Decision Modeling

1
Decision Modeling

• Special Applications ofLinear Programming

2
Some General LP Applications

• Archetypical LP models can serve as templates for
  large, real-life models
• Blending problem
• Transportation problem
• Inventory problem (multi-period)

3
Transportation Problem

• Management must decide how to send products from
  various sources to various destinations to
  satisfy requirements while minimizing cost
• Known parameters
• Inventory at each source location
• Demand at each destination location
• Cost of transportation between each
  source-destination pair

4
Example

• AutoPower Company makes a variety of battery and
  motorized uninterruptible power supplies (UPSs)
• AutoPower has 4 final assembly plants in Europe
  and the diesel motors used by the UPSs are
  produced in the US, shipped to 3 harbors and then
  sent to the assembly plants
• Production plans for the third quarter have been
  set. The requirements (demand at the
  destinations) and the available number of motors
  at the harbors (supply at the origins) are shown
  on the next slide

5
Demand

• Assembly Plant No. of Motors Required
• Leipzig 12,000
• (2) Nancy 15,000
• (3) Liege 23,000
• (4) Tilburg 18,000
• 68,000

Sufficient Capacity
Supply
Harbor Production Capacity (A)
Amsterdam 27,000 (B) Antwerp 30,000 (C)
Le Havre 23,000 80,000
6
Example

• AutoPower must decide how many motors to send
  from each harbor (origin) to each plant
  (destination)
• The cost (/motor) of shipping is given in the
  following table

7
Model Formulation

• See board
• See Excel solution
• See Sensitivity report

8
Variations

• Add manufacturing cost
• Update transportation cost to include
  manufacturing cost
• Maximize contribution margins instead of
  minimizing cost
• Define different products as origins and
  contribution margin in destination markets as
  transportation cost
• Demand exceeds supply
• Add a dummy origin and let transportation cost
  equal opportunity cost of not meeting demand at a
  destination

9
Dynamic Models

• Single time period models (such as the previous
  ones) are called static because time is not an
  important model factor
• In many cases, decisions are made over a time
  horizon divided into time periods
• These multi-period models are called dynamic
  models since the decision for one time period
  influences the decision in other time periods
• In dynamic models, the timing of events must be
  very well defined

10
Dynamic Inventory Models

• In dynamic inventory models, demand is manifested
  in each of several discrete time periods
• Goods are acquired (e.g., manufactured) in
  different time periods
• Inventory can be carried from one time period to
  another
• Only goods that are available during a time
  period can be delivered to the customers

11
The Inventory Equation

• Flows into and out of the inventory must balance
  in any given time period. Let
• It denote the inventory on hand at the end of
  week t
• xt production in week t
• dt demand (filled) in week t
• For any week t, the inventory equation is
• It-1 xt It dt

12
Dynamic Inventory Model Example

• AutoPower generators are assembled in Singapore
  from imported parts, tested in Singapore, and
  exported to AutoPowers Asian customers needing
  uninterrupted electric power. The following
  monthly data are available

13
Model Formulation

• See board
• See Excel solution