660: Fall 2016: HW1 Due Monday September 19th, 11:59PM

Paper For Above instruction

This comprehensive paper addresses the key questions provided in the assignment, covering various topics including process capacity calculations, inventory management, staffing, and resource bottlenecks within healthcare and service operations, as well as manufacturing and supply chain contexts. Each question is explicitly analyzed using foundational operations management principles, emphasizing the application of Little’s Law, process capacity, utilization, inventory turnover, and flow analysis to real-world scenarios.

Question 1: Bakery Cookies Production Rate

Cruz operates an oven capable of baking 20 cookies simultaneously, with an average baking time of 40 minutes per batch. To determine the average number of cookies baked per hour, we first find the number of batches completed in an hour. Since each batch takes 40 minutes, the number of batches per hour (60 minutes) is 60/40 = 1.5 batches. Each batch yields 20 cookies, so total cookies produced per hour is 1.5 x 20 = 30 cookies. Thus, Cruz bakes an average of 30 cookies per hour.

Question 2: Students Waiting at Front Desk

Clare sees 10 students between 10:30am and 11:00am, with a typical service time of 3 minutes per student. The flow rate (arrival rate) is 10 students over 30 minutes, which converts to 20 students per hour (since 10 students / 0.5 hours). The service rate for each student is 3 minutes, or 20 students per hour (60/3 = 20). To find the average number of students either waiting or in process, we use queueing theory's Little’s Law: \(L = \lambda \times W\), where \(L\) is the average number in the system, \(\lambda\) is the arrival rate, and \(W\) is the average time in the system. The average time a student spends in the system, \(W\), includes both waiting and service time. With an arrival rate of 20 students/hour and a service rate of 20 students/hour, the system is at capacity, indicating potential queue buildup. To simplify, the average number of students in the system approximates 0.5 to 1 student, but more precise modeling indicates about 1.5 students, considering system utilization close to 100%.

Question 3: Cars Traveling from Park City

Hayden's commute takes 40 minutes, and there are 60 cars per hour traveling from Park City. Using Little’s Law, the average number of cars on the road is the product of the flow rate and the travel time. The flow rate is 60 cars/hour, and travel time is 40 minutes (or 2/3 of an hour). Therefore, the average number of cars on the way is 60 x (2/3) = 40 cars. Thus, approximately 40 cars are en route from Park City at any given time.

Questions 4–6: Jake’s Inventory and Cost Analysis

Question 4: Jake’s Inventory Turns

Given an annual revenue of $4,300,000 and COGS of $3,200,000, the average inventory cost can be determined, but first, inventory turnover ratio is calculated as COGS divided by average inventory. Since Jake maintains 5.5 days of inventory, the number of inventory turns is 365 days divided by 5.5 days (days of supply), which results in approximately 66.36 turns per year (meaning inventory turns over about 66 times annually).

Question 5: Average Inventory in Dollars

Average inventory value is calculated by dividing the annual COGS by inventory turns: $3,200,000 / 66.36 ≈ $48,209.55. Therefore, Jake's average inventory in monetary terms is roughly $48,210.

Question 6: Inventory Holding Cost

For an item costing $20 and sold at $30, with a 40% annual holding cost rate, the annual cost per unit is 40% of $20 = $8. The total holding cost depends on the average units held. Using the average inventory in dollars ($48,210) and the unit cost ($20), the average units held are $48,210 / $20 ≈ 2,410.5 units. The total annual holding cost is 2,410.5 units x $8 = $19,284.20.

Questions 7–9: B&K Consulting Staffing

Question 7: New MBA Hires

Using Little’s Law for the Associate stage: \( L = \lambda \times T \), where \(L=200\) associates, and \(T=4\) years (the time spent at this stage). Converting years to weeks or hours is unnecessary; instead, the number of hires per year = \(L / T\). Therefore, annual new hires = 200 associates / 4 years = 50 new MBA graduates hired each year.

Question 8: Percentage Becoming Managers

Number of Managers needed yearly is 60, with each staying an average of 6 years. The number of new managers promoted annually is 60 / 6 = 10. The fraction of new hires who become managers is 10 / 50 = 20%, indicating 20% of new hires are promoted to managers, with the remaining 80% dismissed or leaving.

Question 9: Duration of Partnership

If 2 managers are promoted to partners each year, and the total number of partners is 20, the average tenure as a Partner is 20 / 2 = 10 years.

Questions 10–13: Custom Suit Manufacturing Process

Question 10: Process Capacity in Suits/Day

Measurement stage capacity: 30 minutes (~0.5 hours) per order, so per day (10 hours), capacity = 10 hours / 0.5 hours = 20 suits. Material preparation and sewing stages are the bottlenecks with capacities of 10 suits (1 hour / 1 hour) and approximately 4 suits (2.5 hours / 10 hours), respectively. The overall process capacity is limited by the slowest stage, which is sewing at 4 suits per day.

Question 11: Flow Rate at Demand of 0.2 Suits/Hour

Demand rate: 0.2 suits/hour, or 4.8 suits/day (0.2 x 24). The process flow rate should match demand, so approximately 4.8 suits/day are produced, aligning with the bottleneck capacity.

Question 12: Sewing Stage Utilization (Demand of 0.5 Suits/Hour)

Demand: 0.5 suits/hour or 12 suits/day. Sewing capacity: 4 suits/day. Utilization = 12 / 4 x 100% = 300%. Since this exceeds 100%, it indicates the sewing stage is over capacity and cannot meet this demand efficiently.

Question 13: Measurement Stage Utilization (Demand of 0.5 Suits/Hour)

Measurement capacity: 20 suits per day, demand: 12 suits/day, so utilization = 12 / 20 x 100% = 60%, indicating significant available capacity.

Questions 14–19: Hospital Emergency Department Capacity Analysis

Question 14: Nurse Capacity

Each nurse spends 35 minutes per patient, so capacity per nurse per hour is 60 / 35 ≈ 1.71 patients. With 12 nurses, total capacity is 12 x 1.71 ≈ 20.5 patients per hour.

Question 15: X-Ray Technician Capacity

Each technician can X-ray 5 patients per hour, with 4 such technicians, total capacity = 4 x 5 = 20 patients per hour.

Question 16: Trauma Bays Utilization

Assuming 50 patients/hour, with 20% needing trauma bays (10 patients), each trauma bay can handle 30 minutes per patient. Total trauma bay capacity: 3 bays x (60 / 30) = 6 patients/hour. Utilization: 10 / 6 x 100% ≈ 166.7%, indicating a bottleneck.

Question 17: Examination Room Utilization

80% of 50 patients = 40 non-trauma patients. Each spends 45 minutes, with 10 examination rooms, capacity per hour: 10 x 60 / 45 ≈ 13.33 patients. Utilization: 40 / 13.33 x 100% ≈ 300%, showing capacity exceeds demand, but in reality, resource constraints imply rooms are highly utilized or over capacity.

Question 18: Bottleneck Identification

The resource with the lowest capacity relative to demand is the bottleneck. Calculations suggest the trauma bays are heavily over-utilized, making them the bottleneck.

Question 19: Additional Physician Impact

Adding one more physician increases physician capacity: 6 physicians x 19 minutes per patient: capacity = 6 x 60 / 19 ≈ 18.95 patients/hour. Since current capacity is approximately 20, the maximum capacity becomes about 20 patients/hour, marginally increased, indicating slight improvement but the bottleneck remains trauma bays or other resources.

Question 20: Resource Utilization Principles

The correct statement is: "A non-bottleneck stage has excess capacity compared to the bottleneck stage, and the implied utilization of a non-bottleneck stage is always less than 100%," which aligns with operations management principles that non-bottleneck stages have slack capacity, and bottlenecks determine overall throughput.

References

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