IES 371 Engineering Management Chapter 15: Inventory Management Supplement E Week 14 September 7, 2005 Learning Objectives: Understand the practical aspects of various inventory systems Identify the major factors affecting inventory system performance Understand how to calculate the optimal order quantity in various circumstance

Inventory Management Inventory : Stock of items held to meet future demand Determine the amount of inventory to keep in stock Inventory management answers two questions: How much to order: Order Quantity or Economic Order Quantity (EOQ) When to order: Reorder point (R)

Reasons to Hold Inventory Physical Types of Inventory Meet unexpected demand Smooth seasonal or cyclical demand Meet variations in customer demand Take advantage of price discounts Quantity discounts Physical Types of Inventory Raw materials Purchased parts and supplies Labor In-process (partially completed) products Component parts Tools, machinery, and equipment

Pressures for Low Inventories When keeping inventory, there are always some cost incurred Inventory holding cost (or carrying cost) The variable cost of keeping items on hand $/ unit-period Inventory holding cost generally includes: Interest of opportunity cost Storage and handling costs Tax, insurance, and shrinkage

Pressures for High Inventories Customer service Ordering cost ($ / order) Setup cost Transportation cost Payment to suppliers Labor and equipment utilization

Types of Inventory Cycle Inventory Safety stock inventory Anticipation inventory Pipeline inventory

Inventory Reduction Approach Cycle Inventory Safety stock inventory Anticipation inventory Pipeline inventory

ABC Analysis To classify the inventory classes according to how critical (% of dollar value) of each inventory type Class A 5 – 15 % of units 70 – 80 % of value Class B 30 % of units 15 % of value Class C 50 – 60 % of units 5 – 10 % of value

ABC Analysis Percentage of dollar value Percentage of items 10 20 30 40 50 60 70 80 90 100 Percentage of items Percentage of dollar value 100 — 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 — Class C Class A Class B Figure 15.2

Economic Order Quantity (EOQ) EOQ: the lot size or order size that minimizes total annual inventory holding and ordering cost Total inventory cost = Holding cost (HC) + ordering cost (OC) Assumptions for Basic EOQ Model Constant demand with no uncertainty No shortages Constant order lead time Receive order quantity all at once No other constraint

Basic EOQ Model Cycle Inventory Levels Order quantity, Q Demand rate Inventory Level Reorder point, R Time Lead time Lead time Order placed Order receipt Order placed Order receipt

Basic EOQ Model Graphs of Annual Holding, Ordering, and Total Costs Annual cost (dollars) Lot Size (Q) Total cost = HC + OC Ordering cost (OC) Holding cost (HC) Figure 15.4

Basic EOQ Model Q = order size (units) D = annual demand (units/year) Derivation of total annual inventory cost and economic order quantity order quantity functions Q = order size (units) D = annual demand (units/year) S = ordering cost per order ($/order) H = annual per unit carrying cost ($/unit)

Basic EOQ Model Ex 1:Carpet Sell The I-75 Carpet store stocks carpet in its warehouse and sells it through a showroom. The store keeps several brands and styles of carpet in stock; however, its bigger seller is the BIG C carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store would like to know the number of orders that will be made annually and the time between orders given that the store is open every except Sunday, Thanksgiving Day and Christmas Day.

EOQ Sensitivity Analysis Use estimates of relevant costs Ignore uncertainty in demand What happen if the holding / ordering cost is off by 20%, 30%? Consider 4 cases of variations of the model parameters. Both ordering and carrying costs are 10% less than the original estimates Both are 10% higher Ordering cost is 10% higher and carrying cost is10% lower Ordering cost is 10% lower and carrying cost is 10% higher Determine EOQ in each case. Remark on the sensitivity of Q on the estimated total cost.

Basic Types of Inventory Control System Continuous review system Reorder point (ROP) system Fixed order quantity system The ordering interval may not be consistent Manager has direct control Periodic review System (P) Fixed interval reorder system or periodic reorder system The amount to order may not be equal No direct control Tend to have higher inventory to prevent stockout

Continuous review system Order placed IP Q OH Order received Q OH placed IP Time On-hand inventory Order received R TBO L TBO L Figure 15.7

Continuous review system Selecting Reorder Point When demand is certain Reorder point (R) = demand during lead time When demand is uncertain Reorder point (R) = Avg demand during lead time + Safety stock

Variable Demand Safety Stocks buffer added to on hand inventory during lead time Stockout an inventory shortage Service level probability that the inventory available during lead time will meet demand Reorder point, R Q LT Time Inventory level Variable Demand with Reorder Point

Variable Demand Safety Stocks Prevent stockout under uncertain demand Q Inventory level Reorder point, R Safety Stock LT LT Time

Reorder Point for a Service Level Probability of meeting demand during lead time = service level Average demand during lead time Probability of a stockout Safety stock zt L Demand R

Reorder Point with Variable Demand Reorder point with safety stock Service level = probability of NO stockout

Variable Demand Ex 2: PM computer PM Computers assembles microcomputers from generic components. It purchases its color monitors from a manufacturer in Taiwan. There is a long lead time of 25 days. Daily demand is normally distributed with a mean of 2.5 monitors and a standard deviation of 1.2 monitors. Determine the safety stock and reorder point corresponding to a 90% service level

Periodic Review System (P system) Time On-hand inventory T Q1 Order placed L received Q2 Q3 OH Protection interval IP1 IP3 IP2 IP Figure 15.12

Special Inventory Model Noninstantaneous Replenishment Relax assumption of receiving all orders at one time Order quantity received gradually Inventory is used up at the same time Maximum inventory < Q Average inventory level  Q/2 Production quantity Q Demand during production interval Imax On-hand inventory Maximum inventory p – d Time Production and demand Demand only TBO Figure E.1

Special Inventory Model Noninstantaneous Replenishment Imax = (p – d) = Q( ) Q p p – d C = (H) + (S) Imax 2 D Q C = ( ) + (S) D Q Q p – d 2 p ELS = p p – d 2DS H

Noninstantaneous Replenishment Ex 3: Cheese Maker The Wood Valley Dairy makes cheese to supply to stores in its area. The dairy can make 250 lbs of cheese per day, and the demand at area stores is 180 lbs per day. Each time the dairy makes cheeses, it costs $125 to set up the production process. The annual cost of carrying a pound of cheese is $12. Determine the followings: The optimal order size and the minimum total annual inventory cost Length of time to receive an order, production run Number of orders per year Maximum inventory level

Special Inventory Model Quantity Discount Price discount for higher quantity orders Include the purchase price in EOQ model P = Unit price of item TC = ($10 ) TC (d1 = $8 ) TC (d2 = $6 ) Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200

Quantity Discount Ex 4: Sweatshirt in bookstore The UW bookstore purchases sweatshirts with school logo from a vendor. The vendor sells the sweatshirts to the store for $38 a piece. The cost to bookstore for placing an order is $120, and the annual carrying cost is 25% of the cost of sweatshirt. 1700 sweatshirts are estimated to be sold during the year. The vendor has offered the bookstore the following volume discount: What is an optimal order quantity? Order Size Discount 1-299 300-499 500-799 800 and up 0% 2% 4% 5%