McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

*** Important note *** Since the text contains advanced materials on inventory management, which will confuse you, do not refer to the text. Notations and method should be used consistently as this slides do.

Types of Inventory Inventory: supply of items held to meet demand Suppliers Suppliers MRO MRO Raw Material Raw Material Components Components Maintenance, repair & Maintenance, repair & operating supplies operating supplies Work in Work in Process (WIP) Process (WIP) Finished Finished Goods (FGI) Goods (FGI) Transportation Distribution Distribution Customers Customers 7–3

Inventory Control Objectives We need to answer the following questions in order to balance supply and demand, and balance costs and service levels. When do I order? How much do I order? Where do I deploy the inventory? How much? Where? When? 14–4

Functions of Inventory To meet anticipated demand To smooth production requirements To decouple operations To protect against stock-outs

Functions of Inventory (Cont’d) To help hedge against price increases To permit operations through WIP To take advantage of quantity discounts

Disadvantages of Inventories Difficult to Control Determining optimal amounts Storage and maintenance Handling inventory is a non-value added activity

Inventory Management Independent Demand: demand is beyond control of the organization Dependent Demand: demand is driven by demand of another item 14–8

Inventory Counting Systems Periodic inventory System Physical count of items made at periodic intervals Perpetual Inventory System System that keeps track of inventory continuously, thus monitoring current levels of each item

Bullwhip Effect Inventory oscillations become progressively larger looking backward through the supply chain

Managing Inventory Across the Supply Chain Collaborative planning, forecasting and replenishment (CPFR): supply chain partners sharing information Vendor-managed Inventory (VMI): the vendor is responsible for managing inventory for the customer Vendor monitors and replenishes inventory balances Customer saves holding costs Vendor has higher visibility of inventory usage

Inventory Management in the supply chain : Example (Wal-Mart) P&G: Cross-docking:

Managing Inventory – ABC Analysis ABC analysis: ranking inventory by importance Pareto’s Law: small percentage of items have a large impact profit 100 95 80 50 C Items B Items A Items Cumulative Percentage of Revenue 0 20 50 100 Cumulative Percentage of Items 7–13

Financial Impact of Inventory Set-up (Ordering)Cost Purchased items: placing and receiving orders Holding (Carrying ) Costs Opportunity cost (including cost of capital) Storage and warehouse management Taxes and insurance Obsolescence, spoilage, & shrinkage Material handling, tracking and management Ordering cost Carrying cost 7–14 14

Total Inventory Costs Total Inventory Costs: sum of all relevant annual inventory costs. i.e. total set-up cost + total holding cost. 14–15

TIC = annual ordering cost + annual carrying cost Total Inventory Costs TIC = annual ordering cost + annual carrying cost = (D/Q)(S) + (Q/2)(IC) N = D/Q A = Q/2 Where: N = orders per year A = average inventory level D = annual demand S = order cost per order Q = order quantity C = unit cost I = % carrying cost per year 14–16

Total Inventory Costs Note that frequently holding cost is given as a single number meaning H = IC Example: H =$2/item/year 14–17

N = D/Q = 3000 / 500 = 6 order per year Total Inventory Costs If we need 3,000 units per year at a unit price of $20 and we order 500 each time, at a cost of $50 per order with a carrying cost of 20%, what is the TIC? N = D/Q = 3000 / 500 = 6 order per year A = Q/2 = 500 / 2 = 250 average inventory TIC = ordering cost + carrying cost = S (D/Q) + (IC)(Q/2) = $50 (3000/500) + ($20*0.20)*(500/2) = $1,300 Where: N = D/Q Q = 500 A = Q/2 C = $20 D = 3,000 S = $50 I= 0.20 14–18

N = D/Q = 3000 / 200 = 15 order per year Total Inventory Costs If we need 3,000 units per year at a units price of $20 and we order 200 each time, at a cost of $50 per order with a carrying cost of 20%, what is the TIC? N = D/Q = 3000 / 200 = 15 order per year A = Q/2 = 200 / 2 = 100 average inventory TIC = ordering cost + carrying cost = S (D/Q) + ( IC )(Q/2) = 50 (3000/200) + ($20*0.20)*(200/2) = $1,150 Where: N = D/Q Q = 500 A = Q/2 C = $20 D = 3,000 S = $50 I = 0.20 Example 14-2 14–19

Economic Order Quantity (EOQ) Economic Order Quantity (EOQ): minimizes total acquisition costs; point at which holding and orders costs are equal How much to order D = Annual Demand S= Ordering cost I= Percent of unit cost C = Unit cost H= IC= holding cost of item per year 14–20

EOQ Model

Economic Order Quantity (EOQ) Carrying + Order Carrying Cost Cost Order Cost EOQ Order Quantity (Q) 14–22

Economic Order Quantity (EOQ) If we need 3,000 units per year at a unit price of $20, at a cost of $50 per order with a carrying cost of 20%, what is lowest TIC order quantity? D = 3,000 S= $50 C = $20 I = 20% Example 14-3 14–23

EOQ Example What is the optimal order quantity? Example : D=48,000 units/year S= $20/order I= 18%, c=$100

EOQ theorem Example : D=12,000 units/year S= $60/order, H= $10/unit/year Q= order quantity, Q*=optimal order quantity What is the optimal order quantity?

Production Order Quantity Model = POQ Model It is also called Economic Production Quantity Model = EPQ Model

POQ Model ■ Suited for Production Environment ■ Provides Production lot size

POQ Model Equations D= Demand per year S= Setup cost H=Holding cost Let, D= Demand per year S= Setup cost H=Holding cost d=demand per day p=production per day

POQ Model Equations ■ Optimal order quantity or production lot size ■ Max. Inventory level ■ Setup cost ■ Holding cost

Production Order Quantity S= $2,000 I= 25% C = $10 d = 2,000 p = 5,000 Example 14-6 14–30

POQ Example ■ The Watkins Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Demand for the compound is 0.6 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is $3.50 per pound. The company uses an annual interest rate of 22% to account for the cost of capital, and the annual costs of storage and handling of the chemical amount to 12% of the value. Assume that there are 250 working days in a year. What is the optimal lot size, maximum inventory level, and total cost?

Quantity discounts

Quantity Discount Models Material cost: Total material cost is affected by the Discount (%) Unit cost if first $5.00, then $4.80, and finally $4.75 6-33

Quantity Discount Models Total Cost Curves for each of the 3 discount plans 6-34

All-Units quantity discounts 1. Consider the all-units quantity discount schedule below. Units Ordered Price Per Unit EOQ at that Price 1-400 $100 200 401-800 $90 506 801-1000 $80 700 1001-1250 $70 800 1251-1500 $60 900 ≥ 1501 $50 1400   What are the possible optimal order quantities? 

Steps for Solving Quantity Discount Compute EOQ for each discount price: If EOQ < discount minimum level, let Q = minimum. For each EOQ or minimum Q, compute total cost: TC = DC + (D/Q)(S) + (Q/2)(H) Choose the lowest cost quantity from all levels. Q * = IC 2DS 6-36

All-Units quantity discounts A supplier for Lower Florida Keys Health System has introduced all-units quantity discounts to encourage larger order quantities of a special catheter. The price schedule is: Order Quantity Price per Unit 0-299 $60.00 300-499 $58.80 500 or more $57.00  

All-Units quantity discounts   The firm estimates that its annual demand for this item is 936 units, its setup cost is $45 per order, and its annual holding cost is 25% of the catheter’s unit price. What’s the best order size?

All-Units quantity discounts Calculate EOQ

All-Units quantity discounts Total cost for the quantity discount case:

Homework problems for ch 14 Problem 1. The I-75 Carpet Discount store in Washington stocks carpet in its warehouse and sells it through an adjoining showroom. The store keeps several brands and styles of carpet in stock; however, its biggest selling item is Super Shag 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, annual carrying cost of $0.765 per yard, and an ordering cost of $150. a) Decide the optimal order quantity b) Calculate the minimum total annual inventory cost

Homework problems for ch 14 Problem 2. Ashlee’s Beach Chairs company produces upscale beach chairs. Annual demand for the chairs is estimated at 18,000 units. The frames are made in batches before the final assembly process. Ashlee’s frame department can produce 2,500 frames per month. The setup cost is $800 per order, and the annual holding cost is $18 per unit. The company operates 20 days per month. a) Determine the optimal lot size b) Calculate the total holding cost c) Calculate maximum inventory level  

Homework problems for ch 14 Problem 3. Sharp inc, a company that markets painless hypodermic needles to hospitals, would like to reduce its inventory cost by determining the optimal number of hypodermic needles to obtain per order. The annual demand is 1,000 units; the holding cost per unit per year is $0.5. The inventory manager of Sharp inc, calculated the optimal order quantity of 200 units. a) What is the ordering cost per order in the company b) What is the total ordering cost? 

Homework problems for ch 14 Problem 4 . A produce distributor uses 800 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35 percent of the purchase price per crate. Ordering costs are $28 each time. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using the EOQ?

Homework problems for ch 14 Problem 5. Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased for $15 each. The holding cost per bracket per year is 10% of the unit cost and the ordering cost per order is $18.75. There are 250 working days per year. a) What is EOQ? b) In minimizing cost, how many orders would be made each year? c) What would be the total annual inventory cost?(i.e. addition of total ordering and holding cost)

Homework problems for ch 14 Problem 6. A hospital buys disposable surgical packages from Pfishier, Inc. Pfisher’s price schedule is $50.25 per package on order of 1 to 199 packages, and $49.00 per packages on orders of 200 or more packages. Ordering cost is $64 per order, and annual holding cost is 20 percent of the per-unit purchase price. Annual demand is 490 packages. What is the best purchase quantity?