12 Inventory Management PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Outline The Importance of Inventory Managing Inventory Functions of Inventory Types of Inventory Managing Inventory ABC Analysis Record Accuracy Cycle Counting Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs Inventory Models for Independent Demand The Basic Economic Order Quantity (EOQ) Model Minimizing Costs Reorder Points 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Learning Objectives Conduct an ABC analysis Explain and use cycle counting Explain and use the EOQ model for independent inventory demand Compute a reorder point and safety stock 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Inventory Management The objective of inventory management is to strike a balance between inventory investment and customer service 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Functions of Inventory To decouple or separate various parts of the production process To decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers To take advantage of quantity discounts To hedge against inflation 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Types of Inventory Raw material Work-in-process Purchased but not processed Work-in-process Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery and processes productive Finished goods Completed product awaiting shipment 05: Ch12 - Inventory Management (MGMT3102: Fall13)

ABC Analysis 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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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% 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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% 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 Figure 12.2 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Cycle Counting Items are counted and records updated on a periodic basis Often used with ABC analysis to determine cycle Has several advantages Eliminates shutdowns and interruptions Eliminates annual inventory adjustment Trained personnel audit inventory accuracy Allows causes of errors to be identified and corrected Maintains accurate inventory records 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Independent Versus Dependent Demand Independent demand - the demand for item is independent of the demand for any other item in inventory Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Holding, Ordering, and Setup Costs Holding costs - the costs of holding or “carrying” inventory over time Ordering costs - the costs of placing an order and receiving goods Setup costs - cost to prepare a machine or process for manufacturing an order 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Basic EOQ Model Important assumptions Demand is known, constant, and independent Lead time is known and constant Receipt of inventory is instantaneous and complete Quantity discounts are not possible Only variable costs are setup and holding Stockouts can be completely avoided 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Inventory Usage Over Time Inventory level Time Average inventory on hand Q 2 Usage rate Order quantity = Q (maximum inventory level) Minimum inventory Figure 12.3 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 Table 12.4(c) 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Robust Model The EOQ model is robust It works even if all parameters and assumptions are not met The total cost curve is relatively flat in the area of the EOQ 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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% 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

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 05: Ch12 - Inventory Management (MGMT3102: Fall13)

Safety Stock Purpose of Safety Stock Needed when demand is variable The level of safety stock is set based on the desired service level Safety stock is needed to cover uncertainty during the lead-time

In-Class Problems from the Lecture Guide Practice Problems Problem 1: What are the appropriate ABC groups of inventory items? ABC Analysis Stock Number Annual $ Volume Percent of Annual $ Volume J24 12,500 46.2 R26 9,000 33.3 L02 3,200 11.8 M12 1,550 5.8 P33 620 2.3 T72 65 0.2 S67 53 Q47 32 0.1 V20 30   S = 100.0 ABC Groups Class Items Annual Volume Percent of $ Volume A J24, R26 21,500 79.5 B L02, M12 4,750 17.6 C P33, T72, S67, Q47, V20 800 2.9   S = 100.0 05: Ch12 - Inventory Management (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems Assume you have a product with the following parameters: Demand = 360 Holding cost per year = $1.00 per unit Order cost = $100 per order What is the EOQ? Problem 4: Given the data from Problem 3, and assuming a 300-day work year; how many orders should be processed per year? What is the expected time between orders? Problem 5: What is the total cost for the inventory policy used in Problem 3? 05: Ch12 - Inventory Management (MGMT3102: Fall13)

In-Class Problems from the Lecture Guide Practice Problems If demand for an item is 3 units per day, and delivery lead-time is 15 days, what should we use for a re-order point? ROP = Demand during lead-time = 3*15 = 45 05: Ch12 - Inventory Management (MGMT3102: Fall13)