1 | # EGYPT, a static model of fertilizer production |
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2 | # |
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3 | # References: |
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4 | # Robert Fourer, David M. Gay and Brian W. Kernighan, "A Modeling Language |
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5 | # for Mathematical Programming." Management Science 36 (1990) 519-554. |
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6 | |
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7 | ### SETS ### |
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8 | |
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9 | set center; # Locations from which final product may be shipped |
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10 | set port within center; # Locations at which imports can be received |
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11 | set plant within center; # Locations of plants |
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12 | |
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13 | set region; # Demand regions |
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14 | |
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15 | set unit; # Productive units |
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16 | set proc; # Processes |
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17 | |
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18 | set nutr; # Nutrients |
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19 | |
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20 | set c_final; # Final products (fertilizers) |
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21 | set c_inter; # Intermediate products |
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22 | set c_ship within c_inter; # Intermediates for shipment |
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23 | set c_raw; # Domestic raw materials and miscellaneous inputs |
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24 | |
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25 | set commod := c_final union c_inter union c_raw; |
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26 | |
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27 | # All commodities |
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28 | |
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29 | ### PARAMETERS ### |
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30 | |
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31 | param cf75 {region,c_final} >= 0; |
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32 | |
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33 | # Consumption of fertilizer 1974-75 (1000 tpy) |
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34 | |
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35 | param fn {c_final,nutr} >= 0; |
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36 | |
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37 | # Nutrient content of fertilizers |
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38 | |
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39 | param cn75 {r in region, n in nutr} := sum {c in c_final} cf75[r,c] * fn[c,n]; |
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40 | |
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41 | # Consumption of nutrients 1974-75 (1000 tpy) |
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42 | |
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43 | param road {region,center} >= 0; |
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44 | |
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45 | # Road distances |
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46 | |
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47 | param rail_half {plant,plant} >= 0; |
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48 | param rail {p1 in plant, p2 in plant} := |
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49 | if rail_half[p1,p2] > 0 then rail_half[p1,p2] else rail_half[p2,p1]; |
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50 | |
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51 | # Interplant rail distances (kms) |
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52 | |
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53 | param impd_barg {plant} >= 0; |
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54 | param impd_road {plant} >= 0; |
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55 | |
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56 | # Import distances (kms) by barge and road |
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57 | |
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58 | param tran_final {pl in plant, r in region} := |
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59 | if road[r,pl] > 0 then .5 + .0144 * road[r,pl] else 0; |
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60 | |
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61 | param tran_import {r in region, po in port} := |
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62 | if road[r,po] > 0 then .5 + .0144 * road[r,po] else 0; |
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63 | |
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64 | param tran_inter {p1 in plant, p2 in plant} := |
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65 | if rail[p1,p2] > 0 then 3.5 + .03 * rail[p1,p2] else 0; |
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66 | |
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67 | param tran_raw {pl in plant} := |
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68 | (if impd_barg[pl] > 0 then 1.0 + .0030 * impd_barg[pl] else 0) |
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69 | + (if impd_road[pl] > 0 then 0.5 + .0144 * impd_road[pl] else 0); |
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70 | |
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71 | # Transport cost (le per ton) for: |
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72 | # final products, imported final products, |
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73 | # interplant shipment, imported raw materials |
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74 | |
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75 | param io {commod,proc}; # Input-output coefficients |
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76 | |
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77 | param util {unit,proc} >= 0; |
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78 | |
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79 | # Capacity utilization coefficients |
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80 | |
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81 | param p_imp {commod} >= 0; # Import Price (cif US$ per ton 1975) |
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82 | |
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83 | param p_r {c_raw} >= 0; |
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84 | param p_pr {plant,c_raw} >= 0; |
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85 | |
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86 | param p_dom {pl in plant, c in c_raw} := |
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87 | if p_r[c] > 0 then p_r[c] else p_pr[pl,c]; |
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88 | |
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89 | # Domestic raw material prices |
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90 | |
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91 | param dcap {plant,unit} >= 0; |
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92 | |
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93 | # Design capacity of plants (t/day) |
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94 | |
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95 | param icap {u in unit, pl in plant} := 0.33 * dcap[pl,u]; |
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96 | |
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97 | # Initial capacity of plants (t/day) |
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98 | |
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99 | param exch := 0.4; # Exchange rate |
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100 | |
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101 | param util_pct := 0.85; # Utilization percent for initial capacity |
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102 | |
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103 | ### DERIVED SETS OF "POSSIBILITIES" ### |
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104 | |
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105 | set m_pos {pl in plant} := {u in unit: icap[u,pl] > 0}; |
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106 | |
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107 | # At each plant, set of units for which there is |
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108 | # initial capacity |
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109 | |
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110 | set p_cap {pl in plant} := |
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111 | {pr in proc: forall {u in unit: util[u,pr] > 0} u in m_pos[pl] }; |
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112 | |
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113 | # At each plant, set of processes for which |
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114 | # all necessary units have some initial capacity |
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115 | |
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116 | set p_except {plant} within proc; |
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117 | |
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118 | # At each plant, list of processes that are |
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119 | # arbitrarily ruled out |
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120 | |
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121 | set p_pos {pl in plant} := p_cap[pl] diff p_except[pl]; |
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122 | |
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123 | # At each plant, set of possible processes |
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124 | |
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125 | set cp_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] > 0}; |
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126 | |
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127 | set cc_pos {c in commod} := {pl in plant: sum {pr in p_pos[pl]} io[c,pr] < 0}; |
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128 | |
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129 | set c_pos {c in commod} := cp_pos[c] union cc_pos[c]; |
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130 | |
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131 | # For each commodity, set of plants that can |
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132 | # produce it (cp_pos) or consume it (cc_pos), |
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133 | # and their union (c_pos) |
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134 | |
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135 | ### VARIABLES ### |
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136 | |
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137 | var Z {pl in plant, p_pos[pl]} >= 0; |
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138 | |
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139 | # Z[pl,pr] is level of process pr at plant pl |
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140 | |
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141 | var Xf {c in c_final, cp_pos[c], region} >= 0; |
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142 | |
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143 | # Xf[c,pl,r] is amount of final product c |
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144 | # shipped from plant pl to region r |
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145 | |
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146 | var Xi {c in c_ship, cp_pos[c], cc_pos[c]} >= 0; |
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147 | |
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148 | # Xi[c,p1,p2] is amount of intermediate c |
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149 | # shipped from plant p1 to plant p2 |
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150 | |
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151 | var Vf {c_final,region,port} >= 0; |
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152 | |
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153 | # Vf[c,r,po] is amount of final product c |
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154 | # imported by region r from port po |
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155 | |
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156 | var Vr {c in c_raw, cc_pos[c]} >= 0; |
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157 | |
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158 | # Vr[c,pl] is amount of raw material c |
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159 | # imported for use at plant pl |
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160 | |
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161 | var U {c in c_raw, cc_pos[c]} >= 0; |
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162 | |
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163 | # U[c,pl] is amount of raw material c |
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164 | # purchased domestically for use at plant pl |
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165 | |
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166 | var Psip; # Domestic recurrent cost |
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167 | var Psil; # Transport cost |
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168 | var Psii; # Import cost |
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169 | |
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170 | ### OBJECTIVE ### |
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171 | |
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172 | minimize Psi: Psip + Psil + Psii; |
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173 | |
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174 | ### CONSTRAINTS ### |
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175 | |
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176 | subject to mbd {n in nutr, r in region}: |
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177 | |
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178 | sum {c in c_final} fn[c,n] * |
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179 | (sum {po in port} Vf[c,r,po] + |
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180 | sum {pl in cp_pos[c]} Xf[c,pl,r]) >= cn75[r,n]; |
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181 | |
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182 | # Total nutrients supplied to a region by all |
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183 | # final products (sum of imports plus internal |
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184 | # shipments from plants) must meet requirements |
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185 | |
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186 | subject to mbdb {c in c_final, r in region: cf75[r,c] > 0}: |
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187 | |
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188 | sum {po in port} Vf[c,r,po] + |
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189 | sum {pl in cp_pos[c]} Xf[c,pl,r] >= cf75[r,c]; |
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190 | |
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191 | # Total of each final product supplied to each |
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192 | # region (as in previous constraint) must meet |
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193 | # requirements |
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194 | |
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195 | subject to mb {c in commod, pl in plant}: |
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196 | |
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197 | sum {pr in p_pos[pl]} io[c,pr] * Z[pl,pr] |
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198 | |
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199 | + ( if c in c_ship then |
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200 | ( if pl in cp_pos[c] then sum {p2 in cc_pos[c]} Xi[c,pl,p2] ) |
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201 | - ( if pl in cc_pos[c] then sum {p2 in cp_pos[c]} Xi[c,p2,pl] )) |
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202 | |
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203 | + ( if (c in c_raw and pl in cc_pos[c]) then |
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204 | (( if p_imp[c] > 0 then Vr[c,pl] ) |
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205 | + ( if p_dom[pl,c] > 0 then U[c,pl] ))) |
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206 | |
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207 | >= if (c in c_final and pl in cp_pos[c]) then sum {r in region} Xf[c,pl,r]; |
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208 | |
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209 | # For each commodity at each plant: sum of |
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210 | # (1) production or consumption at plant, |
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211 | # (2) inter-plant shipments in or out, |
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212 | # (3) import and domestic purchases (raw only) |
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213 | # is >= 0 for raw materials and intermediates; |
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214 | # is >= the total shipped for final products |
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215 | |
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216 | subject to cc {pl in plant, u in m_pos[pl]}: |
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217 | |
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218 | sum {pr in p_pos[pl]} util[u,pr] * Z[pl,pr] <= util_pct * icap[u,pl]; |
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219 | |
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220 | # For each productive unit at each plant, |
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221 | # total utilization by all processes |
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222 | # may not exceed the unit's capacity |
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223 | |
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224 | subject to ap: |
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225 | |
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226 | Psip = sum {c in c_raw, pl in cc_pos[c]} p_dom[pl,c] * U[c,pl]; |
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227 | |
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228 | # Psip is the cost of domestic raw materials, |
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229 | # summed over all plants that consume them |
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230 | |
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231 | subject to al: |
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232 | |
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233 | Psil = sum {c in c_final} ( |
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234 | |
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235 | sum {pl in cp_pos[c], r in region} |
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236 | tran_final[pl,r] * Xf[c,pl,r] |
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237 | |
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238 | + sum {po in port, r in region} tran_import[r,po] * Vf[c,r,po] ) |
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239 | |
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240 | + sum {c in c_ship, p1 in cp_pos[c], p2 in cc_pos[c]} |
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241 | tran_inter[p1,p2] * Xi[c,p1,p2] |
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242 | |
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243 | + sum {c in c_raw, pl in cc_pos[c]: p_imp[c] > 0} |
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244 | tran_raw[pl] * Vr[c,pl]; |
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245 | |
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246 | # Total transport cost is sum of shipping costs for |
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247 | # (1) all final products from all plants, |
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248 | # (2) all imports of final products, |
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249 | # (3) all intermediates shipped between plants, |
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250 | # (4) all imports of raw materials |
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251 | |
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252 | subject to ai: |
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253 | |
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254 | Psii / exch = sum {c in c_final, r in region, po in port} |
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255 | p_imp[c] * Vf[c,r,po] |
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256 | |
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257 | + sum {c in c_raw, pl in cc_pos[c]} p_imp[c] * Vr[c,pl]; |
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258 | |
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259 | # Total import cost -- at exchange rate -- |
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260 | # is sum of import costs for final products |
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261 | # in each region and raw materials at each plant |
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262 | |
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263 | ### DATA ### |
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264 | |
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265 | data; |
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266 | |
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267 | set center := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ABU_KIR TALKHA SUEZ ; |
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268 | |
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269 | set port := ABU_KIR ; |
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270 | |
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271 | set plant := ASWAN HELWAN ASSIOUT KAFR_EL_ZT ABU_ZAABAL ; |
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272 | |
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273 | set region := ALEXANDRIA BEHERA GHARBIA KAFR_EL_SH DAKAHLIA DAMIETTA |
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274 | SHARKIA ISMAILIA SUEZ MENOUFIA KALUBIA GIZA BENI_SUEF FAYOUM |
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275 | MINIA ASSIOUT NEW_VALLEY SOHAG QUENA ASWAN ; |
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276 | |
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277 | set unit := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS C_AMM_NITR |
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278 | AMM_SULF SSP ; |
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279 | |
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280 | set proc := SULF_A_S SULF_A_P NITR_ACID AMM_ELEC AMM_C_GAS CAN_310 CAN_335 |
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281 | AMM_SULF SSP_155 ; |
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282 | |
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283 | set nutr := N P205 ; |
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284 | |
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285 | set c_final := UREA CAN_260 CAN_310 CAN_335 AMM_SULF DAP SSP_155 C_250_55 |
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286 | C_300_100 ; |
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287 | |
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288 | set c_inter := AMMONIA NITR_ACID SULF_ACID ; |
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289 | |
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290 | set c_ship := AMMONIA SULF_ACID ; |
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291 | |
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292 | set c_raw := EL_ASWAN COKE_GAS PHOS_ROCK LIMESTONE EL_SULFUR PYRITES |
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293 | ELECTRIC BF_GAS WATER STEAM BAGS ; |
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294 | |
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295 | set p_except[ASWAN] := CAN_335 ; |
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296 | set p_except[HELWAN] := CAN_310 ; |
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297 | set p_except[ASSIOUT] := ; |
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298 | set p_except[KAFR_EL_ZT] := ; |
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299 | set p_except[ABU_ZAABAL] := ; |
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300 | |
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301 | param cf75 default 0.0 : |
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302 | |
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303 | CAN_260 CAN_310 CAN_335 AMM_SULF UREA := |
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304 | |
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305 | ALEXANDRIA . . 5.0 3.0 1.0 |
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306 | ASSIOUT 1.0 20.0 26.0 1.0 27.0 |
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307 | ASWAN . 40.0 . . . |
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308 | BEHERA 1.0 . 25.0 90.0 35.0 |
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309 | BENI_SUEF 1.0 . 15.0 1.0 20.0 |
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310 | DAKAHLIA 1.0 . 26.0 60.0 20.0 |
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311 | DAMIETTA . . 2.0 15.0 8.0 |
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312 | FAYOUM 1.0 . 20.0 6.0 20.0 |
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313 | GHARBIA . . 17.0 60.0 28.0 |
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314 | GIZA . . 40.0 6.0 2.0 |
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315 | ISMAILIA . . 4.0 6.0 2.0 |
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316 | KAFR_EL_SH 1.0 . 10.0 45.0 22.0 |
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317 | KALUBIA . . 25.0 16.0 7.0 |
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318 | MENOUFIA 1.0 . 24.0 21.0 30.0 |
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319 | MINIA 2.0 15.0 35.0 1.0 41.0 |
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320 | NEW_VALLEY . . . . 1.0 |
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321 | QUENA . 95.0 2.0 . 3.0 |
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322 | SHARKIA 1.0 . 31.0 50.0 28.0 |
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323 | SOHAG . 65.0 3.0 . 7.0 |
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324 | SUEZ . . 1.0 . . |
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325 | |
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326 | : SSP_155 C_250_55 C_300_100 DAP := |
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327 | |
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328 | ALEXANDRIA 8.0 . . . |
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329 | ASSIOUT 35.0 5.0 .1 . |
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330 | ASWAN 8.0 . . . |
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331 | BEHERA 64.0 1.0 .1 .1 |
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332 | BENI_SUEF 13.0 3.0 . . |
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333 | DAKAHLIA 52.0 1.0 . . |
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334 | DAMIETTA 5.0 . . . |
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335 | FAYOUM 17.0 1.0 . . |
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336 | GHARBIA 57.0 1.0 .2 .1 |
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337 | GIZA 14.0 1.0 .1 . |
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338 | ISMAILIA 4.0 . . . |
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339 | KAFR_EL_SH 25.0 2.0 .1 . |
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340 | KALUBIA 22.0 1.0 . .1 |
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341 | MENOUFIA 33.0 2.0 .1 .1 |
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342 | MINIA 50.0 3.0 .2 .1 |
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343 | NEW_VALLEY 1.0 . . . |
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344 | QUENA 8.0 . . . |
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345 | SHARKIA 43.0 1.0 .1 . |
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346 | SOHAG 20.0 1.0 . . |
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347 | SUEZ 1.0 . . . ; |
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348 | |
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349 | param fn default 0.0 : N P205 := |
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350 | |
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351 | AMM_SULF .206 . |
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352 | CAN_260 .26 . |
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353 | CAN_310 .31 . |
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354 | CAN_335 .335 . |
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355 | C_250_55 .25 .055 |
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356 | C_300_100 .30 .10 |
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357 | DAP .18 .46 |
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358 | SSP_155 . .15 |
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359 | UREA .46 . ; |
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360 | |
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361 | param road default 0.0 : |
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362 | |
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363 | ABU_KIR ABU_ZAABAL ASSIOUT ASWAN HELWAN KAFR_EL_ZT SUEZ TALKHA := |
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364 | |
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365 | ALEXANDRIA 16 210 607 1135 244 119 362 187 |
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366 | ASSIOUT 616 420 . 518 362 504 527 518 |
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367 | ASWAN 1134 938 518 . 880 1022 1045 1036 |
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368 | BEHERA 76 50 547 1065 184 42 288 120 |
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369 | BENI_SUEF 359 163 257 775 105 248 270 261 |
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370 | DAKAHLIA 208 138 515 1033 152 58 219 3 |
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371 | DAMIETTA 267 216 596 1114 233 131 286 66 |
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372 | FAYOUM 341 145 308 826 88 230 252 243 |
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373 | GHARBIA 150 65 485 1003 122 20 226 55 |
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374 | GIZA 287 48 372 890 .9 133 169 146 |
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375 | ISMAILIA 365 142 536 1054 173 241 89 146 |
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376 | KAFR_EL_SH 145 105 525 1043 162 20 266 35 |
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377 | KALUBIA 190 97 439 957 76 66 180 81 |
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378 | MENOUFIA 157 154 472 990 109 33 213 90 |
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379 | MINIA 384 288 132 650 230 372 394 386 |
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380 | NEW_VALLEY 815 619 199 519 561 703 726 717 |
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381 | QUENA 858 662 242 276 604 746 769 760 |
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382 | SHARKIA 240 60 473 991 110 78 214 58 |
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383 | SOHAG 715 519 99 419 461 603 626 617 |
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384 | SUEZ 370 224 541 1059 178 246 . 298 ; |
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385 | |
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386 | param rail_half default 0 : |
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387 | |
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388 | KAFR_EL_ZT ABU_ZAABAL HELWAN ASSIOUT := |
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389 | |
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390 | ABU_ZAABAL 85 . . . |
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391 | HELWAN 142 57 . . |
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392 | ASSIOUT 504 420 362 . |
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393 | ASWAN 1022 938 880 518 ; |
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394 | |
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395 | param : impd_barg impd_road := |
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396 | |
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397 | ABU_ZAABAL 210 .1 |
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398 | ASSIOUT 583 0 |
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399 | ASWAN 1087 10 |
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400 | HELWAN 183 0 |
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401 | KAFR_EL_ZT 104 6 ; |
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402 | |
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403 | param io default 0.0 := |
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404 | |
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405 | [*,AMM_C_GAS] AMMONIA 1.0 |
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406 | BF_GAS -609. |
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407 | COKE_GAS -2.0 |
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408 | ELECTRIC -1960. |
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409 | STEAM -4. |
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410 | WATER -700. |
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411 | |
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412 | [*,AMM_ELEC] AMMONIA 1.0 |
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413 | EL_ASWAN -12.0 |
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414 | |
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415 | [*,AMM_SULF] AMMONIA -.26 |
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416 | AMM_SULF 1.0 |
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417 | BAGS -22. |
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418 | ELECTRIC -19. |
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419 | SULF_ACID -.76 |
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420 | WATER -17. |
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421 | |
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422 | [*,CAN_310] AMMONIA -.20 |
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423 | BAGS -23. |
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424 | CAN_310 1.0 |
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425 | LIMESTONE -.12 |
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426 | NITR_ACID -.71 |
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427 | STEAM -.4 |
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428 | WATER -49. |
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429 | |
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430 | [*,CAN_335] AMMONIA -.21 |
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431 | BAGS -23. |
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432 | CAN_335 1.0 |
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433 | LIMESTONE -.04 |
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434 | NITR_ACID -.76 |
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435 | STEAM -.4 |
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436 | WATER -49. |
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437 | |
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438 | [*,NITR_ACID] AMMONIA -.292 |
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439 | ELECTRIC -231. |
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440 | NITR_ACID 1.0 |
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441 | WATER -.6 |
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442 | |
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443 | [*,SSP_155] BAGS -22. |
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444 | ELECTRIC -14. |
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445 | PHOS_ROCK -.62 |
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446 | SSP_155 1.0 |
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447 | SULF_ACID -.41 |
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448 | WATER -6. |
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449 | |
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450 | [*,SULF_A_P] ELECTRIC -75. |
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451 | PYRITES -.826 |
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452 | SULF_ACID 1.0 |
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453 | WATER -60. |
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454 | |
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455 | [*,SULF_A_S] ELECTRIC -50. |
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456 | EL_SULFUR -.334 |
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457 | SULF_ACID 1.0 |
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458 | WATER -20. ; |
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459 | |
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460 | param util default 0 := |
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461 | |
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462 | [*,*] SULF_A_S SULF_A_S 1 SULF_A_P SULF_A_P 1 |
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463 | NITR_ACID NITR_ACID 1 AMM_ELEC AMM_ELEC 1 |
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464 | AMM_C_GAS AMM_C_GAS 1 SSP SSP_155 1 |
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465 | C_AMM_NITR CAN_310 1 C_AMM_NITR CAN_335 1 |
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466 | AMM_SULF AMM_SULF 1 ; |
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467 | |
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468 | param p_imp default 0.0 := |
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469 | |
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470 | PYRITES 17.5 AMM_SULF 75. |
---|
471 | EL_SULFUR 55. DAP 175. |
---|
472 | UREA 150. SSP_155 80. |
---|
473 | CAN_260 75. C_250_55 100. |
---|
474 | CAN_310 90. C_300_100 130. |
---|
475 | CAN_335 100. ; |
---|
476 | |
---|
477 | param p_r default 0.0 := |
---|
478 | |
---|
479 | ELECTRIC .007 |
---|
480 | BF_GAS .007 |
---|
481 | WATER .031 |
---|
482 | STEAM 1.25 |
---|
483 | BAGS .28 ; |
---|
484 | |
---|
485 | param p_pr default 0.0 := |
---|
486 | |
---|
487 | [HELWAN,COKE_GAS] 16.0 |
---|
488 | [ASWAN,EL_ASWAN] 1.0 |
---|
489 | |
---|
490 | [*,LIMESTONE] ASWAN 1.2 |
---|
491 | HELWAN 1.2 |
---|
492 | |
---|
493 | [*,PHOS_ROCK] ABU_ZAABAL 4.0 |
---|
494 | ASSIOUT 3.5 |
---|
495 | KAFR_EL_ZT 5.0 ; |
---|
496 | |
---|
497 | param dcap default 0.0 := |
---|
498 | |
---|
499 | [ABU_ZAABAL,*] SSP 600 |
---|
500 | SULF_A_P 227 |
---|
501 | SULF_A_S 242 |
---|
502 | |
---|
503 | [ASSIOUT,*] SSP 600 |
---|
504 | SULF_A_S 250 |
---|
505 | |
---|
506 | [ASWAN,*] AMM_ELEC 450 |
---|
507 | C_AMM_NITR 1100 |
---|
508 | NITR_ACID 800 |
---|
509 | |
---|
510 | [HELWAN,*] AMM_C_GAS 172 |
---|
511 | AMM_SULF 24 |
---|
512 | C_AMM_NITR 364 |
---|
513 | NITR_ACID 282 |
---|
514 | |
---|
515 | [KAFR_EL_ZT,*] SSP 600 |
---|
516 | SULF_A_P 50 |
---|
517 | SULF_A_S 200 ; |
---|
518 | |
---|
519 | end; |
---|