Inventory Modeling for Independent Demand MBA 570 Summer
Inventory Modeling for Independent Demand MBA 570 Summer 2011
Learning Objectives � Explain what inventory is � Describe how inventory is classified � Explain ABC analysis � Explain cycle counting � Compare inventory models � Use inventory models to find how much & when to order
What Is Inventory? � Stock of materials � Stored capacity
What Is Inventory? � Stock of materials � Stored capacity � Examples © 1995 Corel Corp. © 1984 -1994 T/Maker Co.
The Functions of Inventory n n To ”decouple” or separate various parts of the production process To provide a stock of goods that will provide a “selection” for customers To take advantage of quantity discounts To hedge against inflation and upward price changes
Types of Inventory n Raw material n Work-in-progress n n Maintenance/repair/operating supply Finished goods
Disadvantages of Inventory � Higher costs ◦ Item cost (if purchased) ◦ Ordering (or setup) cost �Costs of forms, clerks’ wages etc. ◦ Holding (or carrying) cost �Building lease, insurance, taxes etc. � Difficult to control � Hides production problems
Inventory Holding Costs Category % of Inventory Value Housing (building) cost Material handling costs Labor cost Inventory investment costs Pilferage, scrap, & obsolescence Total holding cost 6% 3% 3% 11% 3% 26%
Inventory Classifications © 19841994 T/Maker Co.
Inventory Management
ABC Analysis � Divides on-hand inventory into 3 classes ◦ A class, B class, C class � Basis is usually annual $ volume ◦ $ volume = Annual demand x Unit cost � Policies based on ABC analysis ◦ Develop class A suppliers more ◦ Give tighter physical control of A items ◦ Forecast A items more carefully
Classifying Items as ABC % Annual $ Usage % of Inventory Items
Classifying Items as ABC % Annual $ Usage A B C % of Inventory Items
ABC Classification Example You’re a buyer for Auto Palace. Classify the following items as A, B, or C. Note: Example is for illustration only; too few items.
ABC Classification Solution
ABC Classification Thinking Challenge You’re an inventory control supervisor for USX. Classify the following items as A, B, or C.
ABC Classification Solution*
Cycle Counting n n Physically counting a sample of total inventory on a regular basis Used often with ABC classification l A items counted most often (e. g. , daily)
Advantages of Cycle Counting n n n Eliminates shutdown and interruption of production necessary for annual physical inventories Eliminates annual inventory adjustments Provides trained personnel to audit the accuracy of inventory Allows the cause of errors to be identified and remedial action to be taken Maintains accurate inventory records
Basic Inventory Planning Questions � How much to order? � When to order? Purchase Order Description Qty. Microwave 1000
Inventory Models � Fixed order quantity models ◦ Economic order quantity ◦ Production order quantity ◦ Quantity discount Help answer the inventory planning questions! © 1984 -1994 T/Maker Co.
Economic Order Quantity (EOQ) Model
EOQ Assumptions � Known & constant demand � Known & constant lead time � Instantaneous receipt of material � No quantity discounts � Only order (setup) cost & holding cost � No stockouts
Goal of an Inventory System Minimize Total Cost (TC) TC = Holding + Order/Setup Cost TC = H + S
EOQ Model: How Much to Order? Annual Cost Order Quantity
EOQ Model: How Much to Order? Annual Cost Holding Cost Order Quantity
EOQ Model: How Much to Order? Annual Cost Holding Cost Order (Setup) Cost Order Quantity
EOQ Model: How Much to Order? Annual Cost Total Cost Curve Holding Cost Order (Setup) Cost Order Quantity
EOQ Model: How Much to Order? Annual Cost Total Cost Curve Holding Cost Order (Setup) Cost Optimal Order Quantity (Q*) Order Quantity
Why Holding Cost Increases � More units must be stored if more ordered Purchase Order Description Qty. Microwave 1 Order quantity Purchase Order Description Qty. Microwave 1000 Order quantity
Why Order Cost Decreases � Cost is spread over more units Example: You need 1000 microwave ovens 1 Order (Postage $ 0. 32) Purchase Order Description Qty. Microwave 1000 Order quantity 1000 Orders (Postage $320) Purchase. Order Description Qty. Purchase Description Qty. 1 Microwave Description Qty. Microwave 11 Microwave 1
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Time
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Decrease due to constant demand Time
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Instantaneous receipt of optimal order quantity Time
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Time
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Reorder Point (ROP) Lead Time
EOQ Model: When to Order? Inventory Level Optimal Order Quantity (Q*) Average Inventory (Q*/2) Reorder Point (ROP) Lead Time
EOQ Model Output Example � When the inventory of microwaves gets down to 15 units (reorder point), order 35 units (EOQ). 15 left Purchase Order Description Qty. Microwave 35
EOQ Model Equations D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days
EOQ Thinking Challenge You’re a buyer for Wal-Mart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is 40% of per unit cost. Lead time is 5 days. Wal-Mart is open 365 days/yr. What is the optimal order quantity & ROP?
EOQ Model Equations D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days
EOQ Solution* Q* = 2 XDXS H = 2 X 1000 X 10 = 80 units 0. 40 (78) D 1000 d= = = 2. 74 units /day Working Days /Year 365 ROP = d × L = 2. 74 X 5 = 137. units
Production Order Quantity Model
Production Order Quantity Model � Answers how much to order & when to order � Allows partial receipt of material ◦ Other EOQ assumptions apply � Suited for production environment � Lower holding cost than EOQ model ◦ Material produced, used immediately ◦ Provides production lot size
POQ Model: Inventory Levels Inventory Level Supply Begins Time
POQ Model: Inventory Levels Inventory Level Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Inventory level with NO demand during supply of optimum order quantity Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Inventory level with NO demand during supply of optimum order quantity Q* Supply Begins Ends Q* is optimum order qty Time
POQ Model: Inventory Levels Inventory Level Q* Inventory level with CONSTANT demand during supply of optimum order quantity Supply Begins Ends Q* is optimum order qty Time
POQ Model: Inventory Levels Inventory Level Q* Quantity used before becoming inventory Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Decrease due to no supply & constant demand Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Production portion of cycle Demand portion of cycle with no supply Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Next Cycle Time
POQ Model: Inventory Levels Inventory Level Next Cycle Supply Begins Time
POQ Model: Inventory Levels Inventory Level Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Supply Begins Ends Time
POQ Model: Inventory Levels Inventory Level Max. Inventory Q*·(1 - d/p) Time
POQ Model: Inventory Levels Inventory Level Inventory level with no demand Production Portion of Cycle Q* Supply Begins Supply Ends Max. Inventory Q·(1 - d/p) Demand portion of cycle with no supply Time
POQ Model Equations Optimal Order Quantity = Qp* = 2 x. Dx. S H x (1 - d/p) Max. Inventory Level = Q D Setup Cost = Q x 1 d p x. S Holding Cost = Q 1 - (d/p) H D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day
POQ Model Thinking Challenge You’re a production planner for Stanley Tools makes 30, 000 screw drivers per year. Demand is 100 screw drivers per day & production is 300 per day. Production setup cost is $150 per order. Carrying cost is $1. 50 per screw driver. What is the optimal lot size?
POQ Model Equations Optimal Order Quantity = Qp* = 2 x. Dx. S H x (1 - d/p) Max. Inventory Level = Q D Setup Cost = Q x 1 d p x. S Holding Cost = Q 1 - (d/p) H D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day
Production Order Quantity Model Solution* Qp * = 2× D × S H× 1 - d p = 2 × 30000 × 150 = 3000 1. 5 × 1 300 Max. Inventory Level = 3000× D = Demand Per Year S = Setup Cost H = Holding Cost d = Demand Per Day p = Production Per Day 1 100 = 2000 300
Quantity Discount Model � Answers how much to order & when to order � Allows quantity discounts ◦ Reduced price when item is purchased in larger quantities ◦ Other EOQ assumptions apply � Trade-off is between lower price & increased holding cost
Quantity Discount Model: How Much to Order? Total Cost Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Discount Quantity 1 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Discount Quantity 1 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 Discount Quantity 1 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 Discount Quantity 1 2 TC for Discount 1 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 Discount Quantity Q* 1 2 TC for Discount 1 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 Outside discount range Discount Quantity Q* 1 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Discount Quantity 1 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Q*Disc 1 Qty Discount Quantity 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Outside discount range Q*Disc 1 Qty Discount Quantity 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 X Q* adjusted Disc Qty Discount Quantity 2 1 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Discount Quantity 1 Discount Quantity 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Discount Quantity 1 Q* Discount Quantity 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Outside discount range Disc Qty. Q* 1 Discount Quantity 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 X Discount Quantity 1 Q* adjusted Disc Qty 2 Order Quantity
Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Quantity Ordered Lowest cost not in discount range Discount Quantity 1 2 Order Quantity
Quantity Discount Model Steps � Compute EOQ for each quantity discount price � Is computed EOQ in discount range? ◦ If not, use the lowest cost quantity in discount range � Compute total cost for EOQ or lowest cost quantity in discount range � Select quantity with lowest total cost
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