Consider a process consisting of three resources

Operations Management

Process Fundamentals - Process Analysis Basics

Yuanjie He

Last lecture

• Describe a process

• Measure a process

• Little’s law

• Application of Little’s law to study inventory turnover

• Inventory types and Inventory holding cost

Three measures of process

• Flow unit

• If thinking the process as a black box, there are three essentials to know about a process

– Flow time: the time it takes a flow unit to get through the process

– Flow rate: the rate at which the process is delivering output (measured in flow units/unit of time)

• The maximum flow rate for a process is called capacity

• Resource Utilization = Flow rate / Capacity

• Resource Implied Utilization = Demand / Capacity

– Work in progress (WIP) / Inventory : number of flow units contained within the process

– Average inventory = Average flow rate x Average flow time

Process bottleneck, capacity and flow rate

• Resource capacity: maximum flow rate for a resource

• Process capacity = minimum of all resource capacities

• Now we can find out

– Flow rate = minimum{available input, demand, process capacity}

• Time to fulfill X units = X / flow rate – For example, in a ride in Disneyland, the flow rate is 50 people per 2

minutes (how to find out), how long will it take to serve 300 people who want to take the ride?

Process Fundamentals - Process Analysis Basics Example

Yuanjie He

Process with one flow unit • Q3.1 Consider a process consisting of three resources (bottleneck,

process capacity)

• Capacity of resource 1 = (60 minutes / 10 minutes ) * 2 workers = 12 units per hour

• Capacity of resource 2 = (60 minutes / 6 minutes ) * 1 worker = 10 units per hour

• Capacity of resource 3 = (60 minutes / 16 minutes) * 3 workers = 11.25 units per hour

• Capacity of the process = minimum {resource capacities} = minimum {12, 10, 11.25} = 10

• Bottle neck resource = resource 2

Resource Processing time (minutes/unit)

Number of workers

1 10 2

2 6 1

3 16 3

Process with one flow unit

• What is the flow time for a unit?

• What is the flow rate if demand is eight units per hour?

• What is the utilization of each resource if demand is eight units per hour?

• If demand is 12 units per hour, what is the utilization rate of each resource? What is the implied utilization rate for each resource?

• There is an order of 200 units products, assuming that there is no other work in the process now and the manager would like to know how long this work will take to finish. – If assuming maximum flow rate (process capacity)

– If assuming flow rate at 8 units per hour

Resource Processing time (minutes/unit)

Number of workers

1 10 2

2 6 1

3 16 3

Process with one flow unit • What is the flow time for a unit?

– 10+6+16 = 32 minutes

• What is the flow rate if demand is eight units per hour? – Because demand 8 units per hour is less than the process capacity, the actual flow

rate is minimum{available input, demand, process capacity} = minimum{assuming infinite input, 8, 10} = 8

• What is the utilization of each resource if demand is eight units per hour? – Utilization for resource 1 = flow rate / capacity of resource 1 = 8 units per hour / 12

units per hour = 66.67%

– Utilization for resource 2 = flow rate / capacity of resource 2 = 8 units per hour / 10 units per hour = 80%

– Utilization for resource 3 = flow rate / capacity of resource 3 = 8 units per hour / 11.25 units per hour = 71.11%

• There is an order of 200 units products, assuming that there is no other work in the process now and the manager would like to know how long this work will take to finish. – If assuming maximum flow rate (process capacity)

• Time to fulfill X units = X / flow rate = 200 units / 10 units per hour = 20 hours

– If assuming flow rate at 8 units per hour • Time to fulfill X units = X / flow rate = 200 units / 8 units per hour = 25 hours

Process Fundamentals - Process Analysis with different

types of flow units

Yuanjie He

Process with one flow unit • Q3.1 Consider a process consisting of three resources (bottleneck,

process capacity)

• Capacity of resource 1 = (60 minutes / 10 minutes ) * 2 workers = 12 units per hour

• Capacity of resource 2 = (60 minutes / 6 minutes ) * 1 worker = 10 units per hour

• Capacity of resource 3 = (60 minutes / 16 minutes) * 3 workers = 11.25 units per hour

• Capacity of the process = minimum {resource capacities} = minimum {12, 10, 11.25} = 10

• Bottle neck resource = resource 2

Resource Processing time (minutes/unit)

Number of workers

1 10 2

2 6 1

3 16 3

Process analysis with different types of flow units

Consulting Contact

faculty Contact prior

employers

Decision

letter

Staff

Internship Benchmark

grades

File

Define the common flow unit so that: 1) The capacity of each task can be expressed in terms of the “flow

unit” per unit of time. 2) Demand can be expressed in terms of the “flow unit”.

An intuitive and natural flow unit for this process is an “application”: 1) Given that an “application” is the flow unit . 2) The capacity of each task should be defined in terms of

“applications per unit time”. 3) Demand should be expressed in terms of “applications per unit

time”

Demand and capacity • Demand data (given to us):

• Staffing and processing time data (given to us) and capacity calculations:

Applications

per hour

Consulting 3

Staff 11

Internship 4

Workload (Applications/hour)

Processing Time (minutes

per application)

Number of

Workers

Capacity (applications

per hour) Consulting Staff Interns Total

Implied Utilization

File 3 1

Contact Faculty 20 2

Contact Employers 15 3

Benchmark Grades 8 2

Confirmation Letter 2 1

Demand and capacity • Demand data (given to us):

• Staffing and processing time data (given to us) and capacity calculations:

Applications

per hour

Consulting 3

Staff 11

Internship 4

Workload (Applications/hour)

Processing Time (minutes

per application)

Number of

Workers

Capacity (applications

per hour) Consulting Staff Interns Total

Implied Utilization

File 3 1 20 3 11 4 18 90%

Contact Faculty 20 2

Contact Employers 15 3

Benchmark Grades 8 2

Confirmation Letter 2 1

Defining a different flow unit – one minute of work • Define the flow unit to be “one minute of work”:

– Demands and capacity should then be expressed in terms of “minutes of work”.

• Consider the “Contact employers” task:

– Demand on this task is 14 applications per hour.

– Each application requires 15 minutes of work.

– So demand on this task each hour is 14 x 15 = 210 minutes of work

Workload (Minutes/hour)

Processing Time (minutes

per application)

Number of

Workers

Capacity (minutes per

hour) Consulting Staff Interns Total

Implied Utilization

File 3 1 60 3*3 11*3 4*3 54 90%

Contact Faculty 20 2

Contact Employers 15 3

Benchmark Grades 8 2

Confirmation Letter 2 1

• Defining the flow unit as “one minute of work” yields the same implied utilizations as defining the flow unit as “one application”.

• In other words, the implied utilization does not depend on how the flow unit is defined as long as all demands and capacities are defined with the same flow unit.