12/27/2017 Inventory Management LO20–1: Explain how inventory is used and understand what it costs. LO20–2: Analyze how different inventory control systems work. LO20–3: Analyze inventory using the Pareto principle. TRA 3151, FGCU

Outline The Importance of Inventory Functions of Inventory Types of Inventory Managing Inventory ABC Analysis Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs

Outline – Continued Inventory Models for Independent Demand The Basic Economic Order Quantity (EOQ) Model Minimizing Costs Reorder Points Probabilistic Models and Safety Stock © 2011 Pearson Education, Inc. publishing as Prentice Hall

Amazon.com Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others Growth has forced Amazon.com to become a world leader in warehousing and inventory management © 2011 Pearson Education, Inc. publishing as Prentice Hall

Amazon.com Each order is assigned by computer to the closest distribution center that has the product(s) A “flow meister” at each distribution center assigns work crews Lights indicate products that are to be picked and the light is reset Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors © 2011 Pearson Education, Inc. publishing as Prentice Hall

Amazon.com Crates arrive at central point where items are boxed and labeled with new bar code Gift wrapping is done by hand at 30 packages per hour Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck Order arrives at customer within 2 - 3 days © 2011 Pearson Education, Inc. publishing as Prentice Hall

Importance of Inventory One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service © 2011 Pearson Education, Inc. publishing as Prentice Hall

Inventory Inventory can be visualized as stacks of money sitting on forklifts, on shelves, and in trucks and planes while in transit. For many businesses, inventory is the largest asset on the balance sheet at any given time. Inventory can be difficult to convert back into cash. It is a good idea to try to get your inventory down as far as possible. The average cost of inventory in the United States is 30 to 35 percent of its value.

Definitions Inventory: the stock of any item or resource used in an organization Includes raw materials, finished products, component parts, supplies, maintenance/repair items, and work-in-process Service: Unsold seats, unsold tickets, unoccupied hotel rooms or hospital beds Work-in-process Undergone some change but not completed A function of cycle time for a product

Inventory system: the set of policies and controls that monitor levels of inventory Determines what levels should be maintained, when stock should be replenished, and how large orders should be. Purposes of Inventory: To maintain independence of operations To meet variation in product demand To allow flexibility in production scheduling To provide a safeguard for variation in raw material delivery time To take advantage of economic purchase order size

Inventory Management The objective of inventory management is to strike a balance between inventory investment and customer service © 2011 Pearson Education, Inc. publishing as Prentice Hall

Demand Types Independent demand – the demands for various items are unrelated to each other For example, a workstation may produce many parts that are unrelated but meet some external demand requirement. Cars, appliances, computers, and houses are examples of independent demand inventory Dependent demand – the need for any one item is a direct result of the need for some other item Usually a higher-level item of which it is part. Tires stored at a Goodyear plant are an example of a dependent demand item

Inventory Costs Costs Holding (or carrying) costs Costs for storage, handling, insurance over time Setup (or production change) costs Costs for arranging specific equipment setups, so cost to prepare a machine or process for manufacturing an order Ordering costs Costs of placing an order and receiving goods Shortage costs Costs of running out

Cost (and range) as a Percent of Inventory Value Holding Costs Category Cost (and range) as a Percent of Inventory Value Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26% © 2011 Pearson Education, Inc. publishing as Prentice Hall

Cost (and range) as a Percent of Inventory Value Holding Costs Category Cost (and range) as a Percent of Inventory Value Housing costs (building rent or depreciation, operating costs, taxes, insurance) 6% (3 - 10%) Material handling costs (equipment lease or depreciation, power, operating cost) 3% (1 - 3.5%) Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26% Holding costs vary considerably depending on the business, location, and interest rates. Generally greater than 15%, some high tech items have holding costs greater than 40%. © 2011 Pearson Education, Inc. publishing as Prentice Hall

Supply Chain Inventory Models

Inventory Models Single-period model Used when we are making a one-time purchase of an item Fixed-order quantity model Used when we want to maintain an item “in-stock,” and when we restock, a certain number of units must be ordered Fixed–time period model Item is ordered at certain intervals of time

Inventory Systems – Comparison Single-period inventory model One-time purchasing decision (e.g., vendor selling T-shirts at a football game) Seeks to balance the costs of inventory overstock and under stock Multi-period inventory models Fixed-order quantity models Event triggered (e.g., running out of stock) Fixed-time period models Time triggered (e.g., monthly sales call by sales representative)

Inventory Control-System Design Matrix

Inventory Management Inventory accuracy – refers to how well the inventory records agree with physical count Cycle counting – a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year

ABC Analysis based on Pareto principle Divides inventory into three classes based on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollar volume Class C - low annual dollar volume Used to establish policies that focus on the few critical parts and not the many trivial ones Other criteria such as quality, design changes, high unit cost can be used instead of dollar volume

Percent of Number of Items Stocked Percent of Annual Dollar Volume ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual Dollar Volume Percent of Annual Dollar Volume Class #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A #11526 500 154.00 77,000 33.2% #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% #10500 12.50 12,500 5.4% 72% 23%

Percent of Number of Items Stocked Percent of Annual Dollar Volume ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual Dollar Volume Percent of Annual Dollar Volume Class #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% #01036 50% 100 8.50 850 .4% #01307 .42 504 .2% #10572 250 150 .1% 8,550 $232,057 100.0% 5%

ABC Analysis A Items 80 – 70 – 60 – Percent of annual dollar usage 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percent of inventory items A Items B Items C Items

ABC Classification

Need to determine when and how much to order Multi-Period Models Fixed-Order Quantity Fixed-Time Period Inventory remaining must be continually monitored Has a smaller average inventory Favors more expensive items Is more appropriate for important items Requires more time to maintain – but is usually more automated Is more expensive to implement Counting takes place only at the end of the review period Has a larger average inventory Favors less expensive items Is sufficient for less-important items Requires less time to maintain Is less expensive to implement

Multi-Period Models – Comparison

Multi-Period Models – Process

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.

Fixed-Order Quantity Model Always order Q units when inventory reaches reorder point (R). Inventory is consumed at a constant rate, with a new order placed when the reorder point (R) is reached once again.   Inventory arrives after lead time (L). Inventory is raised to maximum level (Q).  

Total cost of holding and setup (order) Optimal order quantity (Q*) Minimizing Costs Objective is to minimize total costs Annual cost Order quantity Total cost of holding and setup (order) Setup (or order) cost Minimum total cost Optimal order quantity (Q*) Holding cost © 2011 Pearson Education, Inc. publishing as Prentice Hall

Economic Order Quantity (EOQ) The optimal order quantity (Qopt) occurs where total costs are at their minimum        

Example 20.2            

Number of units in each order Setup or order cost per order The EOQ Model Annual setup cost = S D Q Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order = = (S) D Q © 2011 Pearson Education, Inc. publishing as Prentice Hall

Inventory Usage Over Time Inventory level Time Average inventory on hand Q 2 Usage rate Order quantity = Q (maximum inventory level) Minimum inventory © 2011 Pearson Education, Inc. publishing as Prentice Hall

The EOQ Model Q = Number of pieces per order Annual setup cost = S D Q Annual holding cost = H Q 2 Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q 2 © 2011 Pearson Education, Inc. publishing as Prentice Hall

The EOQ Model 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H Annual setup cost = S D Q Annual holding cost = H Q 2 Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Optimal order quantity is found when annual setup cost equals annual holding cost D Q S = H 2 Solving for Q* 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H © 2011 Pearson Education, Inc. publishing as Prentice Hall

An EOQ Example Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units © 2011 Pearson Education, Inc. publishing as Prentice Hall

Expected number of orders An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity D Q* N = = 5 orders per year 1,000 200 © 2011 Pearson Education, Inc. publishing as Prentice Hall

Expected time between orders Number of working days per year An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year = T = Expected time between orders Number of working days per year N T = = 50 days between orders 250 5 © 2011 Pearson Education, Inc. publishing as Prentice Hall

An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = S + H D Q 2 TC = ($10) + ($.50) 1,000 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100 © 2011 Pearson Education, Inc. publishing as Prentice Hall

An EOQ Example Management underestimated demand by 50% D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days 1,500 units TC = S + H D Q 2 TC = ($10) + ($.50) = $75 + $50 = $125 1,500 200 2 Total annual cost increases by only 25% © 2011 Pearson Education, Inc. publishing as Prentice Hall

An EOQ Example Actual EOQ for new demand is 244.9 units D = 1,000 units Q* = 244.9 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days 1,500 units TC = S + H D Q 2 Only 2% less than the total cost of $125 when the order quantity was 200 TC = ($10) + ($.50) 1,500 244.9 2 TC = $61.24 + $61.24 = $122.48 © 2011 Pearson Education, Inc. publishing as Prentice Hall

Lead time for a new order in days Number of working days in a year Reorder Points EOQ answers the “how much” question The reorder point (ROP) tells “when” to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year © 2011 Pearson Education, Inc. publishing as Prentice Hall

Reorder Point Curve Q* Resupply takes place as order arrives Inventory level (units) Time (days) Q* Resupply takes place as order arrives Slope = units/day = d ROP (units) Lead time = L Figure 12.5 © 2011 Pearson Education, Inc. publishing as Prentice Hall

Number of working days in a year Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days d = D Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units © 2011 Pearson Education, Inc. publishing as Prentice Hall

Probabilistic Models and Safety Stock Used when demand is not constant or certain Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year © 2011 Pearson Education, Inc. publishing as Prentice Hall

Establishing Safety Stock Levels Safety stock – refers to the amount of inventory carried in addition to expected demand. Safety stock can be determined based on many different criteria. A common approach is to simply keep a certain number of weeks of supply. A better approach is to use probability. Assume demand is normally distributed. Assume we know mean and standard deviation. To determine probability, we plot a normal distribution for expected demand and note where the amount we have lies on the curve.

Fixed-Order Quantity Model with Safety Stock Demand is variable, but follows a known distribution/ After the reorder is placed, demand during the lead time may be higher than expected, consuming some (or all) of the safety stock  

Example 20.4 For 95% probability, z = 1.64. Excel: Reorder Point     For 95% probability, z = 1.64.     Policy – place a new order for 936 units whenever stock falls to 388 units on hand. This results in a 95% probability of not stocking out during the lead time. Excel: Reorder Point

Reorder Point with a Safety Stock (Buffer added to the inventory on hand during lead time) point, R Q LT Time Inventory level Safety Stock Safety stock: additional amount of inventory kept over and above the average amount required to meet demand

Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + ZsL where Z = number of standard deviations sL = standard deviation of demand during lead time © 2011 Pearson Education, Inc. publishing as Prentice Hall

Probabilistic Demand Risk of a stockout (5% of area of normal curve) Probability of no stockout 95% of the time Mean demand 350 Risk of a stockout (5% of area of normal curve) ROP = ? kits Quantity Safety stock Number of standard deviations z © 2011 Pearson Education, Inc. publishing as Prentice Hall

Safety Stock Example Number of Units Probability 30 .2 40 ROP  50 .3 ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Number of Units Probability 30 .2 40 ROP  50 .3 60 70 .1 1.0 © 2011 Pearson Education, Inc. publishing as Prentice Hall

Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost Total Cost 20 (20)($5) = $100 $0 $100 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 A safety stock of 20 frames gives the lowest total cost ROP = 50 + 20 = 70 frames © 2011 Pearson Education, Inc. publishing as Prentice Hall

Probabilistic Demand Inventory level Time Safety stock 16.5 units ROP  Place order Inventory level Time Minimum demand during lead time Maximum demand during lead time Mean demand during lead time ROP = 350 + safety stock of 16.5 = 366.5 Receive order Lead time Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) © 2011 Pearson Education, Inc. publishing as Prentice Hall

Probabilistic Example Average demand = m = 350 kits Standard deviation of demand during lead time = sdLT = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZsdLT = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits © 2011 Pearson Education, Inc. publishing as Prentice Hall

Fixed-Period (P) Systems Orders placed at the end of a fixed period Inventory counted only at end of period Order brings inventory up to target level Only relevant costs are ordering and holding Lead times are known and constant Items are independent from one another © 2011 Pearson Education, Inc. publishing as Prentice Hall

Fixed-Period Systems Inventory is only counted at each review period May be scheduled at convenient times Appropriate in routine situations May result in stockouts between periods May require increased safety stock © 2011 Pearson Education, Inc. publishing as Prentice Hall

Fixed-Time Period Model Time periods are equal, but ending inventory varies. Reorder quantity varies, depending upon ending inventory level. Beginning inventory is always the same.

Fixed-Time Period Model    

Example 20.5      

Inventory Control and Supply Chain Management Average inventory – expected amount of inventory over time Inventory turns – number of times inventory is cycled through over time – a measure of how efficiently inventory is used   Fixed Order Quantity: D = 1,000 units Q = 300 units SS = 40 units Inventory Turn = 1,000 / (300/2) +40 = 1,000/190 = 5.263 turns per year   Fixed Time Period: Weekly demand(d) = 50 units Review Cycle (T) = 3 weeks SS = 30 units Inventory Turn= 52(50)/(50(3)/2 + 30 = 52(50)/105 = 2600/105 = 24.8 turns /year  

Single Period Model Applications Overbooking of airline flights Ordering of clothing and other fashion items One-time order for events – e.g., t-shirts for a concert

Single Period Inventory Model Consider the problem of deciding how many newspapers to put in a hotel lobby Too few papers and some customers will not be able to purchase a paper, and profits associated with these potential sales are lost. Too many papers and the price paid for papers that were not sold during the day will be wasted, lowering profit.

Solving the Newspaper Problem Consider how much risk we are willing to take of running out of inventory. Assume a mean of 90 papers and a standard deviation of 10 papers. Assume we want an 80 percent chance of not running out. Assume that the probability distribution associated of sales is normal, stocking 90 papers yields a 50 percent chance of stocking out.

Solving the Newspaper Problem From Appendix G, we see that we need approximately 0.85 standard deviation of extra papers to be 80 percent sure of not stocking out. Using Excel, “=NORMSINV(0.8)” = 0.84162

Single-Period Inventory Models    

Example 20.1 Overestimating cancellation: More overbooking     Underestimating cancellation: Less overbooking Overestimating cancellation: More overbooking

Example 20.1 From Appendix G, we see that our desired level falls about 0.55 standard deviations below the mean (z = -0.55) Using Excel, “=NORMSINV(0.2857)” = 0.56599  

Problem 7 Purchasing cost= $0.2 /card Revenue: $2.15 / card Demand = 2,000; standard deviation 500 What is the optimal production quantity? Cu = 2.15 – .2 = 1.95 Co = .2, Cu/(Co+Cu) = 1.95/(.2+1.95) = .90697 From the standard normal table, Z-value is 1.325; Prob. of being in stock = 0.907 So, optimal production quantity = 2,000 + 500(1.325) = 2662.5, e.g. 2663 cards

Problem 10 Purchasing cost= $0.25 / newspaper Revenue: $1.00 / newspaper Demand = 250; standard deviation 50 How many copies should you buy? Cu = 1- 0.25 = 0.75 Co = .25, Cu/(Co+Cu) = 0.75/(.75+0.25) = 0.75 Prob. of being in stock (service level) = 0.75. From the standard normal table, Z-value is 0.67; So, optimal quantity = 250 + 50(0.67) = 283.5, e.g. 284 papers What is the probability of running out of stock? 1- P = 1- 0.75 = 0.25

Problem 7 Purchasing cost= $0.2 /card Revenue: $2.15 / card Demand = 2,000; standard deviation 500 What is the optimal production quantity?

Problem 10 Purchasing cost= $0.25 / newspaper Revenue: $1.00 / newspaper Demand = 250; standard deviation 50 How many copies should you buy?