1. Lecture 6
Inventory Management
Chapter 11

2. Economic Production Quantity (EPQ)
Economic production quantity (EPQ) model: variant of basic EOQ model
Production done in batches or lots
Replenishment order not received in one lump sum unlike basic EOQ model
Inventory is replenished gradually as the order is produced
hence requires the production rate to be greater than the demand rate
This model's variable costs are
annual holding cost, and
annual set-up cost (equivalent to ordering cost).
For the optimal lot size,
annual holding and set-up costs are equal.

3. EPQ = EOQ with Incremental Inventory Replenishment

4. EPQ Model Assumptions
Demand occurs at a constant rate of D items per year.
Production capacity is p items per year.
p > D
Set-up cost: $Co per run.
Holding cost: $Ch per item in inventory per year.
Purchase cost per unit is constant (no quantity discount).
Set-up time (lead time) is constant.
Planned shortages are not permitted.

5. EPQ Model Formulae Optimal production lot-size (formula 11-16 of book)
Run time: Q */p
Time between set-ups (cycle time): Q */D years
Total cost (formula of book)

6. Example: Non-Slip Tile Co.
Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tiles annually.
The set-up cost is $5,000 per run
Holding cost is estimated at 10% of the manufacturing cost of $1 per tile.
The production capacity of the machine is 500,000 tiles per month.
The factory is open 365 days per year.
Determine
Optimal production lot size
Annual holding and setup costs
Number of setups per year
Loss/profit that NST is incurring annually by using their present production schedule

7. Management Scientist Solutions
Optimal TC = $28,868
Current TC = (100,000) + 5,000,000,000/100,000
= $54,167
LOSS = 54, ,868 = $25,299

8. Economic Production Quantity Assumptions
Only one item is involved 
Annual demand is known 
Usage rate is constant 
Usage occurs continually
Production occurs periodically
Production rate is constant
Lead time does not vary 
No quantity discounts 

9. Operations Strategy Too much inventory Wise strategy
Tends to hide problems
Easier to live with problems than to eliminate them
Costly to maintain
Wise strategy
Reduce lot sizes
Reduce safety stock

10. The Balance Sheet – Dell Computer Co.

11. Income Statement – Dell Computer Co.
(in millions, except per share amount)
28-Jan-00
29-Jan-99
Net revenue
$25,265
$18,243
Cost of revenue
20,047
14,137
Gross margin
5,218
4,106
Operating expenses:
Selling, general and administrative
2,387
1,788
Research, development, and engineering
568
272
Total operating expenses
2,955
2,060
Operating income
2,263
2,046
Other income
188 38
Income before income taxes
2,451
2,084
Provision for income taxes
785
624
Net income
$1,666
$1,460
Earnings per common share:
Basic
$0.66
$0.58
Diluted
$0.61
$0.53
Weighted average shares outstanding:
2,536
2,531
2,728
2,772
Retained Earnings:
Balances at beginning of period
606
607
1,666
1,460
Repurchase of common stocks
(1,012)
(1,461)
Balances at end of period
$1,260
$606
Fiscal Year Ended

12. Debt Ratio
What It Measures: The extent to which a firm uses debt financing
How You Compute: The ratio of total debt to total assets

13. Inventory Turnover Ratio
What It Measures: How effectively a firm is managing its inventories.
How You Compute: This ratio is computed by dividing sales by inventories
Inventory turnover ratio =

14. Lecture 6
MGMT 650
Simulation – Chapter 13

15. Simulation Is … Simulation – very broad term
methods and applications to imitate or mimic real systems, usually via computer
Applies in many fields and industries
Simulation models complex situations
Models are simple to use and understand
Models can play “what if” experiments
Extensive software packages available
ARENA, ProModel
Very popular and powerful method

16. Applications Manufacturing facility Bank operation
Airport operations (passengers, security, planes, crews, baggage, overbooking)
Hospital facilities (emergency room, operating room, admissions)
Traffic flow in a freeway system
Waiting lines - fast-food restaurant, supermarkets
Emergency-response system
Military

17. Example – Simulating Machine Breakdowns
The manager of a machine shop is concerned about machine breakdowns.
Historical data of breakdowns over the last 100 days is as follows
Simulate breakdowns for the manager for a 10-day period
Number of Breakdowns
Frequency 10 1 30 2 25 3 20 4 5

18. Simulation Procedure
Expected number of breakdowns = 1.9 per day

19. Statistical Analysis
95 % confidence interval for mean breakdowns for the 10-day period is given by:

20. Monte Carlo Simulation
Monte Carlo method: Probabilistic simulation technique used when a process has a random component
Identify a probability distribution
Setup intervals of random numbers to match probability distribution
Obtain the random numbers
Interpret the results

21. Example 2 – Simulating a Reorder Policy
The manager of a truck dealership wants to acquire some insight into how a proposed policy for reordering trucks might affect order frequency
Under the new policy, 2 trucks will be ordered every time the inventory of trucks is 5 or lower
Due to proximity between the dealership and the local office, orders can be filled overnight
The “historical” probability for daily demand is as follows
Simulate a reorder policy for the dealer for the next 10 days
Assume a beginning inventory of 7 trucks
Demand (x)
P(x)
0.50 1
0.40 2
0.10

22. Example 2 Solutions

23. In-class Example 3 using MS-Excel
The time between mechanics’ requests for tools in a AAMCO facility is normally distributed with a mean of 10 minutes and a standard deviation of 1 minute.
The time to fill requests is also normal with a mean of 9 minutes and a standard deviation of 1 minute.
Mechanics’ waiting time represents a cost of $2 per minute.
Servers represent a cost of $1 per minute.
Simulate arrivals for the first 9 mechanic requests and determine
Service time for each request
Waiting time for each request
Total cost in handling all requests
Assume 1 server only

24. AAMCO Solutions

25. Simulation Models Are Beneficial
Systematic approach to problem solving
Increase understanding of the problem
Enable “what if” questions
Specific objectives
Power of mathematics and statistics
Standardized format
Require users to organize

26. Different Kinds of Simulation
Static vs. Dynamic
Does time have a role in the model?
Continuous-change vs. Discrete-change
Can the “state” change continuously or only at discrete points in time?
Deterministic vs. Stochastic
Is everything for sure or is there uncertainty?
Most operational models:
Dynamic, Discrete-change, Stochastic

27. Discrete Event Simulation Example 1 - A Simple Processing System

28. Advantages of Simulation
Solves problems that are difficult or impossible to solve mathematically
Flexibility to model things as they are (even if messy and complicated)
Allows experimentation without risk to actual system
Ability to model long-term effects
Serves as training tool for decision makers

29. Limitations of Simulation
Does not produce optimum solution
Model development may be difficult
Computer run time may be substantial
Monte Carlo simulation only applicable to random systems

30. Fitting Probability Distributions to Existing Data
Data Summary
Number of Data Points = 187
Min Data Value = 3.2
Max Data Value = 12.6
Sample Mean = 6.33
Sample Std Dev = 1.51
Histogram Summary
Histogram Range = 3 to 13
Number of Intervals = 13

31. ARENA – Input Analyzer Distribution Summary Distribution: Gamma
Expression: 3 + GAMM(0.775, 4.29)
Square Error:
Chi Square Test
Number of intervals = 7
Degrees of freedom = 4
Test Statistic = 4.68
Corresponding p-value = 0.337
Kolmogorov-Smirnov Test
Test Statistic =
Corresponding p-value > 0.15
Data Summary
Number of Data Points = 187
Min Data Value = 3.2
Max Data Value = 12.6
Sample Mean = 6.33
Sample Std Dev = 1.51
Histogram Summary
Histogram Range = 3 to 13
Number of Intervals = 13

32. Simulation in Industry

33. Course Conclusions
Recognize that not every tool is the best fit for every problem
Pay attention to variability
Forecasting
Inventory management - Deliveries from suppliers
Build flexibility into models
Pay careful attention to technology
Opportunities
Improvement in service and response times
Risks
Costs involved
Difficult to integrate
Need for periodic updates
Requires training
Garbage in, garbage out
Results and recommendations you present are only as reliable as the model and its inputs
Most decisions involve tradeoffs
Not a good idea to make decisions to the exclusion of known information