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Operations Management MD021

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**1. **Operations Management (MD021) Inventory Management

**2. **Agenda Inventory Definitions
Processes for Inventory Management
Economic Order Quantity Inventory Models
Reorder Point/Reorder Quantity Inventory Models
Single Period Inventory Models

**3. **Inventory Definitions

**4. **Inventory is a stock or store of goods

**5. **Each firm carries types of inventories relevant to its production demands Raw materials & purchased parts
Partially completed goods – called work in process (WIP)
Finished-goods inventories
manufacturing firms
Merchandise
retail stores

**6. **Each firm carries types of inventories relevant to its production demands Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers

**7. **Inventory is carried for many different reasons across different industries To meet anticipated demand
Meeting demand in a timely manner enhances customer satisfaction
Smooth production requirements across seasons
Produce one season, sell in next (or throughout year)
To decouple successive operations and maintain continuity of production
Protects against machine breakdowns
To protect against stock-outs
Vendors do not always deliver on time

**8. **Inventory is carried for many different reasons across different industries To take advantage of order cycles to minimize purchasing and inventory costs
Minimum order size requirements, full truck loads
To help hedge against price increases
Buy now at low price, store goods for future use
To permit operations to operate
Operations require a certain amount of WIP inventory
To take advantage of quantity discounts
Vendors often give discounts when ordering large quantities

**9. **Operations Strategy Having too much inventory is not good
Tends to hide problems
Makes it easier to live with (i.e. ignore) problems than to eliminate them
Costly to maintain large stocks of inventories
Opportunity costs of potentially doing something else with the money tied up in inventory
Wise objectives
Reduce lot sizes
Reduce safety stock
Reduce ordering costs and holding costs
These are difficult to calculate, and often underestimated, leading to higher order sizes

**10. **Objective of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs (costs of ordering and carrying inventory) within reasonable bounds

**11. **Processes for Inventory Management

**12. **An effective inventory management approach will have certain information A system to keep track of inventory on hand and on order
A reliable forecast of demand
Knowledge of order lead times and lead time variability
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system for inventory items

**13. **Inventory Counting Systems Periodic System
Physical count of items made at periodic intervals
Walgreens (1987) – manager walked around weekly, ordered everything needed across whole store
Perpetual Inventory System
System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
2005 – grocery store scanners (bar codes)
2005 – RFID-based systems

**14. **Perpetual inventory counting systems range from low-tech to high-tech Two-Bin System - Two containers of inventory; reorder when the first bin is empty
Universal Product Code (UPC) – Bar code printed on a label that has information about the item to which it is attached
Radio Frequency Identification (RFID) – Computer chip embedded in a label on side of package, cases, or pallets

**15. **Radio Frequency Identification (RFID) used in tags, chips, implants, and wristbands

**16. **RFID tags are activated by RFID reader devices

**17. **Example of RFID Use: Metro Future Store

**18. **Example of RFID Use: Metro Future Store

**19. **Lead time must be matched against expected demand Lead time: time interval between ordering and receiving the order
If we expect that demand will occur on a certain day in the future, we will need to place an order several days earlier, and account for:
Lead time
Lead time variability

**20. **Managers must estimate several types of inventory-related costs Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Annual cost of 20%-40% of value (unit price) of an item
Ordering costs: costs of ordering and receiving inventory
fixed dollar amount per order, regardless of order size
Shortage costs: costs when demand exceeds supply
difficult to calculate – often assumed

**21. **ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important
B - mod. important
C - least important

**22. **Cycle Counting A physical count of items in inventory. Counts are conducted periodically.
A items counted frequently
B items counted less frequently
C items counted least frequently
Cycle counting management trades off inventory accuracy against costs of counting
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?

**23. **Economic Order Quantity Inventory Models

**24. **Economic Order Quantity (EOQ) Models Economic order quantity (EOQ) model
Economic production quantity (EPQ) model
Quantity discount model

**25. **Assumptions of EOQ Model Only one product is involved
Annual demand requirements are known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

**26. **The Inventory Cycle

**27. **Total Cost Under the Economic Order Quantity Assumptions

**28. **Cost Minimization Goal

**29. **Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

**30. **Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal.

**31. **Economic Production Quantity (EPQ) Relevant when production is done in batches or lots
Capacity to produce a part exceeds the part’s usage or demand rate
Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

**32. **Economic Production Quantity (EPQ) Assumptions Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts

**33. **Economic Production Quantity (EPQ)

**34. **Economic Run Size

**35. **Quantity Discounts Volume (Per Unit) Discounts
1 to 49 = $10/unit
50 to 100 = $9/unit
100 and up = $8/unit
Case Discounts
Single units = $10/unit
Case of 10 = $90 = $9/unit

**36. **Quantity Discounting Total Costs with Purchasing Cost

**37. **Taking the derivative with respect to Q doesn’t change the EOQ formula

**38. **Total Cost with Constant Carrying Costs

**39. **Reorder Point, Reorder Quantity Inventory Models

**40. **Reorder point models Goal is to place an order when the amount of inventory on hand is still sufficient to satisfy demand during the time it takes to receive that order (i.e., the lead time)

**41. **When to Reorder with EOQ Ordering Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered
Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Service Level - Probability that demand will not exceed supply during lead time.

**42. **The reorder point leaves you with lead time inventory plus safety stock

**43. **How do we determine the reorder point quantity? Calculation accounts for …
The rate of demand
The lead time
Demand and/or lead time variability
Stock-out risk (safety stock)

**44. **Assuming demand and lead time are constant (as in EOQ) Reorder Point Quantity
ROP = d X LT
d = demand rate (units per time)
LT = lead time (in same units of time)
Example
Usage = 12 order forms/day
Lead time = 7 days
ROP = (12 forms/day)(7 days) = 84 order forms
Reorder when 84 order forms are left

**45. **When lead times are random, reorder point (ROP) must be adjusted

**46. **When we have an estimate of standard deviation of demand during lead time Example
Demand during lead time = 84 forms
sdLT = 2
ROP = 84 forms + zsdLT = 84 + 1.96(2) = 88 forms
Reorder when 88 order forms are left

**47. **When only demand is variable Example
Usage = 12 order forms/day; sd = 3
Lead time = 7 days
ROP = (12 forms/day)(7 days) + 1.96(7)0.5(3) = 84 + 15.5 = 90
Reorder when 90 order forms are left

**48. **When only lead time is variable Example
Usage = 12 order forms/day
Average Lead time = 7 days; sLT = 1
ROP = (12)(7) + 1.96(12)(1) = 84 + 24 = 108
Reorder when 108 order forms are left

**49. **When both demand and lead time are variable Example
Average Usage = 12 order forms/day; sd = 3
Average Lead time = 7 days; sLT = 1
ROP = (12)(7) + 1.96[(7)(9) + (144)(1)] = 84 + 1.96(14.4) = 84 + 27.7 = 112
Reorder when 112 order forms are left

**50. **Single Period Inventory Model (“The Newsboy Problem”)

**51. **Single Period Inventory Model Single period model: model for ordering of perishables and other items with limited useful lives
how many newspapers should a newsboy on a street corner stock for a specific day?
magazines
fresh fruits
fresh vegetables
seafood
cut flowers
commemorative t-shirts and souvenirs
spare parts

**52. **Single period model balances costs of a shortage against excess costs Shortage cost: generally the unrealized profits per unit (plus loss of customer goodwill)
Cshortage = Cs = revenue per unit – cost per unit
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period
Cexcess = Ce = original cost/unit – salvage value/unit

**53. **Single Period Model Continuous stocking levels
Demand can be approximated using a continuous distribution
Identifies optimal stocking levels
Optimal stocking level balances unit shortage and excess cost
Discrete stocking levels
Demand can be approximated using a discrete distribution
Service levels are discrete rather than continuous
Desired service level is equaled or exceeded

**54. **Continuous stocking level assuming a uniform demand distribution Service level represents the probability that demand will not exceed the stocking level

**55. **Continuous stocking level assuming a uniform demand distribution Example: The movie “Gigli 2” will be released soon. A (somewhat crazy) retailer wants to determine the number of commemorative t-shirts to stock. Based on the rousingly successful “Gigli”, we have:
Demand = uniform(1, 10)
Cost/unit = $5 per t-shirt
Revenue = $10 per t-shirt
Salvage value = $1 per t-shirt
Cs = revenue/unit – cost/unit = $10 - $5 = $5
Ce = cost/unit – salvage value/unit = $5 - $1 = $4
Service Level = Cs/(Cs+Ce) = ($5)/($5 + $4) = 0.555
The optimal stocking level must satisfy demand 55% of the time
Soptimal = 1 + 0.55(10-1) = 1 + 5 = 6 t-shirts

**56. **Discrete stocking levels involve inverse transform from service level to order units