[Help-glpk] ordered and ord in MathProg?

[Noli Sicad]

Hi

While searching the net for materials in MRP (Material Requirement
Planning), I encountered this website,
http://faculty.gsm.ucdavis.edu/~dlw/scm.html (Introduction to
Computational Optimization Models for Production Planning in a Supply
Chain book). The models are implemented in major commercial LP solvers
i.e. AMPL, GAMS, MOSEL,MPL,OPL and AIMMS

The AMPL models use ordered and ord function, so the models are not
running in MathProg. Now, how do you do this in MathProg. Probably
good to have mathprog examples in PP and SCP.

Here is one of the models (mrp.mod + dat) (below).

Thanks, Noli


~~~~~~~~~~

set PP ordered;              # Set of SKU Numbers
set TT ordered;              # Set of Time Buckets

param P integer := card(PP); # Number of SKUs
param T integer := card(TT); # Number of Time Buckets
param M  >= 0;               # Large Number

param LT {PP} integer;      # Lead Time
param R  {PP,PP} integer;   # number of i to make one j
param D {PP, TT} integer;   # External Demand for an item in a period
param I {PP} integer;       # Beginning Inventory
param LS {PP} integer;      # Lot Size


var d {PP, TT} binary;      # production indicator
var x {PP, TT} >=0;         # number of SKUs to produce

# -----------------------------------------------------------------

minimize objective: sum {i in PP, t in TT}
                     (T-ord(t)+1) * x[i,t];

# -----------------------------------------------------------------

subject to MaterialRequirement {i in PP, t in TT}:
  (sum {s in TT: ord(s) <= ord(t)-LT[i] } x[i,s] )
   + I[i]
   - sum {s in TT: ord(s)<=ord(t)}
         (D[i,s] + sum {j in PP} R[i,j]* x[j,s])
   >= 0;

subject to LotSize {i in PP, t in TT}:
   x[i,t] - d[i,t]*LS[i] >= 0;

subject to ProductionIndicator {i in PP, t in TT}:
   d[i,t] - x[i,t]/M >=0;

data;

param M := 10000 ;              # Large number

param: PP: LT := AJ8172 2       # Items with Lead Times
                 LQ8811 3
                 RN0098 4
                 NN1100 1
                 WN7342 12;

set TT := 1jan04                # Time Buckets
          2jan04
          3jan04
          4jan04
          5jan04
          6jan04
          7jan04
          8jan04 ;

param R :                      # Number of i to produce one j
        AJ8172 LQ8811 RN0098 NN1100 WN7342  :=
AJ8172  0      0      0      0      0
LQ8811  2      0      0      0      0
RN0098  1      0      0      0      0
NN1100  0      1      0      0      0
WN7342  0      1      0      0      0  ;

param D:                       # external demand for i in t
        1jan04 2jan04 3jan04 4jan04 5jan04 6jan04 7jan04 8jan04 :=
AJ8172  20     30     10     20     30     20     30     40
LQ8811  0      0      0      0      0      0      0      0
RN0098  0      0      0      0      0      0      0      0
NN1100  0      0      0      0      0      0      0      0
WN7342  0      0      0      0      0      0      0      0;

param I := AJ8172 90           # Beginning Inventory of SKU i
           LQ8811 300
           RN0098 100
           NN1100 0
           WN7342 900;

param LS := AJ8172 100         # Lot Size
            LQ8811 400
            RN0098 100
            NN1100 1
            WN7342 1000;