MPL Model Library MPL Model Library



Mary's Radiation, Example 3.4-1, Hillier and Lieberman


   {  Exmpl_3.4-1_MarysRadiation.mpl  }

   {  Hillier and Lieberman, Introduction to Operations Research, 7th ed.  }

   {  Chapter 3.4,  Example 1,  Blending/Radiation,  Size: 3x2,  Page 44  }


TITLE
   MarysRadiationTherapy;

INDEX
   beam        := (Beam1, Beam2);
   bodyarea    := (CriticalTissues, TumorRegion, CenterTumor);

DATA
   HealthyAnatomy[beam]  := (0.4, 0.5);

   DosageAbsorbed[beam, bodyarea]  := (0.3, 0.5, 0.6,
                                       0.1, 0.5, 0.4);

   Restriction[bodyarea]  := (2.7, 6.0, 6.0);

VARIABLE
   Dosage[beam];

MODEL

   MIN TotalHealthyDosage = SUM(beam:  HealthyAnatomy * Dosage);

SUBJECT TO

   RestrictDosage[bodyarea=CriticalTissues] :

      SUM(beam: DosageAbsorbed * Dosage) <= Restriction;

   RestrictDosage[bodyarea=TumorRegion] :

      SUM(beam: DosageAbsorbed * Dosage) = Restriction;

   RestrictDosage[bodyarea=CenterTumor] :

      SUM(beam: DosageAbsorbed * Dosage) >= Restriction;

END