Process Analysis & Little's Law

Process Analysis

• Organizations function as collections of processes.
• A "black box" analogy describes how an organization takes inputs and turns them into outputs.
• Process Analysis First Step: defining a flow unit.
• Process Analysis Second Step: defining measures to analyze the process.

Performance Measures

• Inventory refers to units of flow contained within a process.
• Flow time represents the total time it takes for a flow unit to traverse the entire process.
• Flow rate indicates the rate at which a process delivers output.
• Little's Law: I = R x T, where I is Inventory, R is Flow Rate, and T is Flow Time.

Little's Law Applications: In-Transit Inventory

• O'Neill, based in California, procures wetsuits from a supplier in Thailand.
• They order an average of 15,000 wetsuits each month (R = 15,000/month).
• Shipping from Thailand to California averages 2 months (T = 2 months).
• The in-transit inventory averages 30,000 units (I = R x T = 15,000 * 2).

Little's Law Applications: Wait Time

• From 9 a.m. to 10 a.m., 200 passengers checked in baggage.
• An average of 40 passengers were waiting in the check-in line.
• The wait time is calculated as T = I / R = 40 passengers / 200 passengers per hour.
• The average passenger waited 0.2 hours, equivalent to 12 minutes (0.2 hours * 60 minutes/hour).

Little's Law Applications: Service Rate

• A Starbucks store has 10 people waiting in line to order around 7 a.m.
• Each customer stays in the store for approximately 4 minutes before leaving.
• The Starbucks serves R = I / T = 10 customers / 4 minutes = 2.5 customers per minute.
• The Starbucks serves 150 customers per hour (2.5 customers/minute * 60 minutes/hour).

Little's Law Applications: Production Process

• Stroehmann is developing a new production process packaged for bread.
• It takes 12 minutes to bake the bread.
• Annually, the company produces 4,000 units of bread per hour.
• To determine how large the should be: T = 12 minutes, R = 4,000 units / hour
• Oven size should be I = R × T = 4,000 units / hour × 0.2 hour = 800 units

Little's Law Applications: Converting Units

• Stroehmann is developing a new production process for their packaged bread.
• It takes 12 minutes to bake the bread.
• The company produces 45,000 units of bread per day.
• The factory runs for 15 hours a day.
• To determine how large the should be: T = 12 minutes, R = 45,000 units / day
• Oven size should be I = R × T = 50 units / minute × 12 minutes = 600 units

Measuring Inventory

• There four ways to count inventory
• There is an inventory cost
• There are five reasons to hold inventories

Ways to Count Inventory

• In terms of flow units: Number of wetsuits, patients, tons of wheat, semiconductor chips, etc, which is useful when the focus is on one particular flow unit.
• In terms of $: Measuring the dollar value of inventory with COGS as the unit of flow in terms of time.
• In terms of days-of-supply: The average number of days a unit spends in the system, which determines the days before inventory runs out at the average flow rate if no replenishments arrive.
• In terms of turns: Shows the number of times the average amount of inventory exits the system.

Inventory Cost Calculations

• Per Unit Inventory Cost (%) = Annual Inventory Cost (%) / Annual Inventory Turns.
• Per Unit Inventory Cost ($) = Annual Inventory Cost (%) / Annual Inventory Turns x (Purchase Cost).
• Assuming annual holding costs of 20% annually, Apple has an inventory turn of 53.18 times per year and the cost is 0.37%.
• Assuming annual holding costs of 20% annually, Smasung has an inventory turn of 7.15 times per year and the cost is 2.79%.

Inventory Measurement Example 2013: Apple vs Sumsung

• Apple: In 2013 Cost of Sales was 112258, Inventory was 2111, FLow time in days was 6.8638, and inventory turns was 53.18.
• Samsung: In 2013 Cost of Sales was 136755644, Inventory was 19134868, FLow time in days was 51.0708, and inventory turns was 7.15.
• Apple Flow Rate = 112258 $/year.
• Apple Days of Supply = 2111/112258 = 0.0188 (years) = 0.0188*365 = 6.86 (days).
• Apple Yearly Inventory Turns = 1/Flow Time (T) =1/0.0188(years) = 53.18.
• Samsung Flow Rate = 136756 wons/year.
• Samsung Days of Supply = 19135/136756 = 0.139 (years) = 0.139*365 = 51.07 (days).
• Samsung Yearly Inventory Turns = 1/Flow Time (T) =1/0.139(years) = 7.15.

Inventory Costs: Example

• Walmart had annual inventory costs of 30%.
• A TV's price tag of $300.
• The TV is procured by the retailer for $200.
• Revenue 2010: $ 405,046
• Cost of goods sold 2010: $ 297,500
• Inventory 2010: $ 33,160
• Net Income 2010: $ 14,335
• Inventory = $33,160
• Flow rate = COGS = $297,500
• Flow time = $33,160/$297,500 = 0.111[year] = 40.68[days]
• Inventory turn =1/ 0.111 [year] = 9
• Per unit Inventory Cost= 30%/ 9 = 3.33%
• Inventory cost for each TV = 3.33% * $200 = $6.667

Practice Problems (Q2.9)

• Costco Inventories 2004: $ 3,643, Sales (net) 2004: $ 48,106, and Cost of Goods Sold 2004: $ 41,651.
• Walmart Inventories 2004: $ 29,447, Sales (net) 2004: $ 286,103, and Cost of Goods Sold 2004: $ 215,493.
• Average annual holding cost for both companies is 30% per year.
• How many days, on average, does a product stay in Costco's inventory before it is sold? Store are open 365 days a year.
  • Inventory (1): $3,643, Flow Rate (2): $41,651 / year, Flow Time= $3,643 / $41,651 / year * 365 days/year = 31.9 days
• How much lower is, on average,is the inventory cost is, the inventory cost for Costco compared to Walmart of a household cleaner valued at $5?
  • Per unit Inventory cost = Annual Inventory Costs / Annual Inventory Turns
• Costco
  • 365days / 31.9 days = 11.44
  • (30% / 11.4) * $5 = 0.131
• Walmart
  • $215,493 / $29,447 =7.32
• 30% / 7.32 = 4.09%
• 4.09% × $5 = $0.205
• $0.205 - $0.131 = $0.074
• Annual Inventory Turns = Annual Inventory Costs / Annual Inventory Turns

Practice Problems (Q2.4)

• A retailer of fashion apparel reported $100,000,000 in revenues over last year.
• On average, the company had $5,000,000 worth of inventory in their warehouses.
• Units of inventory are valued based on COGS
• The retailer has 100% markup on all products
• How many times each year does the retailer turn its inventory?
  • Sales = $100,000,000 and Markup = 100%, Flow rate = COGS = $50,000,000 / year
• Inventory = $5,000,000
• Inventory/Flow rate = $5,000,000 / ($50,000,000/year) = 0.1 [year] = 36.5 [days]
• 1/ Flow Time = 1 / 0.1 = 10
• The company uses a 40% per year cost of inventory. What is the inventory cost for a $30 (COGS) item?
  • Annual inventory costs / Inventory turns = 40% /10 = 4%
  • 4% × $30 = $1.2

Process Flow Analysis

• Involves process flow diagrams for mapping out process steps.
• Examines the activity times and capacity of a single stage process.
• Evaluates the capacity of the entire process to identify constraints.
• Determines the flow rate or process throughput, which can be demand or capacity constrained.

Utilization

• Refers to the extent to which a resource is being used, comparing actual production to potential output
• Calculation: Actual Production / Potential Production
• Utilization cannot exceed 100%.
• Resources with utilization less than 100% means excess capacity exists.
• The bottleneck has the highest utilization.
• In demand constrained processes, the bottleneck resource will have bottleneck resource < 100%
• In capacity constrained processes, the bottleneck resource will have bottleneck resource = 100%
• Utilization only indicates information about excess capacity without revealing the extent by which demand exceeds capacity.

Facts about Implied Utilization

• Implied Utilization can exceed 100%
• Implied Utilization Bottleneck resource has the highest utilization
• In a demand constrained process, implied utilization of the bottleneck resource will be < 100%
• In a capacity constrained process, the bottleneck resource will be > 100%
• There can be multiple resources with implied utilization greater than 100%

Splitting Flow: Example

• There are 10 patients coming to an emergency room every hour.
• Activity/Time: 2 Triage nurse for 10 min, 3 Doctors for 50 min, 4 Nurses for 40 min, and 1 Checkout desk for 5 min.
• Capacity Calculation:
  • Triage: (2 x 60 = 120 [working time/time])
  • Doctor: (3 x 60 = 180 [working time/time])
• Nurse:(4 x 60 = 240 [working time/time])
• Desk: (1 x 60 = 60 [working time/time])
• Demand for each activity:
  • Triage nurse (10 [patients/hr] x 10 =100 [min/hr])
  • Doctor (10 * 2.5 * 50 = 125)
  • Nurse (10 [patients/hr] x 7.5 x 40 = 300 [working time/time])
  • Desk 10 x 5
• Utilization for each resource:
• nurse for 125%
• the rest about or under 83%
• the capacity of the process is 8 patients

One More Example

• The magnetic resonance unit recieves average patients/hours who are 80% regular and 20% contrast. What is the implieid utilization and capcity.
• 25 * 0.8 [regular]*15[min/regular] = 3
• 25 * 0.2 * 25 = 125
• MRI: 2 resources, 2 * 60 * 8 of capacity, an implieid 44,27 %
• Capacity will be 56

EOQ Example

• Determine appropriate time horizon, then Flow Rate, the Ordering Cost, then Holding Cost..
• Determine EOQ, where Q= √ 2K*R / H
• Determine Total Cost, ( √2KR*H)

Quantity Discounts: Example - Babies R US

Determine appropriate time horizon, then Flow Rate, the Ordering Cost, then Holding Cost..

• Determine EOQ, where Q= √ 2K*R / H
• Determine Total Cost, where KR/(Q)+(QH)/2
• Performance: orders = R/Q Length= dayd/(R/Q)

Quantity Discounts Example continued- Babies R US

• In the event where Q is less than 10k, can replace it with 10k to see if it should be replaced.
• Look at initial purchasing cost versus discounted price