Supply Chain Formulas

Cheatsheet Content

Inventory Management Economic Order Quantity (EOQ): Minimizes total inventory costs. $$ EOQ = \sqrt{\frac{2DS}{H}} $$ Where: $D$ = Annual demand (units) $S$ = Ordering cost per order $H$ = Holding cost per unit per year Reorder Point (ROP): When to place a new order. $$ ROP = (Demand \ Rate \times Lead \ Time) + Safety \ Stock $$ Where: $Demand \ Rate$ = Average daily or weekly demand $Lead \ Time$ = Time between placing and receiving an order $Safety \ Stock$ = Buffer inventory to prevent stockouts Safety Stock: $$ Safety \ Stock = Z \times \sigma_L \times \sqrt{Lead \ Time} $$ Where: $Z$ = Z-score for desired service level $\sigma_L$ = Standard deviation of demand during lead time Days of Inventory Outstanding (DIO): $$ DIO = \frac{Average \ Inventory}{Cost \ of \ Goods \ Sold} \times 365 $$ Forecasting Simple Moving Average: Average of previous $n$ periods. $$ F_t = \frac{A_{t-1} + A_{t-2} + \dots + A_{t-n}}{n} $$ Where: $F_t$ = Forecast for period $t$ $A_{t-i}$ = Actual demand in period $t-i$ $n$ = Number of periods in the moving average Weighted Moving Average: Assigns different weights to past data. $$ F_t = \sum_{i=1}^{n} (W_i \times A_{t-i}) $$ Where: $W_i$ = Weight for period $t-i$ (sum of $W_i$ must be 1) Exponential Smoothing: $$ F_t = \alpha A_{t-1} + (1 - \alpha) F_{t-1} $$ Where: $\alpha$ = Smoothing constant (between 0 and 1) Mean Absolute Deviation (MAD): Measures forecast accuracy. $$ MAD = \frac{\sum |Actual - Forecast|}{n} $$ Mean Squared Error (MSE): Another forecast accuracy metric. $$ MSE = \frac{\sum (Actual - Forecast)^2}{n} $$ Logistics & Transportation Total Logistics Cost: $$ Total \ Logistics \ Cost = Transportation \ Cost + Inventory \ Cost + Warehousing \ Cost + Order \ Processing \ Cost $$ Cube Utilization: Percentage of available space used. $$ Cube \ Utilization = \frac{Total \ Volume \ of \ Goods}{Total \ Available \ Volume \ of \ Vehicle} \times 100\% $$ Weight Utilization: Percentage of available weight capacity used. $$ Weight \ Utilization = \frac{Total \ Weight \ of \ Goods}{Total \ Available \ Weight \ Capacity \ of \ Vehicle} \times 100\% $$ On-Time Delivery Rate: $$ On-Time \ Delivery \ Rate = \frac{Number \ of \ On-Time \ Deliveries}{Total \ Number \ of \ Deliveries} \times 100\% $$ Supply Chain Performance Cash-to-Cash Cycle Time: How long cash is tied up in inventory. $$ C2C = DIO + DSO - DPO $$ Where: $DIO$ = Days of Inventory Outstanding $DSO$ = Days Sales Outstanding (Accounts Receivable) $DPO$ = Days Payables Outstanding (Accounts Payable) Inventory Turnover: How many times inventory is sold over a period. $$ Inventory \ Turnover = \frac{Cost \ of \ Goods \ Sold}{Average \ Inventory} $$ Perfect Order Rate: Measures customer satisfaction. $$ Perfect \ Order \ Rate = Product \ Availability \times On-Time \ Delivery \times Order \ Accuracy \times Damage \ Free $$ Supplier On-Time Delivery Rate: $$ Supplier \ OTD = \frac{Number \ of \ On-Time \ Deliveries \ from \ Supplier}{Total \ Deliveries \ from \ Supplier} \times 100\% $$ Production Planning Throughput Rate: Rate at which units are processed. $$ Throughput \ Rate = \frac{Number \ of \ Units \ Produced}{Time \ Period} $$ Capacity Utilization: $$ Capacity \ Utilization = \frac{Actual \ Output}{Maximum \ Possible \ Output} \times 100\% $$ Takt Time: Rate at which products need to be completed to meet customer demand. $$ Takt \ Time = \frac{Available \ Production \ Time}{Customer \ Demand} $$