Chapter 2: The Process View of an Organization

“continuous or semi-continuous”

“intermittent”

Process Structures

Continuous ProcessingRepetitive (assembly lines)Batch processingJob Shops

Job Shop

Batch Process

Worker-paced line

Machine-paced line

Continuous process

Low Volume(unique)

Medium Volume(high variety)

High Volume(lower variety)

Very high volume(standardized)

Utilization of fixed capitalgenerally too low

Unit variable costsgenerally too high

CABG Surgery

Exec. Shirt

Toshiba

Toyota

NationalCranberry

Manzana Insurance

• Categorizes processes into one of five clusters• Similar processes tend to have similar problems• There exists a long-term drift from the upper left to the lower right

The Product-Process Matrix

Exercise

Form a group of 2-3 students

From your experience/observation, select a product

produced for each of these processing models: Job shop

Batch processing

Assembly line

Continuous processing

Share results with the class

Three Measures of Process Performance

Inventory (WIP in a process) Flow time

Time it takes a unit to get through the process Flow rate (throughput rate)

Rate at which the process is delivering outputMaximum rate that a process can generate

supply is called the capacity of the process

InputsOutputs

Goods

Services

Resources Labor & Capital

Process

Goods

Services

Resources Labor & Capital

Flow units(raw material, customers)

First choose an appropriate flow

Unit – a customer, a car, a

scooter, etc.

Example

Topic Flow Unit Flow Rate Flow Time Inventory

U.S. Immigration ApplicationsApproved/rejected cases

(6.3 MM/year)

Average processing time (7.6 months)

Pending cases (4.0 MM)

Champagne Industry

Bottles of Champagne 260 MM bottles per year

3.46 years in cellar 900 Million bottles

MBA Program MBA Student 600 students/year 2 years 1200 students

Muhlenberg College

Outback Steak House

What it is: Inventory (I) = Flow Rate (R) * Flow Time (T)

Implications:• Out of the three performance measures (I,R,T), two can be chosen by management, the other is GIVEN by nature• Hold throughput (flow rate) constant: Reducing inventory = reducing flow time

Little’s Law

7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

11

10

9

8

7

6

5

4

3

2

1

0

Flow Time

Inventory

Inventory=Cumulative Inflow – Cumulative Outflow

Cumulative Inflow

Cumulative Outflow

Time

Patients

Examples Suppose that from 12 to 1 p.m.

200 students per hour enter the GQ and each student is in the system for an average of 45 minutes. What is the average number of students in the GQ? Inventory = Flow Rate * Flow Time = 200 per hour * 45 minutes (=

0.75 hours) = 150 students

If ten students on average are waiting in line for sandwiches and each is in line for five minutes, on average, how many students are arrive each hour for sandwiches? Flow Rate = Inventory / Flow Time

= 10 Students / 5 minutes = 0.083 hour

= 120 students per hour

Problem 2.2: Airline check-in data indicate from 9 to 10 a.m. 255 passengers checked in. Moreover, based on the number waiting in line, airport management found that on average, 35 people were waiting to check in. How long did the average passenger have to wait?

Flow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = 0.137 hours

= 8.24 minutes

Queuing Theory

Waiting occurs in

Service facility Fast-food restaurants post office grocery store bank

Manufacturing

Equipment awaiting repair

Phone or computer network

Product orders

Why is there waiting?

Measures of System Performance

Average number of customers waitingIn the queue (Lq)In the system (L)

Average time customers waitIn the queue (Wq)In the system (W)

System utilization ()

Number of ServersSingle Server . . .

Customers ServiceCenter

Multiple Servers

. . .

Customers

ServiceCenters

Multiple Single Servers

. . .

. . .

. . .

Customers ServiceCenters

Some Models

1. Single server, exponential service time (M/M/1)

2. Multiple servers, exponential service time (M/M/s)

A TaxonomyM / M / s

Poisson Arrival Exponential Number ofDistribution Service Dist Servers

whereM = exponential distribution (“Markovian”)(Both Poisson and Exponential are Markovian – hence the “M” notation)

Given

= customer arrival rate = service rate (1/m = average service time)s = number of servers

Calculate

Lq = average number of customers in the queue

L = average number of customers in the system

Wq = average waiting time in the queue

W = average waiting time (including service)

Pn = probability of having n customers in the system

= system utilization

Note regarding Little’s Law: L = * W and Lq = * Wq

Model 1: M/M/1 Example

The reference desk at a library receives request for assistance at an average rate of 10 per hour (Poisson distribution). There is only one librarian at the reference desk, and he can serve customers in an average of 5 minutes (exponential distribution). What are the measures of performance for this system? How much would the waiting time decrease if another server were added?

M/M/s Queueing Model Template

Data 10 (mean arrival rate) 12 (mean service rate)s = 1 (# servers)

Prob(W > t) = 0.135335when t = 1

Prob(Wq > t) = 0.112779

0 when t = 1

ResultsL = 5 Number of customers in the system

Lq = 4.166666667 Number of customers in the queue

W = 0.5 Waiting time in the systemWq = 0.416666667 Waiting time in the queue

0.833333333 Utilization

P0 = 0.166666667 Prob zero customers in the system

Example: One Fast Server or Many Slow Servers?

Beefy Burgers is considering changing the way that they serve

customers. For most of the day (all but their lunch hour), they

have three registers open. Customers arrive at an average

rate of 50 per hour. Each cashier takes the customer’s order,

collects the money, and then gets the burgers and pours the

drinks. This takes an average of 3 minutes per customer

(exponential distribution). They are considering having just

one cash register. While one person takes the order and

collects the money, another will pour the drinks and another

will get the burgers. The three together think they can serve a

customer in an average of 1 minute. Should they switch to one

register?

3 Slow Servers

1 Fast Server

W is less for one fast server, so choose this option.

Data 50 (mean arrival rate) 20 (mean service rate) Resultss = 3 (# servers) L = 6.011235955 Number of customers in the system

Lq = 3.511235955 Number of customers in the queue

Prob(W > t) = 6.38E-05when t = 1 W = 0.120224719 Waiting time in the system

Wq = 0.070224719 Waiting time in the queueProb(Wq > t) = 4.34E-05

0 when t = 1 0.833333333 Utilization

P0 = 0.04494382 Prob zero customers in the system

Data 50 (mean arrival rate) 60 (mean service rate) Resultss = 1 (# servers) L = 5 Number of customers in the system

Lq = 4.166666667 Number of customers in the queue

Prob(W > t) = 4.54E-05when t = 1 W = 0.1 Waiting time in the system

Wq = 0.083333333 Waiting time in the queueProb(Wq > t) = 3.78E-05

0 when t = 1 0.833333333 Utilization

P0 = 0.166666667 Prob zero customers in the system

Application of Queuing Theory

We can use the results from queuing theory to make the following types of decisions:

How many servers to employ

Whether to use one fast server or a number of slower servers

Whether to have general purpose or faster specific serversGoal: Minimize total cost = cost of servers + cost of waiting

Cost ofService Capacity

Cost of customerswaiting

Total Cost

OptimumService Capacity

Cost

Cost/Benefit Analysis

Cost of service: # Servers *

Cost of each server

Service cost = s * Cs

Cost of Waiting: Cost of

waiting * Time waiting *

number of customers/time unit

Waiting Cost = * Cw * W

If you save more in waiting

than you spend in service,

make the change

Example A fast food restaurant has

three servers, each earning $10 per hour. Fifty customers per hour arrive and a server can serve a customer in three minutes. Should the restaurant add a fourth server if the cost of a customer waiting is estimated at $20 per hour?

Answer

Current Proposed Diff erence

Service Cost 30.00$ 40.00$ 10.00$

Waiting Cost 120.22$ 60.66$ (59.56)$

Example: Southern RailroadThe Southern Railroad Company has been subcontracting for painting

of its railroad cars as needed. Management has decided the company might save money by doing the work itself. They are considering two alternatives. Alternative 1 is to provide two paint shops, where painting is to be done by hand (one car at a time in each shop) for a total hourly cost of $70. The painting time for a car would be 6 hours on average (assume an exponential painting distribution) to paint one car. Alternative 2 is to provide one spray shop at a cost of $175 per hour. Cars would be painted one at a time and it would take three hours on average (assume an exponential painting distribution) to paint one car. For each alternative, cars arrive randomly at a rate of one every 5 hours. The cost of idle time per car is $150 per hour.

Estimate the average waiting time in the system saved by alternative 2.

What is the expected total cost per hour for each alternative? Which is the least expensive?Answer: Alt 2 saves 1.87 hours. Cost of Alt 1 is: $421.25 / hour and cost of Alt 2 is $400.00 /hour.

Answer: Alt 2 saves 1.87 hours. Cost of Alt 1 is: $421.25 / hour and cost of Alt 2 is $400.00 /hour.

Calculating Inventory Turns & Per Unit Inventory Costs

Obtaining dataLook up inventory value on the balance sheetLook up cost of goods sold (COGS) from earnings

statement – not sales!! Common benchmark is inventory turns

Inventory Turns = COGS/ Inventory Value Compute per unit inventory costs:

Per unit inventory costs =

Annual inventory costs (as a % of item cost) / Inventory turns

Annual inventory costs (as a % of item value) include

financing costs, depreciation, obsolescence, storage,

handling, theft

Example

Problem 2.3: A manufacturing company producing medical devices reported $60 million in sales last year. At the end of the year, they had $20 million worth of inventory in ready-to ship devices.

Assuming that units are valued at $1000 per unit and sold at $2000 per unit, what is the turnover rate?

Assume the company uses a 25% per year cost of inventory. What is the inventory cost for a $1000 (COGS) item. Assume that inventory turns are independent of price.

Answer

Sales = $60,000,000 per year / $2000 per unit = 30,000 units sold per year @ $1000 COGS per unit

Inventory = $20,000,000 / $1000 per unit = 20,000 units in inventory

Turns = COGS/Inventory =

$30,000,000/$20,000,000 = 1.5 turns

Cost of Inventory: For a $1000 product, the total inventory cost (for one turn) is $1000* 25% or $250. This divided by 1.5 turns gives an absolute inventory cost of $166.66.

Why Hold Inventory?

Pipeline inventory

Seasonal InventoryTime

CumulativeNumber of patients

1.5 Patients

7:00 8:00 9:00 10:00

1.5 hours

11:00 12:00

7

6

5

4

3

2

1

0

200

400

600

800

1000

1200

1400

Time

Tons of Beets

Inventory

Total Beets Received(In 000’s)

Total Beets Processed

Figure 2.10: Seasonal inventory - Sugar

End of Harvest0

200

400

600

800

1000

1200

1400

Time

Tons of Beets

Inventory

Total Beets Received(In 000’s)

Total Beets Processed

Figure 2.10: Seasonal inventory - Sugar

End of Harvest

Why Hold Inventory?

Cycle Inventory Decoupling inventory/Buffers Safety Inventory

0

200

400

600

800

1000

1200

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Cumulative Inflow and outflow

Days of the month

Figure 2.12: Safety inventory at a blood bank

Safety inventory

Cumulativeinflow

Cumulativeoutflow

Inventory Turnover Statistics

Retail

Hardware stores: 3.5

Retail Nurseries & Garden Supply: 3.3

General Merchandise Stores: 4.7

Grocery Stores: 12.7

New & Used Car Dealers: 6.8

Gas stations & mini-marts: 39.3

Apparel & Accessories: 3.5

Furniture & home furnishings: 4.1

Drug Stores: 5.3

Liquor Stores: 6.6

Other Retail Stores: 4.3

Wholesale

Groceries & related: 17.8

Vehicles & automotive: 6.9

Furniture & fixtures: 5.5

Sporting goods: 4.8

Drug store items: 8.5

Apparel & related: 5.5

Petroleum & related: 42.4

Alcoholic beverages: 8.5

Source: Bizstats.comSource: Bizstats.com

Industries with higher gross margins tend to have lower inventory

turns