OPSM 501: Operations Management

1
OPSM 501 Operations Management
Koç University Graduate School of Business MBA
Program

• Week 11
• The Newsvendor Problem-ways to avoid mismatch

Zeynep Aksin zaksin_at_ku.edu.tr
2
Hammer 3/2 timeline and economics

• Economics
• Each suit sells for p 180
• TEC charges c 110 per suit
• Discounted suits sell for v 90

• The too much/too little problem
• Order too much and inventory is left over at the
  end of the season
• Order too little and sales are lost.
• Marketings forecast for sales is 3200 units.

3
The demand-supply mismatch cost

• Definition the demand supply mismatch cost
  includes the cost of left over inventory (the
  too much cost) plus the opportunity cost of
  lost sales (the too little cost)
• The maximum profit is the profit without any
  mismatch costs, i.e., every unit is sold and
  there are no lost sales
• The mismatch cost can also be evaluated with

Mismatch cost Maximum profit Expected profit
4
Revisit Example 3

• Manufacturing cost60TL,
• Selling price80TL, Discounted price (at the end
  of the season)50TL
• Market research gave the following probability
  distribution for demand.
• Find the optimal q, expected number of units sold
  for this orders size, and expected profit, for
  this order size.

Demand Probability 500 0.10 600 0.2 700 0.2 80
0 0.2 900 0.10 1000 0.10 1100 0.10
P(Dltn-1) 0 0.1 0.3 0.5 0.7 0.8 0.9
Cu20 Co10 P(Dltn-1)lt20/300.66
lt0.66
?q800
For q800 E(units sold)710 E(profit)13,300 Max
profit2077015400
5
When is the mismatch cost high?

• Hammer 3/2s mismatch cost as a percentage of the
  maximum profit is 31,680/223,440 14.2
• Mismatch cost as a percent of the maximum profit
  increases as
• (1) the coefficient of variability of demand
  increases
• (2) the critical ratio decreases

6
Options to reduce the mismatch cost

• Make to order
• Reactive Capacity
• Unlimited
• Limited

7
Make-to-Stock Model
Suppliers
Configuration
Assembly
8
Assemble-to-Order Model
Suppliers
Configuration
Assembly
9
Unlimited, but expensive reactive capacity

• TEC charges a premium of 20 per unit (132 vs.
  110) in the second order.
• There are no restrictions imposed on the 2nd
  order quantity.
• ONeill forecast of total season sales is nearly
  perfect after observing initial season sales.
• How many units should ONeill order in October?

12-9
10
Revisit Example 2 Finding Cu and Co

• A textile company in UK orders coats from China.
  They buy a coat from 250 and sell for 325. If
  they cannot sell a coat in winter, they sell it
  at a discount price of 225. When the demand is
  more than what they have in stock, they have an
  option of having emergency delivery of coats from
  Ireland, at a price of 290.
• The demand for winter has a normal distribution
  with mean 32,500 and std dev 6750.
• How much should they order from China??

11
Example 2 Finding Cu and Co

• A textile company in UK orders coats from China.
  They buy a coat from 250 and sell for 325. If
  they cannot sell a coat in winter, they sell it
  at a discount price of 225. When the demand is
  more than what they have in stock, they have an
  option of having emergency delivery of coats from
  Ireland, at a price of 290.
• The demand for winter has a normal distribution
  with mean 32,500 and std dev 6750.
• How much should they order from China??

Cu75-3540 Co25 F(z)40/(4025)40/650.61?z0.2
8 ? q325000.28675034390
12
Apply Newsvendor logic even with a 2nd order
option

• The too much cost remains the same
• Co c v 110 90 20.
• The too little cost changes
• If the 1st order is too low, we cover the
  difference with the 2nd order.
• Hence, the 2nd order option prevents lost sales.
• So the cost of ordering too little per unit is no
  longer the gross margin, it is the premium we pay
  for units in the 2nd order.
• Cu 132 110 22
• Critical ratio
• Corresponding z-statistic F(0.05)0.5199,
  F(0.06)0.5239, so z 0.06.

13
Profit improvement due to the 2nd order option

• With a single ordering opportunity
• Optimal order quantity 4101 units
• Expected profit 191,760
• Mismatch cost as of revenue 4.9
• The maximum profit is unchanged 223,440
• With a second order option
• Optimal order quantity 3263 units
• Reduction in mismatch cost 38 (19,774 vs
  31,680)
• Mismatch cost as of revenue 3.1

14
Limited reactive capacity

• Units in the 2nd order are no more expensive than
  in the 1st order
• But there is limited capacity for a 2nd order

15
Sample of wetsuits

• 1st order must be at least 10,200 suits so that
  there is enough capacity for the 2nd order.
• Also a minimum order quantity-order once
• What should we produce in the 1st order?

16
Profit and mismatch with only 1 ordering
opportunity

• Use the Newsvendor model to evaluate the optimal
  order quantity, expected profit, maximum profit
  and mismatch cost
• A suits produced in the 1st order earns the
  Newsvendor profit but a suit produced in the 2nd
  order earns the maximum profit.

12-16
17
Produce safer products early, produce risky
products with reactive capacity

• Sort items by their mismatch cost to order
  quantity ratio.
• Fill the 1st order up to the minimum quantity
  (10,200) with the items that have the lowest
  mismatch quantity ratio
• The mismatch cost is reduced by 66!

12-17
18
Push-Pull Supply Chains
The Supply Chain Time Line
Customers
Suppliers
19
A new Supply Chain Paradigm

• A shift from a Push System...
• Production decisions are based on forecast
• to a Push-Pull System
• Parts inventory is replenished based on forecasts
• Assembly is based on accurate customer demand

20
Demand Forecast

• The three principles of all forecasting
  techniques
• Forecasts are always wrong
• The longer the forecast horizon the worst is the
  forecast
• Aggregate forecasts are more accurate
• The Risk Pooling Concept

21
Business models in the Book Industry

• From Push Systems...
• Barnes and Noble
• ...To Pull Systems
• Amazon.com, 1996-1999
• And, finally to Push-Pull Systems
• Amazon.com, 1999-present
• Around 40 warehouses

22
Business models in the Grocery Industry

• From Push Systems...
• Supermarket supply chain
• ...To Pull Systems
• Peapod, 1989-1999
• Stock outs 8 to 10
• And, finally to Push-Pull Systems
• Peapod, 1999-present
• Dedicated warehouses
• Stock outs less than 2

23
Locating the Push-Pull Boundary
24
Organizational Skills Needed
Raw Material
Customers
Push
Pull
High Uncertainty Short Cycle Times Service
Level Responsiveness
Low Uncertainty Long Lead Times Cost
Minimization Resource Allocation
25
ONeill quick response (reactive capacity)
High Risk Push-Pull
Low Risk Push
Speculative Production capacity
Reactive Production capacity
Later orders
Initial forecast
26
Announcement

• Read the HP case for next week
• We will analyze it in-class
• Bring your laptops!