1. Inventory Management for Independent Demand Chapter 12

2. MGMT 326 Foundations of Operations Introduction Strategy Managing Projects Quality Assurance Facilities Planning & Control Products & Processes Product Design Process Design Managing Quality Statistical Process Control Just-in-Time & Lean Systems Facility Location Facility Layout Managing Inventory

3. Objectives of Inventory Management Maintain good customer service Keep costs as low as possible, consistent with the required level of customer service Minimize inventory investment

4. Types of Demand Dependent Demand Demand for raw materials, component parts, and subassemblies used to make a finished product Both the amount of demand and the date required depend on the production schedule

5. Types of Demand (2) Independent Demand Any demand that is not used to meet a production schedule is called independent demand Examples of independent demand: finished goods; retail and distributor inventories; service inventories; maintenance, repair, and operating (MRO) inventories MRO includes fuels, repair parts, office supplies, cleaning supplies

6. Dependent and Independent Demand: Types of Inventory Dependent demand: used to meet a production schedule in manufacturing Independent demand: not used to meet a production schedule Work-in-process (WIP) Raw materials Component parts Manufacturer Service Company Finished goods MRO Retail and distributor inventories Service inventories MRO

7. Relevant Inventory Costs Measurable Cost of Inventory = Item Costs Holding Costs Order Costs for purchased items OR Setup Costs for items made by your company Shortage costs: Administrative & transportation costs related to back orders +++ Shortages and back orders result in lost sales and lost goodwill. These costs are relevant but hard to measure.

8. Item Costs Item costs For purchased items, the item cost is the purchase price, plus shipping For work in process, the item cost is the cost of materials and labor used in the item For finished goods, the item cost is the cost of goods sold.

9. Inventory Holding Costs Inventory holding costs include capital costs, storage costs, and risk costs Capital costs: If inventory is financed with borrowed money, the capital cost is the interest rate paid If inventory is financed from retained earnings, the capital cost is the opportunity cost of not putting the money into other investments Storage costs: the costs of space, people, and equipment used in inventory storage

10. Inventory Holding Costs (2) Risk costs: cost of taxes and insurance on inventory, damage, obsolescence, and theft Inventory holding costs are usually computed as a percentage of item costs

11. Ordering and Setup Costs For purchased items, ordering costs are the fixed costs associated with placing an order with a supplier For items made internally, setup costs are used instead of order costs. The setup cost is the cost of work that must be done before production actually begins.

12. Shortage Costs Administrative and transportation costs related to back orders Lost good will and lost sales due to product shortages – hard to measure

13. Inventory Management Policies An inventory management policy should determine How much to order When to order

14. Fixed Order Quantity Method An inventory policy for independent demand. Based on the following rules: 1. Order the same amount, Q, each time Q is called the order quantity 2. Place an order when the amount in inventory gets down to the reorder point, R Compute Q and R for each item.

15. Fixed Order Quantity Method (2) Relevant Costs Assume Quantity discounts are not available Orders are placed early enough that shortages do not occur Relevant costs Order costs Inventory holding costs

16. Fixed Order Quantity Method (3) Notation Q = order quantity D = annual demand for the item S = cost of placing one order H = inventory holding cost per unit per year (commonly called holding cost) L = lead time (time between order placement and order receipt) R = reorder point TC = annual cost of placing orders + annual cost of holding inventory

17. Fixed Order Quantity Method (4) Annual Cost of Placing Orders Annual cost of placing orders = (orders per year) (cost of 1 order)

18. Fixed Order Quantity Method (5) Annual Inventory Cost Figure 12.2, page 430 Given: D = annual demand = 10,400 Weekly demand = 200 L = lead time = 1 week Q = order quantity = 600 Average inventory = (Q/2) = 600/2 = 300 Inventory cost =

19. Fixed Order Quantity Method (5)

20. Economic Order Quantity The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding inventory (TC).

21. Economic Order Quantity (2) Demand (D) is known and constant H is known and constant Order costs (S) are constant The order quantity arrives in a single shipment No quantity discounts are available All demand will be met (no shortages)

22. We want to minimize TC D, S, and H are constant. TC is a function of Q.

23. Economic Order Quantity (3) Let Q * be the economic order quantity. Then For Q *, annual order cost = annual inventory cost

24. Simple Reorder Point Use this method when daily demand is constant. R = reorder point d = daily demand (may have to compute this) L = lead time (Caution: if lead time is given in weeks, convert this to days). R = dL

25. Reorder Point with Safety Stock R = dL+SS Safety stock (SS) is extra inventory that is kept to meet unexpected demand. Reorder point without safety stock Reorder point with safety stock

26. Reorder Point with Safety Stock (2) How much safety stock (SS) ? Service level is the probability of having enough inventory to meet demand during lead time The probability of a stockout is (1-service level) Demand during lead time is normally distributed with mean dL and standard deviation  dL z is the number of standard deviations required to meet the desired service level SS = z  dL Reorder point with safety stock: R = + z  dL

27. Reorder Point with Safety Stock (3) Example Given D = annual demand = 10,000 N = number of business days per year = 250 The company operates 5 days per week = average daily demand  dL = standard deviation of demand during lead time = 20 L = lead time = 1 week Service level = 96% Find: reorder point with safety stock: R = + z  dL

28. Reorder Point with Safety Stock (4) Solving the Problem 1. If average daily demand ( ) is not given, compute it. Note: = D/N and D = = 10,000/250 = 40 2. If the lead time is given in weeks or months, compute lead time in days. L = 1 week = 1(5) = 5 days Note: 1 week is the number of days per week that the company operates. This may be 5, 6, or 7.

29. Reorder Point with Safety Stock (5) Solving the Problem (2) 3. Find the z value for the service level (96%) Probability of a stockout = 1 – service level = 4% z 50%46% Appendix B gives this area.

30. Reorder Point with Safety Stock (6) Solving the Problem (3) 3. Find the z value for the service level (96%) (cont.) (a) Write the service level as a decimal 96% = 0.9600 (b) Subtract 0.5000 from the service level 0.9600 – 0.5000 = 0.4600 (c) Use the table in Appendix B, page 650, to find the area that is closest to 0.9600 The closest area in the table is 0.4599, which occurs when z = 1.75 Use z = 1.75

31. Reorder Point with Safety Stock (6) Solving the Problem (4) 4. Compute R R = L+ z  dL = 40(5) + 1.75(20) = 200 + 35 = 235 Note: If the computation gives a fractional value, round up to nearest integer. Example: Computed R = 210.2  R = 2.11

32. Economic Production Quantity Key question: How many units of a part or product should be made at one time? The economic production quantity (EPQ) is the production quantity (lot size) that minimizes the total annual cost of setups and holding inventory.

33. Economic Production Quantity (2) Notation Q = Amount to make (lot size) D = annual demand for the item d = daily demand for the item p = daily production rate S = cost of one setup H = inventory holding cost per unit per year (commonly called holding cost) TC = annual cost of setups + annual cost of holding inventory The EPQ is the quantity that minimizes TC

34. Economic Production Quantity (3) Assumption: Daily demand < daily production. When the item is being made, some is sold or used to make a product. The remainder goes into inventory. When production stops, the inventory is used until there is no inventory left. Then production resumes. Ending inventory = beginning inventory + production - sales or usage

35. Economic Production Quantity (4) Length of production run = Q/p During production, d units are sold or used each day. (p – d) units go into inventory. Maximum inventory: Total cost: Economic production quantity (EPQ):

36. Economic Production Quantity (5) When to use economic order quantity (EOQ): Demand is independent Compute how much to order (order quantity) When to use economic production quantity (EPQ): Parts or products will be produced – demand is dependent Compute how much to make at one time (production lot size)