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: \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 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., 8,056 students per year, if that's the inflow rate).\n * Flow Time: Average graduation time (e.g., 4 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 * \text{WIP} = \text{Flow Time} \times \text{Flow Rate} \n * Using the example numbers: \text{WIP} = 4 \text{ years} \times 8,056 \text{ students/year} = 32,224 \text{ students} \n * Step 2: Calculate Total Annual Spending.\n * \text{Total Annual Spending} = \text{Spending per student per year} \times \text{WIP} \n * \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 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 * \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, 0.5 days to sell inventory, then in one day, inventory can be turned \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: \text{Inventory Turns} = \frac{1}{\text{Flow Time}} \n * From Little's Law: \text{WIP} = \text{Flow Time} \times \text{Flow Rate} \n * Rearranging for Flow Time: \text{Flow Time} = \frac{\text{WIP}}{\text{Flow Rate}} \n * Substituting Flow Time into the Inventory Turns formula:\n * \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 * \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 8 .\n * Dell's Inventory Turns were calculated to be approximately 22 .\n * These calculated numbers align with the observed high inventory turns for companies like Dell, signifying their renowned efficiency in inventory management.