Law Part 2: Little's Law Applications - Purdue Example & Inventory Turns

Little's Law Refresher\n\n* Little's Law applies under specific conditions:\n * The system must be in a steady state.\n * It must be a demand-constrained process.\n * The flow rate must be equal to the demand rate.\n* The law states that: WIP (Work-In-Process)=Flow Time×Flow Rate\text{WIP (Work-In-Process)} = \text{Flow Time} \times \text{Flow Rate}\n * WIP refers to the average amount of inventory in the system.\n * Flow time is the average time for a unit to pass through the process.\n * Flow rate is the average rate at which units pass through the process.\n\n## Purdue University Process Example Revisited\n\n* Scenario: Given class size (flow rate) and average graduation time (flow time) for Purdue University students. Additionally, each student spends $5,000\$5,000 annually at local businesses.\n* Question: What is Purdue students' total annual spending at local businesses?\n* Given Process Measures:\n * Flow Rate: Class size (e.g., 8,0568,056 students per year, if that's the inflow rate).\n * Flow Time: Average graduation time (e.g., 44 years).\n* Calculating Total Spending:\n * The annual spending is determined by the spending per student per year multiplied by the number of students currently in the process (i.e., not yet graduated).\n * The number of students in the process corresponds to WIP (Work-In-Process).\n * Step 1: Calculate WIP using Little's Law.\n * WIP=Flow Time×Flow Rate\text{WIP} = \text{Flow Time} \times \text{Flow Rate}\n * Using the example numbers: WIP=4 years×8,056 students/year=32,224 students\text{WIP} = 4 \text{ years} \times 8,056 \text{ students/year} = 32,224 \text{ students}\n * Step 2: Calculate Total Annual Spending.\n * Total Annual Spending=Spending per student per year×WIP\text{Total Annual Spending} = \text{Spending per student per year} \times \text{WIP}\n * Total Annual Spending=$5,000/student/year×32,224 students=$161,120,000\text{Total Annual Spending} = \$5,000/\text{student/year} \times 32,224 \text{ students} = \$161,120,000 \n\n## Inventory Turns: An Important Application of Little's Law\n\n* Operational Cost Significance: Inventory constitutes a large proportion of operational costs for many companies (e.g., a manufacturer with $65,000\$65,000 in inventory).\n* Purpose of Inventory Turns: It's a useful measure to benchmark and compare inventory efficiency between companies.\n* Definition: Inventory Turns is the number of times that inventory is sold or used within a year.\n* Interpretation:\n * Frequent inventory turns indicates that inventory is kept for a short time before being sold or leaving the process.\n * This implies efficient inventory management and less capital tied up in stock.\n* Conceptual Formula: Inventory Turns is the reciprocal of the average time it takes to sell inventory.\n * Inventory Turns=1Average time to sell inventory\text{Inventory Turns} = \frac{1}{\text{Average time to sell inventory}}\n * The "average time to sell inventory" corresponds directly to the Flow Time of the inventory through the system.\n* Example: If it takes, on average, 0.50.5 days to sell inventory, then in one day, inventory can be turned 10.5=2\frac{1}{0.5} = 2 times per day.\n\n## Calculating Inventory Turns Using Financial Information and Little's Law\n\n* Information Sources from Financial Statements:\n * Cost of Goods Sold (COGS): Found on the company's income statement.\n * Represents the direct costs attributable to the production of goods sold (e.g., cost of materials, direct labor). \n * This measure corresponds to the Flow Rate, as it represents the rate at which the value of goods flows out of the process.\n * Total Inventory: Found on the company's balance sheet.\n * This measure corresponds to WIP (Work-In-Process), as it is the total amount of inventory currently held.\n* Connecting Financial Measures to Little's Law for Inventory Turns:\n * We know: Inventory Turns=1Flow Time\text{Inventory Turns} = \frac{1}{\text{Flow Time}}\n * From Little's Law: WIP=Flow Time×Flow Rate\text{WIP} = \text{Flow Time} \times \text{Flow Rate} \n * Rearranging for Flow Time: Flow Time=WIPFlow Rate\text{Flow Time} = \frac{\text{WIP}}{\text{Flow Rate}}\n * Substituting Flow Time into the Inventory Turns formula:\n * Inventory Turns=1(WIPFlow Rate)=Flow RateWIP\text{Inventory Turns} = \frac{1}{\left(\frac{\text{WIP}}{\text{Flow Rate}}\right)} = \frac{\text{Flow Rate}}{\text{WIP}}\n * Therefore, using financial data:\n * Inventory Turns=Cost of Goods SoldTotal Inventory\text{Inventory Turns} = \frac{\text{Cost of Goods Sold}}{\text{Total Inventory}}\n* HP and Dell Example Calculation (demonstrated calculation in lecture):\n * By plugging their respective Cost of Goods Sold (Flow Rate) and Total Inventory (WIP) into the formula, the calculated inventory turns match reported figures.\n * For example (as implied by lecture):\n * HP's Inventory Turns were calculated to be approximately 88.\n * Dell's Inventory Turns were calculated to be approximately 2222.\n * These calculated numbers align with the observed high inventory turns for companies like Dell, signifying their renowned efficiency in inventory management.