decision analysis

1
Lecture
5
MGMT 650 Inventory Models Chapter 11
2
Announcements

• HW 3 solutions and grades posted in BB
• HW 3 average 134.4 (out of 150)
• Final exam next week
• Open book, open notes.
• Final preparation guide posted in BB
• Proposed class structure for next week
• Lecture 600 750
• Class evaluations 750 800
• Break 800 830
• Final 830 945

3
Inventory Management In-class Example

• Number 2 pencils at the campus book-store are
  sold at a fairly steady rate of 60 per week. It
  cost the bookstore 12 to initiate an order to
  its supplier and holding costs are 0.005 per
  pencil per year.
• Determine
• The optimal number of pencils for the bookstore
  to purchase to minimize total annual inventory
  cost,
• Number of orders per year,
• The length of each order cycle,
• Annual holding cost,
• Annual ordering cost, and
• Total annual inventory cost.
• If the order lead time is 4 months, determine the
  reorder point.
• Illustrate the inventory profile graphically.
• What additional cost would the book-store incur
  if it orders in batches of 1000?

4
Management Scientist Solutions
5
Management Scientist Solutions Chapter 11
Problem 4
EOQ

(Time between placing 2 consecutive orders - in
days)
6
EOQ with Quantity Discounts

• The EOQ with quantity discounts model is
  applicable where a supplier offers a lower
  purchase cost when an item is ordered in larger
  quantities.
• This model's variable costs are
• annual holding,
• Ordering cost, and
• purchase costs.
• For the optimal order quantity, the annual
  holding and ordering costs are not necessarily
  equal.

7
EOQ with Quantity Discounts

• Assumptions
• Demand occurs at a constant rate of D
  items/year.
• Ordering Cost is Co per order.
• Holding Cost is Ch CiI per item in inventory
  per year
• note holding cost is based on the cost of the
  item, Ci
• Purchase Cost (C)
• C1 per item if quantity ordered is between 0 and
  x
• C2 if order quantity is between x1 and x2 , etc.
• Lead time is constant

8
EOQ with Quantity Discounts

• Formulae
• Optimal order quantity the procedure for
  determining Q will be demonstrated
• Number of orders per year D/Q
• Time between orders (cycle time) Q /D years
• Total annual cost (formula 11.28 of book)
• (holding ordering
  purchase)

9
Example EOQ with Quantity Discount

• Walgreens carries Fuji 400X instant print film
• The film normally costs Walgreens 3.20 per roll
• Walgreens sells each roll for 5.25
• Walgreens's average sales are 21 rolls per week
• Walgreenss annual inventory holding cost rate is
  25
• It costs Walgreens 20 to place an order with
  Fujifilm, USA
• Fujifilm offers the following discount scheme to
  Walgreens
• 7 discount on orders of 400 rolls or more
• 10 discount for 900 rolls or more, and
• 15 discount for 2000 rolls or more
• Determine Walgreens optimal order quantity

10
Management Scientist Solutions
11
Economic Production Quantity (EPQ)

• The economic production quantity model is a
  variant of basic EOQ model
• Production done in batches or lots
• A replenishment order is 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.

12
EPQ EOQ with Incremental Inventory Replenishment
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EPQ Model Assumptions

• Demand occurs at a constant rate of D items per
  year.
• Production rate is P items per year (and 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.

14
EPQ Model Formulae

• Optimal production lot-size (formula 11.16 of
  book)
• Q 2DCo /(1-D/P )Ch
• Number of production runs per year D/Q
• Time between set-ups (cycle time) Q /D years
• Total annual cost (formula 11.14 of book)
• (1/2)(1-D/P )Q Ch DCo/Q
• (holding ordering)

15
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 tile
  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 factor 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

16
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

17
Lecture
5
Forecasting Chapter 16
18
Forecasting - Topics

• Quantitative Approaches to Forecasting
• The Components of a Time Series
• Measures of Forecast Accuracy
• Using Smoothing Methods in Forecasting
• Using Trend Projection in Forecasting

19
Time Series Forecasts

• Trend - long-term movement in data
• Seasonality - short-term regular variations in
  data
• Cycle wavelike variations of more than one
  years duration
• Irregular variations - caused by unusual
  circumstances
• Random variations - caused by chance

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Forecast Variations
Irregularvariation
Trend
Cycles
90
89
88
Seasonal variations
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Smoothing Methods

• In cases in which the time series is fairly
  stable and has no significant trend, seasonal, or
  cyclical effects, one can use smoothing methods
  to average out the irregular components of the
  time series.
• Four common smoothing methods are
• Moving averages
• Weighted moving averages
• Exponential smoothing

22
Example of Moving Average

• Sales of gasoline for the past 12 weeks at your
  local Chevron (in 000 gallons). If the dealer
  uses a 3-period moving average to forecast sales,
  what is the forecast for Week 13?

• Past Sales
• Week Sales Week
  Sales
• 1 17
  7 20
• 2 21
  8 18
• 3 19
  9 22
• 4 23
  10 20
• 5 18
  11 15
• 6 16 12 22

23
Management Scientist Solutions

MA(3) for period 4 (172119)/3 19
Forecast error for period 3 Actual Forecast
23 19 4
24
MA(5) versus MA(3)
25
Exponential Smoothing

• Premise - The most recent observations might have
  the highest predictive value.
• Therefore, we should give more weight to the more
  recent time periods when forecasting.

Ft1 Ft ?(At - Ft)
26
Linear Trend Equation
Suitable for time series data that exhibit a long
term linear trend
Ft
Ft a bt
a

• Ft Forecast for period t
• t Specified number of time periods
• a Value of Ft at t 0
• b Slope of the line

0 1 2 3 4 5 t
27
Linear Trend Example
Linear trend equation
F11 20.4 1.1(11) 32.5
Sale increases every time period _at_ 1.1 units
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Actual vs Forecast
Linear Trend Example
35
30
25
20
Actual
Actual/Forecasted sales
15
Forecast
10
5
0
1
2
3
4
5
6
7
8
9
10
Week
F(t) 20.4 1.1t
29
Measure of Forecast Accuracy

• MSE Mean Squared Error

30
Forecasting with Trends and Seasonal Components
An Example

• Business at Terry's Tie Shop can be viewed as
  falling into three distinct seasons (1)
  Christmas (November-December) (2) Father's Day
  (late May - mid-June) and (3) all other times.
• Average weekly sales () during each of the three
  seasons
• during the past four years are known and given
  below.
• Determine a forecast for the average weekly sales
  in year 5 for each of the three seasons.
• Year
• Season 1 2
  3 4
• 1 1856 1995
  2241 2280
• 2 2012 2168
  2306 2408
• 3 985 1072
  1105 1120

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Management Scientist Solutions

32
Interpretation of Seasonal Indices

• Seasonal index for season 2 (Fathers Day)
  1.236
• Means that the sale value of ties during season 2
  is 23.6 higher than the average sale value over
  the year
• Seasonal index for season 3 (all other times)
  0.586
• Means that the sale value of ties during season 3
  is 41.4 lower than the average sale value over
  the year

33
Lecture
5
Decision Analysis Chapter 14
34
Decision Environments

• Certainty - Environment in which relevant
  parameters have known values
• Risk - Environment in which certain future events
  have probabilistic outcomes
• Uncertainty - Environment in which it is
  impossible to assess the likelihood of various
  future events

35
Decision Making under Uncertainty

• Maximin - Choose the alternative with the best of
  the worst possible payoffs
• Maximax - Choose the alternative with the best
  possible payoff

36
Payoff Table An Example
Possible Future Demand
Low Moderate High
Small facility 10 10 10
Medium facility 7 12 12
Large facility - 4 2 16
Values represent payoffs (profits)
37
Maximax Solution

Note choose the minimize the payoff option if
the numbers in the previous slide represent costs
38
Maximin Solution

39
Minimax Regret Solution

40
Decision Making Under Risk - Decision Trees
41
Decision Making with Probabilities

• Expected Value Approach
• Useful if probabilistic information regarding the
  states of nature is available
• Expected return for each decision is calculated
  by summing the products of the payoff under each
  state of nature and the probability of the
  respective state of nature occurring
• Decision yielding the best expected return is
  chosen.

42
Example Burger Prince

• Burger Prince Restaurant is considering opening a
  new restaurant on Main Street.
• It has three different models, each with a
  different seating capacity.
• Burger Prince estimates that the average number
  of customers per hour will be 80, 100, or 120
  with a probability of 0.4, 0.2, and 0.4
  respectively
• The payoff (profit) table for the three models is
  as follows.
• s1 80 s2 100 s3 120
• Model A 10,000 15,000
  14,000
• Model B 8,000 18,000
  12,000
• Model C 6,000 16,000
  21,000
• Choose the alternative that maximizes expected
  payoff

43
Decision Tree
Payoffs
.4
s1
10,000
.2
s2
2
15,000
s3
.4
d1
14,000
.4
s1
8,000
d2
1
.2
3
s2
18,000
s3
d3
.4
12,000
.4
s1
6,000
4
s2
.2
16,000
s3
.4
21,000
44
Management Scientist Solutions