Economic Order Quantity The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding inventory (TC).

Economic Order Quantity Assumptions Demand (D) is known and constant H is known and constant Order costs (S) are constant The order quantity arrives in a single shipment No quantity discounts are available All demand will be met (no shortages)

We want to minimize TC D, S, and H are constant. TC is a function of Q.

Economic Order Quantity (3) Let Q * be the economic order quantity. Then For Q *, annual order cost = annual inventory cost

Simple Reorder Point Use this method when daily demand is constant. R = reorder point d = daily demand (may have to compute this) L = lead time (Caution: if lead time is given in weeks, convert this to days). R = dL

Reorder Point with Safety Stock Safety stock (SS) is extra inventory that is kept to meet unexpected demand. Reorder point without safety stock Reorder point with safety stock

Reorder Point with Safety Stock (2) How much safety stock (SS) ? Reorder point with safety stock: Service level is the probability of having enough inventory to meet demand during lead time The probability of a stockout is (1 - service level) Demand during lead time is normally distributed with mean and standard deviation  dL

Reorder Point with Safety Stock (2) How much safety stock (SS) ? z is the number of standard deviations required to meet the desired service level SS = z  dL Reorder point with safety stock: R = + z  dL

Reorder Point with Safety Stock Example Given D = annual demand = 10,000 N = number of business days per year = 250 The company operates 5 days per week = average daily demand  dL = standard deviation of demand during lead time = 20 L = lead time = 1 week Service level = 96% Find: reorder point with safety stock: R = + z  dL

Computing Reorder Point with Safety Stock 1. If average daily demand ( ) is not given, compute it. Note: = D/N and D = = 10,000/250 = If the lead time is given in weeks or months, compute lead time in days. L = 1 week = 1(5) = 5 days Note: 1 week is the number of days per week that the company operates. This may be 5, 6, or 7.

Computing Reorder Point with Safety Stock (2) 3. Find the z value for the service level (96%) Probability of a stockout = 1 – service level = 4% z 50%46% Appendix B gives this area.

Computing Reorder Point with Safety Stock (3) 3. Find the z value for the service level (96%) (cont.) (a) Write the service level as a decimal 96% = (b) Subtract from the service level – = (c) Use the table in Appendix B, page 652, to find the area that is closest to The closest area in the table is , which occurs when z = 1.75 Use z = 1.75

Computing Reorder Point with Safety Stock (4) 4. Compute R R = L+ z  dL = 40(5) (20) = = 235 Note: If the computation gives a fractional value, round up to nearest integer. Example: Computed R =  R = 211

Economic Production Quantity Key question: How many units of a part or product should be made at one time? The economic production quantity (EPQ) is the production quantity (lot size) that minimizes the total annual cost of setups and holding inventory.

Economic Production Quantity (2) Notation Q = Amount to make (lot size) D = annual demand for the item d = daily demand for the item p = daily production rate S = cost of one setup H = inventory holding cost per unit per year (commonly called holding cost) TC = annual cost of setups + annual cost of holding inventory The EPQ is the quantity that minimizes TC

Economic Production Quantity (3) Assumption: Daily demand < daily production. When the item is being made, some is sold or used to make a product. The remainder goes into inventory. When production stops, the inventory is used until there is no inventory left. Then production resumes. Ending inventory = beginning inventory + production - sales or usage

Economic Production Quantity (4) Length of production run = Q/p During production, d units are sold or used each day. (p – d) units go into inventory. Maximum inventory: Total cost: Economic production quantity (EPQ):

EOQ vs. EPQ When to use economic order quantity (EOQ): Demand is independent Compute how much to order (order quantity) When to use economic production quantity (EPQ): Parts or products will be produced: demand is dependent Compute how much to make at one time (production lot size)