Lessons from Project Phase-I

1
Lessons from Project Phase-I

• Good modeling practices
• Extensive model documentation
• Generality of the model
• Writing constraints
• Good reporting practices
• To a manager, not a professor !
• Executive Summary - about the business
• Clarity, brevity,

2
Model documentation

• Includes defining meaningful variable names
• Doesnt hurt in any way
• What if somebody has to continue the work you
  started ?
• What if you have to take over somebody elses
  work ?
• Ever debugged somebodys code ? That should be a
  good lesson !

3
Model generality

• EXTREMELY IMPORTANT
• What do you do when (not IF !) the world
  changes ?
• Addition/deletion of ports, DCs, etc.
• Prices, duties, etc. change frequently

4
Model generality

• Integrating model and data is a very, very bad
  idea.
• We wont deduct too many points for that this
  time, but from Phase-II onwards, if you have data
  in your model

5
A word of caution on writing constraints

• 5x1 x2 ? 10
• x1 5x2 ? 10
• against
• 6x1 6x2 ? 20
• Which is better ?

6
Reporting

• Whenever, you make or solve a model in the real
  world, you will present it to higher management
  (senior managers, VPs, etc.)
• Theyre NOT interested in methodology, or your
  math, unless
• You show them the impact
• on business !!

7
Reporting

• Make sure your solution makes sense
• Logically follows from the data (at least some
  major decisions)
• Includes all relevant components, e.g.
• Purchasing
• Transportation
• Inventory
• Capital
• Duties and taxes

8
Executive summary

• Solution overview (Best strategy)
• Take the solution back through your
  calculations
• Where is the money going ?
• Cost breakdowns by logical categories
• Types, Segments, Regions, etc.
• What are other key issues to consider ?
• Any alternatives ? With what tradeoffs ?
• At most 1-2 pages with charts, tables, etc.

9
Main report and appendices

• Detailed solution and discussion, along with
  methodology, assumptions, etc.
• Your VALUE ADDITION !!!
• Can you suggest something beyond the solution of
  the problem given to you ?
• Appendices - for the nerds !

10
Project Phase-I Model Sets

• set SOURCES
• set PORTS
• set DCS
• set EDGES (SOURCES cross PORTS) union
  (PORTS cross DCS)

11
Project Phase-I Model Variables

• /------------------------------------------------
  -- The Variables in the model are the no. of
  containers shipped each year on each edge
• --------------------------------------------------
  -/
• var ShipmentsEDGES integer gt 0
• This is a network flow problem, so integral data
  implies integral solutions.

12
Project Phase-I Model Constraints

• Do not exceed supply at any source
• s.t. ObserveCapacity source in SOURCES
• sum(source, t) in EDGES Shipmentssource, t
  lt SourceCapsource
• Conserve Flow at Ports
• s.t. ConserveFlow port in PORTS
• sum(f, port) in EDGES Shipmentsf, port
• sum(port, t) in EDGES Shipmentsport, t
• Meet Demand at DCS
• s.t. MeetDemand dc in DCS
• sum(t, dc) in EDGES Shipmentst,dc gt
  Demanddc

13
Project Phase-I Model Objective function

• minimize TotalCost
• Purchase Price Duties
• Freight Costs
• Moving Inventory Costs (pipeline)
• Waiting Inventory Costs (Note these should
  include the waiting time at the sources, but we
  forgot to tell you how often ships are scheduled
  to sail)

14
A not so good way for variables, but it works too

• If you dont want to work with EDGES, you may
  define variables by segment, like
• ShipSourcePort SOURCES, PORTS
• ShipPortDC PORTS, DCS
• Not the best way, but its acceptable too.
• Using EDGES is much more elegant.

15
A caution on number of variables and constraints

• Student versions of Xpress and AMPL support 300
  variables and 300 constraints.
• To see how many youve used, use the AMPL command
  
• option show_stats 1

16
Project Phase-I Answer

• 18000 containers/year - Brazil to Norfolk
• 2000 containers/year - Brazil to Long Beach
• 10000 containers/year - China to Long Beach
• 18000 containers/year - Norfolk to NY
• 12000 containers/year - Long Beach to LA
• Obvious solution ! Why ?

17
Project Phase-I Answer

• Total cost 1.3-1.4 billion, depending on your
  assumptions
• 1.2 billion purchase cost
• 72 million duties
• In this phase, purchase cost (excluding duties)
  doesnt affect the decision, so we can remove it
  from the objective function
• However, still need to report it !

18
Project Phase-II

• Something close to the real thing
• Much more detailed model than Phase-I, so get on
  it ASAP !
• Multiple products
• Multiple modes of transport
• Weight and cube constraints
• Use option solver cplex before solve

19
Project Phase-II

• Recall this ?
• / -----------------------------------------------
  --------------------
• set param var s.t
• Solve the problem
• You may need a command like
• option solver cplex
• -----------------------------------------------
  --------------------/
• solve
• Why ?

20
Project Phase-II

• Not a network flow problem anymore, so
• Integral data does not imply integral solutions !
• AMPL solvers
• MINOS - default, doesnt solve IPs
• CPLEX