decision analysis

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 gt 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 11.15 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 .04167(100,000)
  5,000,000,000/100,000
• 54,167
• LOSS 54,167 - 28,868 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
• 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.
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
0 10
1 30
2 25
3 20
4 10
5 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 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 SimulationExample 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 0.003873 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
0.0727 Corresponding p-value gt 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