1. IV. Little’s Law and Labor Costs • Operational Measure: Inventory • Little’s Law • Direct labor cost

2. Why is there inventory?

3. Patient Log Flow rate = 11 patients/day = 1/hr Inventory: 2.076 patients Flow time: 2.076 hrs.

4. Throughput Rate R [units/unit time] Inventory I [units] ... ... ... ... ... Flow Time T [unit time] Little’s Law • Little’s Law: • Years (days, weeks, months) of Supply: • Turnover Ratio (or Turns):

5. Process Flow Examples Job Flow: A shiny new vehicle leaves the assembly line of Toyota’s Georgetown, KY, plant every 50 seconds. At any moment of time, there are 918 vehicles on the line. How much time does it take for a vehicle to be assembled? Material Flow: Wendy’s processes an average of 5,000 lb. of hamburgers per week. The typical inventory of raw meat is 2,500 lb. What is the average hamburger’s flow time and Wendy’s turnover ratio? T = I / R = 2500/5000 = 0.5 weeks Turnover = 1/T = 1/0.5 = 2 /week

6. Process Flow Examples Resource Utilization: In the past year, Shouldice hospital admitted 14,965 patients. This year, a 20% increase is expected. The hospital has 390 beds. (a) If each patient stays on average 8 days in the hospital, how many beds were empty, on average, last year? (b) On average, how many beds you expect to be empty this year? 390 – 328*120% = 390 – 394 = – 4 beds. Cash Flow: Motorola sells $300 million worth of cellular equipment per year. The average accounts receivable in the cellular group is $45 million. What is the average bill-to-collection time?

7. Process Flow Examples Customer Flow: On a typical weekday in January, 4,200 customers visit a Wal-Mart store in Rochester. It is estimated that, on average, there are 350 customers in the store. Assuming that the store is open 14 hours a day, how much time an average customer spends in the store? Employee Flow: The total number of employees in a certain company remains constant. Due to turnover, on average, the company hires 150 men and 200 women each year. If a woman stays with the company 50% longer than a man, what proportion of total employees are women? Iw = Rw * Tw = 200 TwIm = Rm * Tm= 150 Tm Tw = 1.5 Tm

8. Waiting time at a fast-food restaurant

9. Inventory Value Profiles: Wal-Mart vs. K-Mart

10. A Labor Intense Process Components Finished Xootrs Activity 1 (1 worker) Activity 2 (1 worker) Activity 3 (1 worker) 13 min 11 min 8 min Activity time

11. Labor Content (time/unit) • Making scooters at capacity • Labor content (time/unit) = • Labor cost ($/unit) at $12 per hr or $0.2 per min = • Suppose we add a second worker for the second activity • Labor content = • Labor cost is • How to calculate direct labor cost? • Cost of direct labor =

12. Labor Utilization • Idle time • At capacity, • If demand constrained, at 4 scooter/hr: • Idle time with multiple workers • If we add a second worker for the second activity, • Idle time of a worker at a resource = • Average labor utilization

13. Labor Utilization • Idle time • At capacity, • Labor cost paid to idle time = • Line balancing. • If demand constrained, at 4 scooter/hr: • Idle time of a worker = • Average labor utilization

14. Process of Making Scooters

15. Direct labor Cost • Labor content: total labor time invested in the production of a unit. • Labor content for a dozen cookies = • Idle time for all workers at a resource = cycle time × number of workers at the resource – activity timeat the resource • Idle time for Kristen = • Idle time for Roommate = • Idle time without Roommate =

16. Today’s Takeaways • Little’s Law: I=RT • Labor Cost: labor content, labor utilization, labor idle time, direct labor costs

17. Summary: Classes 1-4 • Process view of operations: transform inputs into outputs. • Competitive advantage (cost, time, quality, variety) and operations management • Process types: • job shop, batch, discrete flow, continuous flow • MTS vs. MTO • Product-process matrix • Process flow diagram and Gantt chart • Operational measures • (actual) Flow Time (T) • Theoretical vs actual • Actual flow time =value-added + non-value-added = active + non-active • Critical path • Levers for improvement • Flow Rate (R): cycle time, capacity, bottleneck, utilization (r), implied utilization, machine or server idle time, levers for improvement, • Inventory (I) • Years (months, days,..) of supply = I/R = T • Turns = R/I • Pipeline principle: in the long run, on average, input flow rate = output flow rate • Little’s Law: I = RT • Direct labor cost ($/unit) = wages per unit time/throughput rate per unit time = wages per unit. • Labor utilization = labor content / (labor content + labor idle time)