Chapter 17 Inventory Control

Learning Objectives Explain the different purposes for keeping inventory. Understand that the type of inventory system logic that is appropriate for an item depends on the type of demand for that item. Calculate the appropriate order size when a one-time purchase must be made. Describe what the economic order quantity is and how to calculate it. Summarize fixed–order quantity and fixed–time period models, including ways to determine safety stock when there is variability in demand. Discuss why inventory turn is directly related to order quantity and safety stock.

Inventory You should visualize inventory 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 is often not very liquid 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 LO 1

Inventory Inventory—stock of any item/resource used in an organization. Carried in anticipation of use and can include: raw materials finished products component parts supplies work-in-process people, etc. Inventory system—set of policies & controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

Inventory Problems When to order the products How much to order Issue of timing How much to order Issue of quantity These problems often addressed with the objective of inventory cost minimization Total annual cost And meet prescribed service levels

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

for Carrying Inventory Wrong Reasons for Carrying Inventory Poor quality Inadequate maintenance of machines Poor production schedules Unreliable suppliers Poor worker’s attitudes Just-in-case

Supply Chain Inventories—Make-to-Stock Environment LO 1

Models Discussed The single-period model Fixed–order quantity 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 The item is ordered at certain intervals of time LO 2

Definition of Inventory Inventory: the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process Manufacturing inventory: refers to items that contribute to or become part of a firm’s product Inventory system: the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be LO 2 3

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 LO 2 4

Inventory Costs Holding (or carrying) costs: H Costs for storage, handling, insurance, taxes, spoilage, capital, and so on Setup (or production change) costs: S Costs for arranging specific equipment setups, and so on Ordering costs: S Costs of placing an order, clerical, supplies Shortage costs: Costs of running out, rain checks, goodwill Purchase cost: C Outdate costs (for perishable products) LO 3 5

Independent Versus Dependent Demand 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 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 LO 2

Inventory Control-System Design Matrix: Framework Describing Inventory Control Logic

Inventory Systems Single-period inventory model One time purchasing decision (Example: vendor selling t-shirts at a football game) Example: Vendor selling T-shirts at sporting events Newspaper sales (Newsboy Model) Seeks to balance the costs of inventory overstock and under stock LO 2 7

Inventory Systems Multi-period inventory models Fixed-order quantity models Event triggered (Example: running out of stock) Inventory is monitored all the time Order Q when inventory reaches R, the reorder point Also known as FOSS, (Q, R) or EOQ system Fixed-time period models Time triggered (Example: Monthly sales call by sales representative) Inventory is monitored periodically Also known as FOIS, (S, s), or EOI system

A 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 they will lose the profit associated with these sales Too many papers and will have paid for papers that were not sold during the day, lowering profit LO 3

A Simple View of the Problem Consider how much risk we are willing to take for running out of inventory Assume a mean of 90 papers and a standard deviation of 10 papers Assume they want an 80 percent chance of not running out Assuming that the probability distribution associated of sales is normal, stocking 90 papers yields a 50 percent chance of stocking out LO 3

A Simple View of the Problem Continued To be 80 percent sure of not stocking out, we need to carry a few more than 90 papers From the “cumulative standard normal distribution” table, we see that we need approximately 0.85 standard deviation of extra papers to be 80 percent sure of not stocking out With Excel, “=NORMSINV(0.8)” = 0.84162 LO 3

Single-Period Inventory Model Formulas We should increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of Cu/Co+Cu LO 3 8

Example 17.1: Hotel Reservation Mean of 5 Standard deviation of 3 Cost $80 Overbook cost is $200 LO 3

Example: Hotel Reservations Cost of overbooking by n=Expected cost you overbooked by n + Expected cost of m no shows Best overbooking strategy is one with minimum cost Example n=4: .05(800) + .08(600) + . . . + .04(400) + .01(480) = $239 Number of Reservations Overbooked No Proba- Shows bility 0 1 2 3 4 5 6 7 8 9 10 0 0.05 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.08 80 0 200 400 600 800 1000 1200 1400 1600 1800 0.10 160 80 0 200 400 600 800 1000 1200 1400 1600 0.15 240 160 80 0 200 400 600 800 1000 1200 1400 0.20 320 240 160 80 0 200 400 600 800 1000 1200 0.15 400 320 240 160 80 0 200 400 600 800 1000 0.11 480 400 320 240 160 80 0 200 400 600 800 0.06 560 480 400 320 240 160 80 0 200 400 600 0.05 640 560 480 400 320 240 160 80 0 200 400 0.04 720 640 560 480 400 320 240 160 80 0 200 0.01 800 720 640 560 480 400 320 240 160 80 0 Total Cost ($) 338 272 228 212 239 321 446 601 773 959 1156 LO 3

Multi-Period Models There are two general types of multi-period inventory systems Fixed–order quantity models Also called the economic order quantity, EOQ, and Q-model Event triggered Fixed–time period models Also called the periodic system, periodic review system, fixed-order interval system, and P-model Time triggered LO 5

Key Differences To use the fixed–order quantity model, the inventory remaining must be continually monitored In a fixed–time period model, counting takes place only at the review period The fixed–time period model Has a larger average inventory Favors more expensive items Is more appropriate for important items Requires more time to maintain LO 5

Fixed–Order Quantity and Fixed–Time Period Differences LO 5

Comparison for Fixed–Order Quantity and Fixed–Time Period Inventory Systems LO 5

Fixed-Order Quantity Model Models 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 LO 4

Basic Fixed–Order Quantity Model Lead time Place Order Receive order Use inventory LO 4

Basic Fixed-Order Quantity (EOQ) Model Formula Definitions of Symbols: TC = Total cost ($) H = Holding cost ($/unit) S = Setup cost ($/unit) Q = Order quantity (units) C = Cost/unit ($) D = Annual demand (units) R = Reorder point (units) L = Lead time (time units) Q Max Q Min D*C and LO 4 12

Annual Product Costs, Based on Size of the Order LO 4

Example 17.2 We wish to find the economic order quantity and the reorder point given annual demand of 1,000 units, ordering cost of $5 per order, holding costs of $1.25 per unit per year, a lead time of 5 days and per unit cost of $12.50. LO 4

Establishing Safety Stock Levels Safety stock: 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 LO 4

Fixed–Order Quantity Model with Safety Stock LO 5

Fixed–Order Quantity Model with Safety Stock Safety stock variable (based on Service Level) Where, = number of standard deviations for a given service probability = standard deviation of usage during the lead time See problems 24 & 25 LO 5

Example 17.4 LO 5

Fixed-Time Period Models LO 5 18

Fixed–Time Period Inventory Model LO 5

Example 17.5 Daily demand of 10 units Daily standard deviation of 3 units Review period of 30 days Lead time of 14 days Satisfying 98 percent of demand from items in stock 150 Units in inventory LO 5

Inventory Control and Supply Chain Management LO 6

Price Break Models Seller offers you incentive to buy more Price varies with the order size Two possibilities The Holding Cost is fixed Compute Q using H Find TC for Q and lower cost C Q corresponding to lowest-cost TC is opyimal LO 4

Example: Fixed Holding Cost Demand for tires at a local Goodyear Gemini service workshop is 12,000 units/year. Normal cost for tires is $30/unit. Orders between 100-499 will cost $27.75/unit, 500-999 will cost $25.5/unit, and 1000 units or more will cost $24/unit. Ordering cost is $150/order and holding cost is $5/unit/year. What policy should the company adopt? Q Cost/Unit 1. 1-99 $30.00 1. 2. 100-499 $27.75 2. Since 500<849<999 ignore 1 & 2 and compare 3 & 4? 3. 500-999 $25.50 « 849 » 4. 1000+ $24.00 TC $ TC+ TC+ Policy: Order 1000 at a time, at cost of $24/unit Q*

Price Break Models Holding cost is variable Sort prices from lowest to highest and calculate the order quantity for each price until a feasible order quantity is found If the first feasible order quantity is the lowest price, this is best, otherwise, calculate the total cost for the first feasible quantity and calculate total cost at each price lower than the first feasible order quantity LO 4

Example: Variable Holding Cost Suppose in the discount tire example that holding cost is charged at 18% of the cost of the tires. What policy should the company adopt? The Q could be infeasible The Q could be semi-feasible The Q could be feasible Q Cost/Unit $H/Unit 1. 1-99 $30.00 30.00(.18) = 5.40 2. 100-499 $27.75 27.75(.18) = 5.00 3. 500-999 $25.50 25.50(.18) = 4.59 866 4. 1000+ $24.00 24.00(.18) = 4.32 913 Semi-feasible & are infeasible Feasible Policy: Order 1000 at a time cost of $24/unit

Curves for Three Separate Order Quantity Models in a Three-Price-Break Situation LO 4

Example 17.8: The Data and Order Quantities i = 20 percent Cost per unit… 1-499 $5.00 500-999 $4.50 1,000 and up $3.90 LO 4

Example 17.8: The Solution LO 4

Example: Variable Holding Cost Flagstaff Products offers the following discount schedule for its 4’x8’ sheets of plywood. Order Quantity Unit Cost 9 Sheets or less $ 18.00 10 to 50 Sheets $ 17.50 More than 50 Sheets $ 17.25 Home Sweet Home Company (HSH) orders plywood from Flagstaff Products. HSH has an ordering cost of $45.00. The carrying cost is 20% of cost, and the annual demand is 100 sheets. What do recommend as the ordering policy for HSH? Infeasible Infeasible Feasible

Economic Production Quantity (EPQ) Product produced and consumed simultaneously Plant within a plant situation EOQ definitions apply plus: d = constant usage rate p = production rate EPQ = TC =

Example: EPQ A product, , is assembled with another component, , which is produced in another department at a rate of 100 units/day. The use rate for at assembly department is 40/day. Find optimal production order size, reorder point, and total cost if there are 250 working days/year, S=$50, H=$0.5/unit/year, P=$7/ , L=7 days, and D=10000. EPQ = R = dL = 40(7) = 280 units TC =

ABC Classification LO 2

ABC Classification Items kept in inventory are not of equal importance in terms of: dollars invested profit potential sales or usage volume stock-out penalties 30 60 A B C % of $ Value Use So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items

ABC Classification Based on Pareto Study The scheme 20% of people 80% of wealth (80/20 rule) Used in most areas of business The scheme Class A items Fewest in number—10-20% Highest in dollar value—70-80% Exercise greatest control here

ABC Classification The Scheme Natural break or company policy scheme Class B items Moderate in number--30-35% Moderate in dollar value--15-20% Exercise average control here Class C items Highest in number--about 50% Lowest in dollar value--5-10% Exercise the least control here Natural break or company policy scheme

Example: ABC Classification Use ABC method to classify the following five products in a company’s inventory. Annual Cost/ Item Demand Unit (1) (2) Item ADU (3) (4) 1 50 x $ 200 = 10000 1 3 80K 80% 80 2 10 x $ 200 = 2000 2 1 10K 10% 10 3 100 x $ 800 = 80000 3 4 5K 5% 15 4 50 x $ 100 = 5000 4 5 3K 3% 03 5 15 x $ 200 = 3000 5 2 2K 2% 05 $ 100,000 STEP A B C Steps for the ABC Classification Find annual dollar usage (ADU) for each item Rank ADU in descending order of magnitude Find percentage of usage to total inventory cost Find running sum of percentage of dollar usage and classify

Inventory Accuracy and Cycle Counting 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 LO 2 27

Rudolph Manufacturing Example: Rudolph Manufacturing H=$0.10 S=$50 C=$1 p=100 units Order Quantity units Holding $ Setup $ Total $ 1 2 3 4 # Production Runs 3 6 9 12 Time b/w Runs Then Or If Inventory $