egypt.mod

著名的大规模线性规划求解器源码GLPK.C语言版本,可以修剪.内有详细帮助文档.

# EGYPT, a static model of fertilizer production
#
# References:
# Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language
# for Mathematical Programming." Management Science 36 (1990) 519-554.

###  SETS  ###

set center;                # Locations from which final product may be shipped
set port within center;    # Locations at which imports can be received
set plant within center;   # Locations of plants

set region;                # Demand regions

set unit;                  # Productive units
set proc;                  # Processes

set nutr;                  # Nutrients

set c_final;               # Final products (fertilizers)
set c_inter;               # Intermediate products
set c_ship within c_inter; # Intermediates for shipment
set c_raw;                 # Domestic raw materials and miscellaneous inputs

set commod := c_final union c_inter union c_raw;

                           # All commodities

###  PARAMETERS  ###

param cf75 {region,c_final} >= 0;

                           # Consumption of fertilizer 1974-75 (1000 tpy)

param fn {c_final,nutr} >= 0;

                           # Nutrient content of fertilizers

param cn75 {r in region, n in nutr} := sum {c in c_final} cf75[r,c] * fn[c,n];

                           # Consumption of nutrients 1974-75 (1000 tpy)

param road {region,center} >= 0;

                           # Road distances

param rail_half {plant,plant} >= 0;
param rail {p1 in plant, p2 in plant} :=
    if rail_half[p1,p2] > 0 then rail_half[p1,p2] else rail_half[p2,p1];

                           # Interplant rail distances (kms)

param impd_barg {plant} >= 0;
param impd_road {plant} >= 0;

                           # Import distances (kms) by barge and road

param tran_final {pl in plant, r in region} :=
              if road[r,pl] > 0 then .5 + .0144 * road[r,pl] else 0;

param tran_import {r in region, po in port} :=
              if road[r,po] > 0 then .5 + .0144 * road[r,po] else 0;

param tran_inter {p1 in plant, p2 in plant} :=
              if rail[p1,p2] > 0 then 3.5 + .03 * rail[p1,p2] else 0;

param tran_raw {pl in plant} :=
            (if impd_barg[pl] > 0 then 1.0 + .0030 * impd_barg[pl] else 0)
          + (if impd_road[pl] > 0 then 0.5 + .0144 * impd_road[pl] else 0);

                           # Transport cost (le per ton) for:
                           #   final products, imported final products,
                           #   interplant shipment, imported raw materials

param io {commod,proc};    # Input-output coefficients

param util {unit,proc} >= 0;

                           # Capacity utilization coefficients

param p_imp {commod} >= 0; # Import Price (cif US$ per ton 1975)

param p_r {c_raw} >= 0;
param p_pr {plant,c_raw} >= 0;

param p_dom {pl in plant, c in c_raw} :=
              if p_r[c] > 0 then p_r[c] else p_pr[pl,c];

                           # Domestic raw material prices

param dcap {plant,unit} >= 0;

                           # Design capacity of plants (t/day)

param icap {u in unit, pl in plant} := 0.33 * dcap[pl,u];

                           # Initial capacity of plants (t/day)

param exch := 0.4;         # Exchange rate

param util_pct := 0.85;    # Utilization percent for initial capacity

###  DERIVED SETS OF "POSSIBILITIES"  ###

set m_pos {pl in plant} := {u in unit: icap[u,pl] > 0};

                           # At each plant, set of units for which there is
                           # initial capacity

set p_cap {pl in plant} :=
             {pr in proc: forall {u in unit: util[u,pr] > 0} u in m_pos[pl] };

                           # At each plant, set of processes for which
                           # all necessary units have some initial capacity

set p_except {plant} within proc;

                           # At each plant, list of processes that are
                           # arbitrarily ruled out

set p_pos {pl in plant} := p_cap[pl] diff p_except[pl];

                           # At each plant, set of possible processes

set cp_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] > 0};

set cc_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] < 0};

set c_pos {c in commod} := cp_pos[c] union cc_pos[c];

                           # For each commodity, set of plants that can
                           # produce it (cp_pos) or consume it (cc_pos),
                           # and their union (c_pos)

###  VARIABLES  ###

var Z {pl in plant, p_pos[pl]} >= 0;

                           # Z[pl,pr] is level of process pr at plant pl

var Xf {c in c_final, cp_pos[c], region} >= 0;

                           # Xf[c,pl,r] is amount of final product c
                           # shipped from plant pl to region r

var Xi {c in c_ship, cp_pos[c], cc_pos[c]} >= 0;

                           # Xi[c,p1,p2] is amount of intermediate c
                           # shipped from plant p1 to plant p2

var Vf {c_final,region,port} >= 0;

                           # Vf[c,r,po] is amount of final product c
                           # imported by region r from port po

var Vr {c in c_raw, cc_pos[c]} >= 0;

                           # Vr[c,pl] is amount of raw material c
                           # imported for use at plant pl

var U {c in c_raw, cc_pos[c]} >= 0;

                           # U[c,pl] is amount of raw material c
                           # purchased domestically for use at plant pl

var Psip;                  # Domestic recurrent cost
var Psil;                  # Transport cost
var Psii;                  # Import cost

###  OBJECTIVE  ###

minimize Psi:  Psip + Psil + Psii;

###  CONSTRAINTS  ###

subject to mbd {n in nutr, r in region}:

    sum {c in c_final} fn[c,n] *
                (sum {po in port} Vf[c,r,po] +
                 sum {pl in cp_pos[c]} Xf[c,pl,r])  >=  cn75[r,n];

                           # Total nutrients supplied to a region by all
                           # final products (sum of imports plus internal
                           # shipments from plants) must meet requirements

subject to mbdb {c in c_final, r in region: cf75[r,c] > 0}:

    sum {po in port} Vf[c,r,po] +
    sum {pl in cp_pos[c]} Xf[c,pl,r]  >=  cf75[r,c];

                           # Total of each final product supplied to each
                           # region (as in previous constraint) must meet
                           # requirements

subject to mb {c in commod, pl in plant}:

    sum {pr in p_pos[pl]} io[c,pr] * Z[pl,pr]

   + ( if c in c_ship then
                ( if pl in cp_pos[c] then sum {p2 in cc_pos[c]} Xi[c,pl,p2] )
              - ( if pl in cc_pos[c] then sum {p2 in cp_pos[c]} Xi[c,p2,pl] ))

   + ( if (c in c_raw and pl in cc_pos[c]) then
                 (( if p_imp[c] > 0 then Vr[c,pl] )
                + ( if p_dom[pl,c] > 0 then U[c,pl] )))

  >= if (c in c_final and pl in cp_pos[c]) then sum {r in region} Xf[c,pl,r];

                           # For each commodity at each plant:  sum of
                           #   (1) production or consumption at plant,
                           #   (2) inter-plant shipments in or out,
                           #   (3) import and domestic purchases (raw only)
                           # is >= 0 for raw materials and intermediates;
                           # is >= the total shipped for final products

subject to cc {pl in plant, u in m_pos[pl]}:

    sum {pr in p_pos[pl]} util[u,pr] * Z[pl,pr]  <=  util_pct * icap[u,pl];

                           # For each productive unit at each plant,
                           # total utilization by all processes
                           # may not exceed the unit's capacity

subject to ap:

    Psip  =  sum {c in c_raw, pl in cc_pos[c]} p_dom[pl,c] * U[c,pl];

                           # Psip is the cost of domestic raw materials,
                           # summed over all plants that consume them

subject to al:

    Psil  =  sum {c in c_final} (

               sum {pl in cp_pos[c], r in region}
                                              tran_final[pl,r] * Xf[c,pl,r]

             + sum {po in port, r in region} tran_import[r,po] * Vf[c,r,po] )

           + sum {c in c_ship, p1 in cp_pos[c], p2 in cc_pos[c]}
                                               tran_inter[p1,p2] * Xi[c,p1,p2]

           + sum {c in c_raw, pl in cc_pos[c]: p_imp[c] > 0}
                                                    tran_raw[pl] * Vr[c,pl];

                           # Total transport cost is sum of shipping costs for
                           #   (1) all final products from all plants,
                           #   (2) all imports of final products,
                           #   (3) all intermediates shipped between plants,
                           #   (4) all imports of raw materials

subject to ai:

    Psii / exch  =  sum {c in c_final, r in region, po in port}
                                                      p_imp[c] * Vf[c,r,po]

                  + sum {c in c_raw, pl in cc_pos[c]} p_imp[c] * Vr[c,pl];

                           # Total import cost -- at exchange rate --
                           # is sum of import costs for final products