What is Inventory? Definition--The stock of any item or resource used in an organization Raw materials Finished products Component parts Supplies Work in process Raw material - Suppliers may only ship in batches - Larger purchases many reduces costs Finished Products - When it has strategic Importance - Level capacity plans - Products displayed to customers (Costco) Work in Process - Uncouples phases of production - Reduced material handling costs An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. Supply Chain Management - Aggregate Planning and Inventory Control

Inventory System Purpose The set of policies and controls that determine what inventory levels should be maintained, when stock should be replenished, and how large orders should be Raw material - Suppliers may only ship in batches - Larger purchases many reduces costs Finished Products - When it has strategic Importance - Level capacity plans - Products displayed to customers (Costco) Work in Process - Uncouples phases of production - Reduced material handling costs An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. Supply Chain Management - Aggregate Planning and Inventory Control

Purposes of Inventory 1. To maintain independence of operations 2. To meet variation in product demand 3. To allow flexibility in production scheduling 4. To provide a safeguard for variation in raw material delivery time 5. To take advantage of economic purchase-order size 1. WIP 2. FGI 3. FGI - relieve pressure caused by customer demand 4. Raw material 5. raw material Why not hold inventories? - carrying costs - lose of responsiveness - diluted ROI (inventories are an investment) - Reduced Capacity (inventory eats capacity) - decreased quality caused by large lot production Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Costs Holding (or carrying) costs Setup (or production change) costs Ordering costs Shortage (or backlog) costs Holding (or carrying) costs. Costs for storage, handling, insurance, etc. Setup (or production change) costs. Costs for arranging specific equipment setups, etc. Ordering costs. Costs of someone placing an order, etc. Shortage costs. Costs of canceling an order, etc. Supply Chain Management - Aggregate Planning and Inventory Control

Independent vs. Dependent Demand Independent Demand (Demand not related to other items) Dependent Demand (Derived/Calculated) Supply Chain Management - Aggregate Planning and Inventory Control

Classifying Inventory Models Fixed-Order Quantity Models Event triggered Make exactly the same amount Use re-order point to determine timing Fixed-Time Period Models Time triggered Count the number needed to re-order Fixed -order quantity models - EOQ Event trigger - level of inventory (order point) Must constantly monitor inventory Fixed time period model - periodic review Order up to Larger average inventory - covers uncertianty in L+T Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Control Inventory Inventory Models Fixed Order Quantity Models Fixed Time Period Models Single Period Models Constant Demand Uncertainty in Demand EOQ w/ Quantity Discounts Simple EOQ EOQ w/usage Find the EOQ and R Determine p and d Calculate Total costs Find the EOQ and R Select Q and find R Supply Chain Management - Aggregate Planning and Inventory Control

Fixed-Order Quantity Models Assumptions Demand for the product is constant and uniform throughout the period Lead time (time from ordering to receipt) is constant Price per unit of product is constant Inventory holding cost is based on average inventory Ordering or setup costs are constant All demands for the product will be satisfied (No back orders are allowed) Define Lead Time price per unit is constant throughout time period Supply Chain Management - Aggregate Planning and Inventory Control

EOQ Model--Basic Fixed-Order Quantity Model R = Reorder point Q = Economic order quantity L = Lead time L Q R Time Inventory Level What is average inventory??? Reorder point - Inventory position --> on hand +on order - backlogs Supply Chain Management - Aggregate Planning and Inventory Control

Basic Fixed-Order Quantity Model Total Annual Cost = Annual Purchase Cost Ordering Holding + Derive the Total annual Cost Equation, where: TC - Total annual cost D - Annual demand (and d-bar = average daily demand = D/365) C - Cost per unit Q - Order quantity S - Cost of placing an order or setup cost R - Reorder point L - Lead time H - Annual holding and storage cost per unit of inventory TC = DC + (D/Q)S + (Q/2)H TC/Q = -DQ-2S + (1/2)H set 0=-DQ-2S = (1/2)H DQ-2s = (1/2)H (2DS)/H = Q2 Q = sq. rt. of (2DS)/H Supply Chain Management - Aggregate Planning and Inventory Control

Cost Minimization Goal Order Quantity (Q) C O S T Total Cost Holding Costs Annual Cost of Items (DC) Ordering Costs QOPT Supply Chain Management - Aggregate Planning and Inventory Control

average demand per time unit Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero Reorder Point, R = dL d = average demand per time unit _ L = Lead time (constant) Supply Chain Management - Aggregate Planning and Inventory Control

EOQ Example Annual Demand (D) = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order (S) = $10 Holding cost per unit per year (H) = $2.40 Lead time (L) = 7 days Cost per unit (C) = $15 Determine the economic order quantity and the reorder point. Supply Chain Management - Aggregate Planning and Inventory Control

Solution Why do we round up? 91 or 92 units??? When the inventory level reaches 20, order 91 units. Supply Chain Management - Aggregate Planning and Inventory Control

Problem Retailer of Satellite Dishes How much should we order? D = 1000 units S = $ 25 H = $ 100 How much should we order? What are the Total Annual Stocking Costs? EOQ = (2DS)/H^.5 = ((2*1000*25)/100)^.5 = 500^.5 = 22.3 or 22 TSC = (1000/22)*25 + (22*100)/2 = 1136 + 1100 = 2236 Supply Chain Management - Aggregate Planning and Inventory Control

EOQ with Quantity Discounts What if we get a price break for buying a larger quantity? To find the lowest cost order quantity: Since “C” changes for each price-break, H=iC Where, i = percentage of unit cost attributed to carrying inventory and , C = cost (or price) per unit Find the EOQ at each price break. Identify relevant and feasible order quantities. Compare total annual costs The lowest cost wins. Supply Chain Management - Aggregate Planning and Inventory Control

EOQ with Quantity Discounts Example Copper may be purchased for $ .82 per pound for up to 2,499 pounds $ .81 per pound for 2,500 to 5,000 pounds $ .80 per pound for orders greater than 5,000 pounds Demand (D) = 50,000 pounds per year Holding costs (H) are 20% of the purchase price per unit Ordering costs (S) = $30 How much should the company order to minimize total costs? Supply Chain Management - Aggregate Planning and Inventory Control

Problem 28 (Costs in $,000) (Order Quantity 100's of units) 44 43 Feasible (Costs in $,000) <2500 42 <2500 - 4999 >5000 41 40 20 40 60 80 100 (Order Quantity 100's of units) Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Control Inventory Inventory Models Fixed Order Quantity Models Fixed Time Period Models Single Period Models Constant Demand Uncertainty in Demand Find the L Find Z Safety Stock Find the EOQ and R Supply Chain Management - Aggregate Planning and Inventory Control

What if demand is not Certain? Use safety stock to cover uncertainty in demand. Given: service probability which is the probability demand will NOT exceed some amount. The safety stock level is set by increasing the reorder point by the amount of safety stock. The safety stock equals z•L where, L = the standard deviation of demand during the lead time. For example for a 5% chance of running out z 1.65 Assuming demand is N(,2) Supply Chain Management - Aggregate Planning and Inventory Control

Problem Annual Demand = 25,750 or 515/wk @ 50 wks/year Annual Holding costs = 33% of item cost ($10/unit) Ordering costs are $250.00 d = 25 per week Leadtime = 1 week Service Probability = 95% Find: a.) the EOQ and R b.) annual holding costs and annual setup costs c.) Would you accept a price break of $50 per order for lot sizes that are larger than 2000? Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Control Inventory Inventory Models Fixed Order Quantity Models Fixed Time Period Models Single Period Models Current Inventory Find theT+L Find Z Find order quantity (q) Supply Chain Management - Aggregate Planning and Inventory Control

Fixed-Time Period Models Check the inventory every review period and then order a quantity that is large enough to cover demand until the next order will come in. The model assumes uncertainty in demand with safety stock added to the order quantity. More exposure to variability than fixed-order models Current inventory is I the review period is T quantity to be ordered is q The amount of SS is larger than that of the Fixed Order Quantity Supply Chain Management - Aggregate Planning and Inventory Control

Fixed-Time Period Model with Safety Stock Formula q = Average demand + Safety stock - Inventory currently on hand q = demand during lead time and review period + SS - on hand more exposure to variability than fixed order quantity Supply Chain Management - Aggregate Planning and Inventory Control

Determining the Value of sT+L (number of days exposed to stockout) The standard deviation of a sequence of random events equals the square root of the sum of the variances. Supply Chain Management - Aggregate Planning and Inventory Control

Example of the Fixed-Time Period Model Given the information below, how many units should be ordered? Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units. T=30 d=20 L=10 P=0.96 I=200 Supply Chain Management - Aggregate Planning and Inventory Control

Example of the Fixed-Time Period Model: Solution So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period. Supply Chain Management - Aggregate Planning and Inventory Control

Problem A pharmacy orders antibiotics every two weeks (14 days). the daily demand equals 2000 the daily standard deviation of demand = 800 lead time is 5 days service level is 99 % present inventory level is 25,000 units What is the correct quantity to order to minimize costs? Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Control Inventory Inventory Models Fixed Order Quantity Models Fixed Time Period Models Single Period Models Constant Demand Uncertainty in Demand Supply Chain Management - Aggregate Planning and Inventory Control

Single – Period Model for items w/obsolescence (newsboy problem) For a single purchase Amount to order is when marginal profit (MP) is equal to marginal loss (ML). Adding probabilities (P = probability of that unit being sold) for the last unit ordered we want P(MP)(1-P)ML or P  ML /(MP+ML) Increase order quantity as long as this holds. Supply Chain Management - Aggregate Planning and Inventory Control

Single–Period Model (Text Prob. #21) Famous Albert’s Cookie King Demand (dozen) Probability of Demand 1,800 0.05 2,000 0.10 2,200 0.20 2,400 0.30 2,600 2,800 3,000 Each dozen sells for $0.69 and costs $0.49 with a salvage value of $0.29. How many cookies should he bake? Supply Chain Management - Aggregate Planning and Inventory Control

ABC Classification System Items kept in inventory are not of equal importance in terms of: dollars invested profit potential sales or usage volume stock-out penalties 60 % of $ Value A 30 B C % of Use 30 60 Inventory Control - Accuracy is recommended to be higher for A items (± .2%) versus ± 1% for B’s and ± 5% for C’s So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 50% are the “C” items. Supply Chain Management - Aggregate Planning and Inventory Control

Inventory Accuracy and Cycle Counting Do inventory records agree with physical count? Cycle Counting Frequent counts When? (zero balance, backorder, specified level of activity, level of important item, etc.) Which Items to count? Most important (ABC analysis) Items that are at an appropriate time When to count? Low or zero balance Backorder with positive inventory After some activity By Whom? Designated inventory control people By the people removing or adding to inventory Supply Chain Management - Aggregate Planning and Inventory Control