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facility_c.c
/* Copyright 2021, Gurobi Optimization, LLC */ /* Facility location: a company currently ships its product from 5 plants to 4 warehouses. It is considering closing some plants to reduce costs. What plant(s) should the company close, in order to minimize transportation and fixed costs? Based on an example from Frontline Systems: http://www.solver.com/disfacility.htm Used with permission. */ #include <stdlib.h> #include <stdio.h> #include <math.h> #include "gurobi_c.h" #define opencol(p) p #define transportcol(w,p) nPlants*(w+1)+p #define MAXSTR 128 int main(int argc, char *argv[]) { GRBenv *env = NULL; GRBmodel *model = NULL; int error = 0; int p, w, col; int *cbeg = NULL; int *cind = NULL; int idx, rowct; double *cval = NULL; double *rhs = NULL; char *sense = NULL; char vname[MAXSTR]; int cnamect = 0; char **cname = NULL; double maxFixed = -GRB_INFINITY, sol, obj; /* Number of plants and warehouses */ const int nPlants = 5; const int nWarehouses = 4; /* Warehouse demand in thousands of units */ double Demand[] = { 15, 18, 14, 20 }; /* Plant capacity in thousands of units */ double Capacity[] = { 20, 22, 17, 19, 18 }; /* Fixed costs for each plant */ double FixedCosts[] = { 12000, 15000, 17000, 13000, 16000 }; /* Transportation costs per thousand units */ double TransCosts[4][5] = { { 4000, 2000, 3000, 2500, 4500 }, { 2500, 2600, 3400, 3000, 4000 }, { 1200, 1800, 2600, 4100, 3000 }, { 2200, 2600, 3100, 3700, 3200 } }; /* Create environment */ error = GRBloadenv(&env, "facility.log"); if (error) goto QUIT; /* Create initial model */ error = GRBnewmodel(env, &model, "facility", nPlants * (nWarehouses + 1), NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT; /* Initialize decision variables for plant open variables */ for (p = 0; p < nPlants; ++p) { col = opencol(p); error = GRBsetcharattrelement(model, "VType", col, GRB_BINARY); if (error) goto QUIT; error = GRBsetdblattrelement(model, "Obj", col, FixedCosts[p]); if (error) goto QUIT; sprintf(vname, "Open%i", p); error = GRBsetstrattrelement(model, "VarName", col, vname); if (error) goto QUIT; } /* Initialize decision variables for transportation decision variables: how much to transport from a plant p to a warehouse w */ for (w = 0; w < nWarehouses; ++w) { for (p = 0; p < nPlants; ++p) { col = transportcol(w, p); error = GRBsetdblattrelement(model, "Obj", col, TransCosts[w][p]); if (error) goto QUIT; sprintf(vname, "Trans%i.%i", p, w); error = GRBsetstrattrelement(model, "VarName", col, vname); if (error) goto QUIT; } } /* The objective is to minimize the total fixed and variable costs */ error = GRBsetintattr(model, "ModelSense", GRB_MINIMIZE); if (error) goto QUIT; /* Make space for constraint data */ rowct = (nPlants > nWarehouses) ? nPlants : nWarehouses; cbeg = malloc(sizeof(int) * rowct); if (!cbeg) goto QUIT; cind = malloc(sizeof(int) * (nPlants * (nWarehouses + 1))); if (!cind) goto QUIT; cval = malloc(sizeof(double) * (nPlants * (nWarehouses + 1))); if (!cval) goto QUIT; rhs = malloc(sizeof(double) * rowct); if (!rhs) goto QUIT; sense = malloc(sizeof(char) * rowct); if (!sense) goto QUIT; cname = calloc(rowct, sizeof(char*)); if (!cname) goto QUIT; /* Production constraints Note that the limit sets the production to zero if the plant is closed */ idx = 0; for (p = 0; p < nPlants; ++p) { cbeg[p] = idx; rhs[p] = 0.0; sense[p] = GRB_LESS_EQUAL; cname[p] = malloc(sizeof(char) * MAXSTR); if (!cname[p]) goto QUIT; cnamect++; sprintf(cname[p], "Capacity%i", p); for (w = 0; w < nWarehouses; ++w) { cind[idx] = transportcol(w, p); cval[idx++] = 1.0; } cind[idx] = opencol(p); cval[idx++] = -Capacity[p]; } error = GRBaddconstrs(model, nPlants, idx, cbeg, cind, cval, sense, rhs, cname); if (error) goto QUIT; /* Demand constraints */ idx = 0; for (w = 0; w < nWarehouses; ++w) { cbeg[w] = idx; sense[w] = GRB_EQUAL; sprintf(cname[w], "Demand%i", w); for (p = 0; p < nPlants; ++p) { cind[idx] = transportcol(w, p); cval[idx++] = 1.0; } } error = GRBaddconstrs(model, nWarehouses, idx, cbeg, cind, cval, sense, Demand, cname); if (error) goto QUIT; /* Guess at the starting point: close the plant with the highest fixed costs; open all others */ /* First, open all plants */ for (p = 0; p < nPlants; ++p) { error = GRBsetdblattrelement(model, "Start", opencol(p), 1.0); if (error) goto QUIT; } /* Now close the plant with the highest fixed cost */ printf("Initial guess:\n"); for (p = 0; p < nPlants; ++p) { if (FixedCosts[p] > maxFixed) { maxFixed = FixedCosts[p]; } } for (p = 0; p < nPlants; ++p) { if (FixedCosts[p] == maxFixed) { error = GRBsetdblattrelement(model, "Start", opencol(p), 0.0); if (error) goto QUIT; printf("Closing plant %i\n\n", p); break; } } /* Use barrier to solve root relaxation */ error = GRBsetintparam(GRBgetenv(model), GRB_INT_PAR_METHOD, GRB_METHOD_BARRIER); if (error) goto QUIT; /* Solve */ error = GRBoptimize(model); if (error) goto QUIT; /* Print solution */ error = GRBgetdblattr(model, "ObjVal", &obj); if (error) goto QUIT; printf("\nTOTAL COSTS: %f\n", obj); printf("SOLUTION:\n"); for (p = 0; p < nPlants; ++p) { error = GRBgetdblattrelement(model, "X", opencol(p), &sol); if (error) goto QUIT; if (sol > 0.99) { printf("Plant %i open:\n", p); for (w = 0; w < nWarehouses; ++w) { error = GRBgetdblattrelement(model, "X", transportcol(w, p), &sol); if (error) goto QUIT; if (sol > 0.0001) { printf(" Transport %f units to warehouse %i\n", sol, w); } } } else { printf("Plant %i closed!\n", p); } } QUIT: /* Error reporting */ if (error) { printf("ERROR: %s\n", GRBgeterrormsg(env)); exit(1); } /* Free data */ free(cbeg); free(cind); free(cval); free(rhs); free(sense); for (p = 0; p < cnamect; ++p) { free(cname[p]); } free(cname); /* Free model */ GRBfreemodel(model); /* Free environment */ GRBfreeenv(env); return 0; }