Managerial Decision Modeling with Spreadsheets

1. Managerial Decision Modeling with Spreadsheets Chapter 12 Inventory Control Models

2. Learning Objectives • Understand importance of inventory control. • Use Economic Order Quantity (EOQ) model to determine how much to order. • Compute reorder point (ROP) in determining when to order more inventory. • Use EOQ with non-instantaneous receipt model to determine how much to order or produce. • Handle EOQ problems that allow quantity discounts. • Understand use of safety stock with known and unknown stockout costs. • Understand importance of ABC inventory analysis.

3.  12.1 Introduction • Inventory is one of most expensive and important assets to many companies. • Managers have long recognized good inventory control is crucial.

4. 12.2 Importance Of Inventory Control • Inventory control serves several important functions and adds flexibility to firm’s operations. • Five main uses of inventory are: •   1.  Decoupling function. • 2.  Storing resources. • 3.  Irregular supply and demand. • 4.  Quantity discounts. • 5.  Avoiding stockouts and shortages.

5. 12.3 Inventory Control Decisions • Fundamental decisions made when controlling inventory: •   1.      How much to order • 2.      When to order •  Inventory model is utilized to determine how much to order and when to order.

6. 12.3 Inventory Control Decisions • Major objective in controlling inventory is to minimize total inventory costs: • 1.      Cost of items. • 2.      Cost of ordering.        • 3.      Cost of carrying, or holding, inventory. • 4.      Cost of stockouts. • 5.      Cost of safety stock, additional inventory held • to help avoid stockouts.

7. Inventory Cost Factors

8. 12.4 Economic Order Quantity (EOQ): Determining How Much To Order • Economic Order Quantity Model Assumptions: • Demand is known and constant. • Lead time - time between placement of and receipt of the order is known and constant. • Receipt of inventory is instantaneous. • Quantity discounts are not possible. • Only variable costs are cost of placing an order, ordering cost, and cost of holding or storing inventory over time, holding or carrying cost. • If orders are placed at right time, stockouts or shortages can be avoided completely.

9. Inventory Usage Over Time

10. Ordering and Inventory Costs • Objective of inventory models is to minimize total costs. • With assumptions given, significant costs are ordering cost and carrying cost.

11. Ordering and Inventory Costs • Total Cost as Function of Order Quantity

12. Ordering and Inventory Costs • Average inventory on hand is:  • Average inventory level = ( 0 + Q ) / 2 = Q / 2 • Other inventory parameters are: • Q* = Optimal order quantity (i.e., EOQ). • D = Annual demand in units for inventory item. • Co = Ordering cost per order. • Ch = Holding or carrying cost per unit per year. • P = Purchase cost per unit of inventory item. • Holding cost could be constant or calculated as cost of capital: • Ch = I x P

13. Inventory Costs and EOQ • Total ordering cost = ( D / Q ) x Co • Total carrying cost = ( Q / 2 ) x Ch • Total cost = Total ordering cost + Total carrying cost + Total purchase cost • = ( D / Q ) x Co + ( Q / 2 ) x Ch + P x D • Economic Order Quantity is:

14. Plot of Costs Versus Order Quantity Sumco Pump Company

15. 12.5 Reorder Point: Determining When To Order • Second inventory question is when to order. • Time between placing and receipt of an order, called lead time or delivery time, is often few days or few weeks. • When to order decision is usually expressed in terms of reorder point (ROP), inventory level at which an order should be placed. • Reorder point, ROP, is given as:  • ROP = (demand per day) x (lead time in days) • = d x L • Demand, d, expressed in units demanded per day and lead time, L, expressed in days.

16. Reorder Point Curve

17. Reorder Point Sumco Pump Company • Recall EOQ = 200 and total cost of $5,100. • Calculations based on annual demand of 1,000 units, ordering cost of $10 per order, annual carrying cost of $0.50 per unit, and purchase cost of $5 per pump housing. • Assume lead time of 3 business days between time firm places an order and time order is received. • Assume there are 250 business days in year. • To calculate reorder point, first determine daily demand rate, d. • Since there are 250 business days in year and annual demand is 1,000, daily demand rate is 4 (= 1,000 / 250) pump housings.

18. 12.6 EOQ With Non-instantaneous Receipt • Firm may build up inventory gradually over period of • time. • Example, firm may receive shipments from suppliers uniformly over period of time. • Or firm may be producing at rate of p per day and simultaneously selling at rate of d per day • (where p > d). • Average inventory level = [ 0 + Q ( 1 - d / p )] / 2 = • = Q ( 1 - d / p ) / 2

19. 12.6 EOQ With Non-instantaneous Receipt • Or firm may be producing at rate of p per day and simultaneously selling at rate of d per day • (where p > d). • Avg. inventory level = Q (1 - d / p) / 2

20. Finding Economic Production Quantity • Parameters are: • Q* = Optimal order or production quantity (EPQ) • Cs = Setup cost per setup •  For given order quantity Q: • Total setup cost = ( D / Q ) x Cs • Total carrying cost = [ Q ( 1- d / p) / 2 ] x Ch • Total cost = Total setup cost + Total carrying cost + Total production cost • = (D / Q) x Cs + [Q (1- d / p) / 2] x Ch + P x D •  Calculate EPQ as: 

21. Brown Manufacturing Example • Produces mini-sized refrigeration packs in batches. • Estimated demand for year is 10,000 units. • Operates for 167 business days each year. • Annual demand translates to daily demand rate of 60 units per day. • It costs about $100 to set up manufacturing process, and carrying cost is $0.50 per unit per year. • When production process has been set up, 80 refrigeration packs can be manufactured daily. • Each pack costs $5 to produce. • How many packs should Brown produce in each batch?

22. EPQ Model Brown Manufacturing • Calculates and reports EPQ as well as following output measures: • maximum inventory (= Q*[1- d /p]) • average inventory (= Q*[1- d /p] / 2) • number of setups (= D / Q*) • total holding cost (= Ch x Q*[1- d /p] / 2) • total setup cost (= Cs x D / Q*) • total purchase cost (= P x D) • total cost (= Ch x Q*[1- d /p] / 2 + Cs x D /Q* + P x D)

23. EPQ Model Brown Manufacturing • Total setup cost = total carrying cost ($250 each). • EPQ: Q* = 4,000 units. • Total cost, including production cost of $50,000, is $50,500.

24. Inventory Costs Plot Brown Manufacturing

25. 12.7 Quantity Discount Models • To increase sales, companies offer quantity discounts to customers. • Quantity discount is simply reduced cost for item when purchased in larger quantities. • It is common to have discount schedule with several discounts for large orders. • Total cost = Total ordering cost + Total carrying cost • Total purchase cost = (D/Q) x Co + (Q/2) x Ch + P x D • Find EOQ that incorporates cost with discount to minimize total cost.

26. 12.7 Quantity Discount Models • Find EOQ that incorporates cost with discount to minimize total cost.

27. Four Steps to Analyze Quantity Discount Models • For each discount price, calculate a Q* value using EOQ formula. • For any discount level, if Q* computed in Step 1 is too low to qualify for discount, adjust Q* upward to lowest quantity that qualifies for discount. • Using total cost equation,compute total cost for every Q* determined in steps 1 and 2. • If Q* had to be adjusted upward because it was below allowable quantity range, be sure to use adjusted Q* value. • Select Q* with lowest cost as computed in Step 3. • It will be order quantity to minimize total cost.

28. Total Cost Curve for Quantity Discount Model

29. Brass Department Store Example • Stocks toy cars. • Store given quantity discount schedule for cars as shown in Table 12.2. • Normal cost for cars is $5. • For orders between 1,000 and 1,999 units, unit cost is $4.80, and for orders of 2,000 or more units, unit cost is $4.75. • Ordering cost is $49 per order, annual demand is 5,000 race cars, and inventory carrying charge as percentage of cost, I, is 20% or 0.2. • What order quantity will minimize total cost?

30. Plot of Total Cost Versus Order Quantity Brass Department Store

31. 12.8 Use Of Safety Stock

32. 12.9 ABC Analysis • Recognizes fact some inventory items are more important than others. • Purpose of analysis is to divide all of company's inventory items into three groups: A, B, and C. • Depending on group, decide how inventory levels should be controlled.

33. Silicon Chips, Inc. Example • Maker of super-fast DRAM chips, has organized its 10 inventory items on an annual dollar-volume basis. • Parts are identified by item number, part number, annual demands, and unit costs. • How should company classify items into groups A, B, and C?

34. Silicon Chips, Inc. Example • How should company classify items into groups A, B, and C?

35. Summary • Focus was to answer two questions in inventory planning: (1) how much to order, and • (2) when to order. • EOQ makes a number of assumptions: • (1) known and constant demand and lead times. • (2) instantaneous receipt of inventory. • (3) no quantity discounts. • (4) no stockouts or shortages. • (5) only variable costs are ordering and carrying • costs.

36. Summary • If assumptions do not hold, more complex models are needed: • (1) economic production quantity. • (2) quantity discount models. • Discussed computation of safety stocks when demand during lead time was unknown for two cases: • (1) cost of stockout is known. • (2) cost of stockout is unknown. • Presented ABC analysis to determine how inventory items should be classified based on their importance and value.