OM Week 3

Parallelization Formula

Combined Capacity = Capacity 1 + Capacity 2 + … + Capacity N

For parallel resources add [BLANK]

1. Cycle Times

2. Output Rates

Step-by-step Parallelization Method

1. Express each parallelized resource as output rates (same time basis)

2. Add the output rates

3. Convert to cycle time

Every operations decision ultimately comes down to

How does this affect our profit?

In the short run Labor is a [BLANK] cost and in the long run it is a [BLANK] cost

1. Fixed/Variable

2. Fixed\/Variable

PBIT Formula

PBIT = (p-v) x Q - FC = CM x Q - FC

• p =

• v =

• FC =

• Q =

• Price

• Variable cost

• Fixed costs

• Flow rate/Volume

Break-Even Volume Formula

Q* = FC/CM = FC/p - v

• The minimum volume at which we do not lose money

• Each unit sold contributes CM = p - v toward fixed costs

• We need enough units to “fill the FC hole”

• Number of units needed: Q* = FC/CM

Below Q means we are at [BLANK]

1. Loss

2. Breakeven

3. Proft

Loss

At Q means we are at [BLANK]

1. Loss

2. Breakeven

3. Proft

Break-even

Above Q means we are at [BLANK]

1. Loss

2. Breakeven

3. Proft

Profit

Where on this graph are we at a Loss, Break-even, and Profit

Loss

• Under the dark red line but above the light red line

Breakeven

• Where the two lines intersect

Profit

• Under the light red line but above the dark red line

Cost reductions [BLANK 1] for FC, and [BLANK 2] for VC

1. help 1:1/are multiplied by volume

2. help 1:1/are multiplied by volume

1. help 1:1

2. are multiplied by volume

When does Parallelization make financial sense?

If additional units exceed Wage/Contribution Margin

Break-Even Condition for Parallelization Formula

Change in Q > w/CM

• Change in Q = additional units/hr after adding worker

• Additional revenue: change in Q x p

• Variable Cost: change in Q x v

• Labor: w

What are the two questions we must ask ourselves before adding a worker (Parallelizing)?

1. Are we capacity constrained (If not, don’t add)

2. Will we gain enough units to cover the wage?

• Change in Q > w/CM

What is the significance of queues?

Understanding queues lets you predict and manage how long things take and how much stuff piles up

• Affects both customer experience and your costs

When arrival rate > service rate the system is [BLANK]

• Stable/Unstable

Unstable

What are the three perspectives on why queues matter?

1. Customer experience

• Longer waits = frustrated customers = lost business

1. Inventory costs money

• Every item “in the system” ties up capital

1. Operational planning

• How much space do we need for WIP?

• How many orders are “in progress” right now?

• When will the last patient be done today?

Little’s law Formula

I = R x T

• I = Average Inventory (work in process)

• R = Flow Rate (throughput)

• T = Flow Time (throughput time)

Little’s Law holds true for what type of processes?

Stable

How must the average input rate compare to the average output rate in order for a system to be stable?

They must equal each other

If Demand > Capacity

• Queue grows infinitely

• System is unstable

• Little’s Law applies with R = Capacity

If Capacity > Demand

• No growing queues

• system is stable

• Little’s Law applies with R = Demand

What is the practical rule for stable systems?

use R = min(Demand, Capacity) = actual flow rate though the system

• Assumes excess demand is lost/turned away, so arrivals = departures at steady state

What are the three forms of Little’s law?

What do they all intuitively mean?

Which unknown must you solve for?

1. I = R x T, solve for Inventory, “How much WIP should I expect?”

2. T = I/R, solve for Flow Time, “How long until an order is done?”

3. R = I/T, solve for Flow Rate, “What’s our actual throughput?”

Inventory Turns Formula

Turns = 1/T = R/I = COGS/Average Inventory

Inventory Turns

How many times per year we “turn over” our inventory

Why are higher inventory turns better (3 reasons)?

1. Less capital tied up in inventory

2. Fresher products (important for food, tech)

3. Lower holding costs

Days of Inventory Formula

Days of Inventory = T = 365/Annual Turns

Days of Inventory

How many days worth of inventory we hold on average

How is Days of Inventory connected to Little’s Law?

Days of Inventory is just Flow Time (T) expressed in days

• T = I/R = Avg Inventory/Daily COGS = Days of Inventory