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    <P><CENTER>&nbsp;<FONT SIZE="+2">Location &amp; Routing in Logistics</FONT></CENTER></P>

    <P><CENTER><I><FONT SIZE="+1">Wuhan University of Technology</FONT></I></CENTER></TD>
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</TABLE></CENTER></P>

<P><CENTER><FONT COLOR="#ffff99">C</FONT><B><I><FONT COLOR="#004000"
 SIZE="+2">Lecture Notes</FONT></I></B></CENTER></P>

<UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Concepts &amp; terminology
  of graphs &amp; networks, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Graphs%20%26%20Networks%20Intro.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Graphs%26Networks.pdf">pdf(8)</A></FONT>
  <UL>
    <LI><FONT SIZE="+1">The milkman's problem, <A HREF="Stacks_pdf1/Milkman.PDF">pdf(1)</A>,
    <A HREF="Stacks_pdf8/Milkman.PDF">pdf(4)</A></FONT>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Shortest path problem, </FONT><FONT
   SIZE="+1"><A HREF="Stacks_pdf1/ShortPath.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/ShortPath.pdf">pdf(8)</A></FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Capacity expansion as shortest
    path problem, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Capacity_Expand_short_path.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Capacity_Expand_short_path.pdf">pdf(4)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Equipment replacement as
    shortest path problem, pdf(1), pdf(4)</FONT>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Transportation problem, </FONT><FONT
   SIZE="+1"><A HREF="Stacks_1/TransportProblem.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_8/TransportProblem.pdf">pdf(4)</A></FONT>
  <UL>
    <LI><FONT SIZE="+1">Computing reduced costs using dual variables,
    <A HREF="Stacks_pdf1/Transportation_Simplex_Multipliers.pdf">pdf(1)</A>,
    <A HREF="Stacks_pdf4/Transportation_Simplex_Multipliers.pdf">pdf(4)</A></FONT>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Assignment problem, </FONT><FONT
   SIZE="+1"><A HREF="Stacks_pdf1/Assignment%20Problem.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Assignment.pdf">pdf(8)</A></FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Optimality of Hungarian algorithm,
    </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Hungarian_optimality.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Hungarian_optimality.pdf">pdf(4)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Airline crew assignment problem,
    </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Airline_Crew.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Airline_Crew.pdf">pdf(8)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Examples of Hungarian algorithm,
    </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Hungarian_examples.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Hungarian_examples.pdf">pdf(6)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Generalized Assignment Problem,
    </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/GAP_Relax.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/GAP_Relax.pdf">pdf(8)</A></FONT>
    <UL>
      <LI><FONT COLOR="#000000" SIZE="+1">Example: &quot;strong&quot;
      Lagrangian relaxation of GAP, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/GAP2_Example.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/GAP2_Example.pdf">pdf(4)</A></FONT>
    </UL>
    <LI><FONT SIZE="+1">Quadratic Assignment Problem, <A HREF="Stacks_pdf1/QAP.pdf">pdf(1)</A>,
    <A HREF="Stacks_pdf8/QAP.pdf">pdf(8)</A></FONT>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Minimum-cost network flow
  model, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/LINGO_sets.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/LINGO_sets.pdf">pdf(8)</A></FONT>
  <LI><FONT COLOR="#000000" SIZE="+1">Binary integer programming
  models, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/ILP_Models_Intro.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/ILP_Models_Intro.pdf">pdf(8)</A></FONT>
  <UL>
    <LI><FONT SIZE="+1">Integer programming models, part I, <A HREF="Stacks_pdf1/ILP_Models_Part1.pdf">pdf(1)</A>,
    <A HREF="Stacks_pdf8/ILP_Models_Part1.pdf">pdf(8)</A></FONT>
    <LI><FONT SIZE="+1">Integer programming models, part II, <A 
    HREF="Stacks_pdf1/ILP_Models_Part2.pdf">pdf(1)</A>, <A HREF="Stacks_pdf8/ILP_Models_Part2.pdf">pdf(8)</A></FONT>
    <LI><FONT SIZE="+1">Mathematical programming languages, <A HREF="Stacks_pdf1/Modeling_Languages_Intro.pdf">pdf(1)</A>,
    <A HREF="Stacks_pdf8/Modeling_Languages_Intro.pdf">pdf(4)</A></FONT>
    <UL>
      <LI><FONT SIZE="+1">LINGO models with sets, <A HREF="Stacks_pdf1/LINGO_sets.pdf">pdf(1)</A>,
      <A HREF="Stacks_pdf8/LINGO_sets.pdf">pdf(4)</A></FONT>
      <LI><FONT SIZE="+1">Miscellaneous modeling exercises, <A HREF="Stacks_pdf1/Misc_MILP_Model_Exercises.pdf">pdf(1)</A>,
      <A HREF="Stacks_pdf8/Misc_MILP_Model_Exercises.pdf">pdf(4)</A></FONT>
    </UL>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Covering problems</FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">The set covering problem</FONT>
    <UL>
      <LI><FONT COLOR="#000000" SIZE="+1">Introduction, </FONT><FONT
       SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-1.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-1.pdf">pdf(8)</A></FONT>
      <LI><FONT COLOR="#000000" SIZE="+1">Lagrangian relaxation, </FONT><FONT
       SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-2.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-2.pdf">pdf(8)</A></FONT>
      <LI><FONT COLOR="#000000" SIZE="+1">Eliminating sets, </FONT><FONT
       SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-3.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-3.pdf">pdf(8)</A></FONT>
      <LI><FONT COLOR="#000000" SIZE="+1">Subgradient method, </FONT><FONT
       SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-4.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-4.pdf">pdf(8)</A></FONT>
      <LI><FONT COLOR="#000000" SIZE="+1">Dual ascent, </FONT><FONT
       SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-5.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-5.pdf">pdf(8)</A></FONT>
      <LI><FONT COLOR="#000000" SIZE="+1">Computational experience,
      </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-6.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-6.pdf">pdf(8)</A></FONT>
    </UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Applications of covering
    models, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Covering_Applications.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Covering_Applications.pdf">pdf(4)</A></FONT>
    <LI><FONT SIZE="+1">Covering models in location problems, <A
    HREF="Stacks_pdf1/Covering_in_Location.pdf">pdf(1)</A>, <A HREF="Stacks_pdf1/Covering_in_Location.pdf">pdf(4)</A></FONT>
    <LI><FONT SIZE="+1">Set covering models in LINGO, <A HREF="Stacks_pdf1/SCPmodeling-LINGO.pdf">pdf(1)</A>,
    <A HREF="Stacks_pdf1/SCPmodeling-LINGO.pdf">pdf(4)</A></FONT>
  </UL>
  <LI><FONT SIZE="+1">Branch-&amp;-Bound method</FONT><FONT COLOR="#000000"
   SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Branch%26Bound.pdf">pdf(1)</A></FONT><FONT
   COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Branch%26Bound.pdf">pdf(8)</A></FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Relaxations, </FONT><FONT
     SIZE="+1"><A HREF="Stacks_pdf1/RELAXATIONS.PDF">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/RELAXATIONS.pdf">pdf(4)</A></FONT>
    <UL>
      <LI><FONT COLOR="#000000" SIZE="+1">LP relaxation</FONT>
      <UL>
        <LI><FONT COLOR="#000000" SIZE="+1">Knapsack problem, </FONT><FONT
         SIZE="+1"><A HREF="Stacks_pdf1/Knapsack_Problem.pdf">pdf(1)</A></FONT><FONT
         COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Knapsack_Problem.pdf">pdf(8)</A></FONT>
        <LI><FONT COLOR="#000000" SIZE="+1">Branch-&amp;-bound algorithm
        for knapsack problem, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Knapsack_BB.pdf">pdf(1)</A></FONT><FONT
         COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Knap_bb.pdf">pdf(8)</A></FONT>
      </UL>
      <LI><FONT COLOR="#000000" SIZE="+1">Lagrangian relaxation &amp;
      duality, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Lagrangian%20Duality.pdf">pdf(1)</A></FONT><FONT
       COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Lagrangian_Dual.pdf">pdf(8)</A></FONT>
      <UL>
        <LI><FONT COLOR="#000000" SIZE="+1">Lagrangian relaxation of
        0/1 integer program, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/LagDual_BIP.pdf">pdf(1)</A></FONT><FONT
         COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/LagDual_BIP.pdf">pdf(4)</A></FONT>
        <LI><FONT COLOR="#000000" SIZE="+1">Lagrangian relaxation of
        covering problem, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Set%20Covering-2.pdf">pdf(1)</A></FONT><FONT
         COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Set%20Covering-2.pdf">pdf(8)</A></FONT>
      </UL>
    </UL>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Location</FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Location in the continuous
    plane (Weber problem), </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Webers.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Webers.pdf">pdf(8)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Median location in a network,
    </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Median%20Problem.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Median_Location.pdf">pdf(8)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Center <I>(minimax)</I> location
    in a network, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf1/Network%20Center.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Center_Location.pdf">pdf(8)</A></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Discrete location problems,
    pdf(1), pdf(8)</FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Uncapacitated plant location
    <I>(UCLP)</I>, pdf(1), pdf(8)</FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Capacitated plant location
    <I>(CPL)</I>, pdf(1), pdf(8)</FONT>
    <UL>
      <LI><FONT COLOR="#000000" SIZE="+1">Benders' decomposition of
      CPL</FONT>
    </UL>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Routing</FONT>
  <UL>
    <LI><FONT COLOR="#000000" SIZE="+1">Arc-covering (Chinese Postman
    Problem)</FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Undirected graph, </FONT><FONT
     SIZE="+1"><A HREF="http://www.engineering.uiowa.edu/~dbricker/Stacks_pdf1/Postman_1.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1"><A HREF="Stacks_pdf8/Postman.pdf">pdf(8)</A></FONT><FONT
     COLOR="#000000" SIZE="+1"></FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Directed graph, </FONT><FONT
     SIZE="+1"><A HREF="Stacks_pdf1/Postman_2.pdf">pdf(1)</A></FONT><FONT
     COLOR="#000000" SIZE="+1">, </FONT><FONT SIZE="+1">pdf(8)</FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Node-covering (Traveling
    Salesman Problem)</FONT>
    <LI><FONT COLOR="#000000" SIZE="+1">Vehicle routing problems</FONT>
  </UL>
  <LI><FONT COLOR="#000000" SIZE="+1">Benders' decomposition</FONT>
</UL>

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<I>Last modified: 8 November 2004</I></FONT></P>

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