OM Week 10

Crash Limit

The maximum number of days you can shorten it

Each extra day of speedup has a

Cost per day

Crashing

Spending extra to shorten an activity

• Overtime crews, rush fees, expedited delivery, temporary staff

4 Steps of The Crashing Decision

1. Filter to critical path activities only: Only these determine the project duration. Crashing anything else just adds slack that nobody needs

2. Filter to activities with remaining crash capacity: If an activity is already at its minimum duration, skip it

3. Among what is left, pick the cheapest per day: You are buying time → buy it at the lowest price

4. Recompute all path lengths: The critical path may have changed → go back to step 1

2 Main Components of The Variable World

1. Uneven arrivals

2. Uneven Processing Times

Average Capacity > Average Demand is necessary for stability but variability

Can still create queues

Queues form because capacity supply and demand arrivals

Do not line up perfectly in time

Variability creates [BLANK 1] mismatches

High Utilization makes those mismatches [BLANK 2]

1. Temporary

2. Painful

Basic Process Analysis says

“No Waiting”

Demand Rate Formula

1/a

• a is min/email

Process Capacity Formula

m/p

• each employee does 1/p per min; m employees in parallel

Flow Rate Formula

min(1/a, m/p)

• Limited by the tighter constraint

When does the model predict no waiting?

What is a flaw of this prediction?

• When Capacity > Demand

• Ignores how much arrivals and service times bounce around averages

What do the following stand for:

• Iq

• I

• Ip

• Average Inventory in queue

• Average Inventory in system

• Average Inventory in processing

What are the 5 assumptions of queueing formulas?

1. No balking or abandoning

2. Single waiting line with ample space

3. m >= 1 servers

4. Random but stable arrival and processing patterns

5. Must have u < 1

What are the three supporting formulas or the queueing formulas?

1. u = p/am

2. CVa = oa/a

3. CVp = op/p

Approximate Waiting-Time Formula

What does each component of the waiting time formula stand for?

• p/m = processing time factor

• u(SQRT(2(m+1))) - 1/1 - u = utilization factor

• CVa² + CVp² /2 = variability factor

Waiting gets worse when (3 points)

• Jobs take longer

• Servers are busier

• Arrivals/Service are more variable

What do the coefficients of variation tell us (3 points)?

• Arrivals are very vary variable

• processing times are variable but less so

• Demand-side randomness is the bigger issue here

Variability mainly creates

Waiting inventory

What stays the same when we move from Basic Process Analysis (No Randomness) to adding Variability (3 points)?

• Average processing time

• Average flow rate

• Average number being actively worked on

What changes when we move from Basic Process Analysis (No Randomness) to adding Variability (3 points)?

• Waiting time

• Queue length

• Total Flow Time

Adding labor units reduces waiting but raises

Direct Labor cost per unit of output

• Core economic tradeoff

In variable systems, the first bit of extra capacity is often the [BLANK] variable

• Most/Least

Most

variability creates waiting lines by

Causing temporary mismatches between demand and capacity

The approximate queueing formula says waits rise with (3 points)

• Processing time

• Utilization

• Variability