Allow excess imports to avoid solution failure.

GAMS/IntExtOpt.gms

@@ -157,6 +157,7 @@ $gdxin
        netImportAmount(import_types)      net imports - Mt
        netImportIncrease(import_types)
        netImportDecrease(import_types)
+       excessImports(import_types)
 
        landCoverArea(land_cover, protection, location)  land cover area in Mha
        landCoverChange(land_cover_before, land_cover_after, protection, location) land cover change in Mha
@@ -175,7 +176,7 @@ $gdxin
 ;
 
 
- POSITIVE VARIABLE cropArea, fertI, irrigI, otherIntensity, yield, feedAmount, importAmount, exportAmount, woodPriceFactor, cropProduction,
+ POSITIVE VARIABLE cropArea, fertI, irrigI, otherIntensity, yield, feedAmount, importAmount, exportAmount, woodPriceFactor, cropProduction, excessImports,
                    landCoverArea, landCoverChange, woodYieldRota, rotationIntensity, woodSupply, totalProduction, netImportIncrease, netImportDecrease;
 
 
@@ -347,7 +348,7 @@ $gdxin
 
  NET_IMPORT_CALC(import_types) .. netImportAmount(import_types) =E= importAmount(import_types) - exportAmount(import_types);
 
- MAX_NET_IMPORT_CONSTRAINT(import_types) .. netImportAmount(import_types) =L= maxNetImport(import_types);
+ MAX_NET_IMPORT_CONSTRAINT(import_types) .. netImportAmount(import_types) =L= maxNetImport(import_types) + excessImports(import_types);
  
  MIN_NET_IMPORT_CONSTRAINT(import_types) .. netImportAmount(import_types) =G= minNetImport(import_types);
  
@@ -395,6 +396,8 @@ $gdxin
                             - sum(animal, feedDiversityCost(animal) * sum(feed_crop, sqr(feedAmount(animal, feed_crop) * cropDM(feed_crop))) / (sum(feed_crop, feedAmount(animal, feed_crop) * cropDM(feed_crop)) + 0.01))
 *                           Net import change cost                            
                             - sum(import_types, exp(tradeAdjustmentCostRate(import_types) * (netImportIncrease(import_types) + netImportDecrease(import_types))) - 1)
+*                           Allow import constraint to be relaxed at a high cost if needed to avoid solution failture                            
+                            - sum(import_types, 1000 * excessImports(import_types));
 ;
 
  MODEL LAND_USE /  ALL / ;