1. IV. Little’s Law and Labor Costs
Operational Measure: Inventory
Little’s Law
Direct labor cost
Articles:
Can Marketing and Manufacturing Coexist? – HBR
Competing on Capabilities: The New Rules of Corporate Strategy – HBR

2. Why is there inventory? Why is there inventory?
Imagine taking a walk through a factory at night. You would probably find inventories at various locations in the factory. Easy to identify which ones are RM, WIP and FGs. In the same spirit, we might walk through a hospital and find patients, some just arrived, others undergoing surgery, and others are likely to be discharged the coming day. Taking such a single walk through the processes, will not leave us with a good understanding of the underlying operations, just a snapshot of how the process look like at one single moment in time. Unfortunately, it is this same snapshot approach that underlies most management (accounting) reports: balance sheets itemize inventory into 3 categories. Hospital administrators typically distinguish btw pre- and post-operative patients. They fall short of telling us WHY these inventories exist in the first place. Thus, a static, snapshot approach, neither helps us to analyze business processes (why is there inventory?), nor does it help us improve them (is this the right amount of inventory?)
Now, imagine we would be willing to stay for some longer period of time. We arrive early on our first day and take a count of the patients in the unit (8). From then onwards, we take a more comfortable position outside of the unit, recording any patient inflow and outflow. At the end of our stay, we plot a graph.
The vertical distance corresponds to the inventory level. Although we have been outside, we are able to keep track the inventory level by comparing the cumulative inflow and outflow.
If the patients leave the surgery unit in the same order they entered it, the horizontal gap would measure the exact amount of time each patient spent therein. Otherwise, this gap provides the average length of stay.
The slop of the two graphs: flow rate.

3. Patient Log Flow rate = 11 patients/day = 1/hr
Inventory: patients
Flow time: hrs.
From the graph or the patient log, the flow rate was 11/day.
Invnetory fluctuates throughout the day, reflecting the differences btw inflow and outflow of patients. A brute force approach to compute average inventory is to count the inventory at every moment in time throughout the day, say every 5 minutes, and then take the average (or do the integral). It yields
Flow time: 2:04:33 = hours.

4. Throughput Rate R [units/unit time]
Little’s Law
Inventory
I [units]
Throughput Rate R [units/unit time]
...
Flow Time T [unit time]
Little’s Law:
Years (days, weeks, months) of Supply:
Rate of flow into a system is usually not equal to the rate of flow out of the system at time t.
Inventory is often times described as years of supplier. If you keep 60 units of inventory and demand is 30 units per month, then you are stocking 2 months worth of inventory. Low inventory means fewer months of supplier. Firms in the automobile industry carry about two months’ supply of finished goods. Ford has the lowest target level among the big three.
Anyone heard of turnover ratio? The same example, a unit on average stays in the system for T = 2 months and your inventory turns over once every two months, or 6 times per year or 1/T = R/I = 0.5 times per month. Turnover rate the Faster the better. Faster return on investment (all assets). Smaller investment to generate the same sales. To avoid obsolescence. Sometimes, more inventory is better, especially when the value of the inv increases or under high inflation. Inv turns vary from industry to industry. Although 6 or 7 turns per year is typical, the average high tech firm settles down for only 3 turns. At the other extreme, some automobile firms report 40 turns per years for selected products. Wal-Mart retail stores twice a week (industry average once every two weeks).
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 Tw Im = Rm * Tm = 150 Tm Tw = 1.5 Tm
If you want to find out how long customers at a fast-food restaurant – on average – spend in line waiting for their food, you could do the following:
Observe the queue at a couple of random points during the day, giving you an average inventory. Say I = 7 customers.
Look in the cash register to see how many customers have received service on that day, giving you the average flow rate. Say there were 600 customers over a period of 8 hours, yielding a R = 75/hr.
Use little’s law. T = I/R = hrs = 5.6 minutes.

8. Waiting time at a fast-food restaurant
Implications for managing costs and growth: Aim for the same or better throughput with lower inv and flow time. Identify what causes inv or FT to grow. Little’s Law is a diagnostic tool, not a prescription tool (describe what is happening, not what to do).

9. Inventory Value Profiles: Wal-Mart vs. K-Mart
For Wal-Mart, go to
Click SEC Filings and look for 10-K for Income Statement (annual Sales and COS), and Q-10 for Quarterly Balance Sheet (cash, receivable and inventory)
For K-Mart, go to and choose Most Recent Operating Report. Choose 10-k and Q-10. For Q-10, click Document 1: Quarterly Report.
For Wal-Mart:
R ($/wk)
I ($)
T = I/R (wks)
Turns per wk = 1/T
Cash
4, (sales)
1,911.8
0.46
2.19
Receivables
1,789.8
0.43
2.34
Inventory
3, (CGS)
23,474
7.12
0.14

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
Worker 1
Worker 2
Worker 3
Total
Activity time (min/unit)
Capacity (units/hr)
Cycle time (min/unit)
Flow rate = capacity
Idle time (min/unit)
Direct labor cost
($/unit)
Labor utilization
Flow rate = 3.57/hr

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 time at the resource
Idle time for Kristen =
Idle time for Roommate =
Idle time without Roommate =
Labor content reflects how much labor is invested into the production of one unit. We could visualize this measure as follows. There would be a lip of paper attached to a product and each worker would write the amount of time she spent working on the product on this slip. The sum of all numbers entered on the slip is the labor content.

16. Today’s Takeaways Little’s Law: I=RT
Labor Cost: labor content, labor utilization, labor idle time, direct labor costs
Articles:
Can Marketing and Manufacturing Coexist? – HBR
Competing on Capabilities: The New Rules of Corporate Strategy – HBR

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)