workforce5_c.c.
/ *版权所有2021，Gurobi优狗万app足彩化，LLC * / / *分配工人转移;每个工人都可能或可能无法在特定日期上使用。我们使用多目标优化来解决模型。最高优先级目标最小化了松弛的总和（即，未发现的转移总数）。二级目标最大限度地减少了所有工人之间工作的最大和最小班次之间的差异。允许第二优化将第一个目标降低到较小的值为10％和2 * / #include #include #include #include #include“gurobi_c.h”int solveandprint（grbmodel * model，int nshifts，int nworkers，char **工人，int *状态）;#define xcol（w，s）nshifts * w + s #define slackcl（s）nshifts * nworkers + s #define totslackcol nshifts *（nworkers + 1）#define totshiftscol（w）nshifts *（nworkers + 1）+1+w #define minshiftcol（nshifts + 1）*（nworkers + 1）#define maxshiftcol（nshifts + 1）*（nworkers + 1）+1 #define maxstr 128 int main（int argc，char * argv []）{grbenv *env = null;grbenv * menv = null;grbmodel * model = null;int ERROR = 0，状态; int s, w, col; int *cbeg = NULL; int *cind = NULL; int idx; double *cval = NULL; char *sense = NULL; char vname[MAXSTR], cname[MAXSTR]; /* Sample data */ const int nShifts = 14; const int nWorkers = 8; /* Sets of days and workers */ char* Shifts[] = { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6", "Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13", "Sun14" }; char* Workers[] = { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu", "Tobi" }; /* Number of workers required for each shift */ double shiftRequirements[] = { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 }; /* Worker availability: 0 if the worker is unavailable for a shift */ double availability[][14] = { { 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 }, { 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 }, { 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 }, { 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 }, { 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 }, { 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; /* Create environment */ error = GRBloadenv(&env, "workforce5.log"); if (error) goto QUIT; /* Create initial model */ error = GRBnewmodel(env, &model, "workforce5", (nShifts + 1) * (nWorkers + 1) + 2, NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT; /* get model environment */ menv = GRBgetenv(model); if (!menv) { fprintf(stderr, "Error: could not get model environment\n"); goto QUIT; } /* Initialize assignment decision variables: x[w][s] == 1 if worker w is assigned to shift s. This is no longer a pure assignment model, so we must use binary variables. */ for (w = 0; w < nWorkers; ++w) { for (s = 0; s < nShifts; ++s) { col = xcol(w, s); sprintf(vname, "%s.%s", Workers[w], Shifts[s]); error = GRBsetcharattrelement(model, "VType", col, GRB_BINARY); if (error) goto QUIT; error = GRBsetdblattrelement(model, "UB", col, availability[w][s]); if (error) goto QUIT; error = GRBsetstrattrelement(model, "VarName", col, vname); if (error) goto QUIT; } } /* Initialize slack decision variables */ for (s = 0; s < nShifts; ++s) { sprintf(vname, "%sSlack", Shifts[s]); error = GRBsetstrattrelement(model, "VarName", slackcol(s), vname); if (error) goto QUIT; } /* Initialize total slack decision variable */ error = GRBsetstrattrelement(model, "VarName", totSlackcol, "totSlack"); if (error) goto QUIT; /* Initialize variables to count the total shifts worked by each worker */ for (w = 0; w < nWorkers; ++w) { sprintf(vname, "%sTotShifts", Workers[w]); error = GRBsetstrattrelement(model, "VarName", totShiftscol(w), vname); if (error) goto QUIT; } /* Initialize max and min #shifts variables */ sprintf(vname, "minShifts"); error = GRBsetstrattrelement(model, "VarName", minShiftcol, vname); sprintf(vname, "maxShifts"); error = GRBsetstrattrelement(model, "VarName", maxShiftcol, vname); /* Make space for constraint data */ cbeg = malloc(sizeof(int) * nShifts); if (!cbeg) goto QUIT; cind = malloc(sizeof(int) * nShifts * (nWorkers + 1)); if (!cind) goto QUIT; cval = malloc(sizeof(double) * nShifts * (nWorkers + 1)); if (!cval) goto QUIT; sense = malloc(sizeof(char) * (nShifts + nWorkers)); if (!sense) goto QUIT; /* Constraint: assign exactly shiftRequirements[s] workers to each shift s, plus the slack */ idx = 0; for (s = 0; s < nShifts; ++s) { cbeg[s] = idx; sense[s] = GRB_EQUAL; for (w = 0; w < nWorkers; ++w) { cind[idx] = xcol(w, s); cval[idx++] = 1.0; } cind[idx] = slackcol(s); cval[idx++] = 1.0; } error = GRBaddconstrs(model, nShifts, idx, cbeg, cind, cval, sense, shiftRequirements, Shifts); if (error) goto QUIT; /* Constraint: set totSlack column equal to the total slack */ idx = 0; for (s = 0; s < nShifts; ++s) { cind[idx] = slackcol(s); cval[idx++] = 1.0; } cind[idx] = totSlackcol; cval[idx++] = -1.0; error = GRBaddconstr(model, idx, cind, cval, GRB_EQUAL, 0.0, "totSlack"); if (error) goto QUIT; /* Constraint: compute the total number of shifts for each worker */ for (w = 0; w < nWorkers; ++w) { idx = 0; for (s = 0; s < nShifts; ++s) { cind[idx] = xcol(w,s); cval[idx++] = 1.0; } sprintf(cname, "totShifts%s", Workers[w]); cind[idx] = totShiftscol(w); cval[idx++] = -1.0; error = GRBaddconstr(model, idx, cind, cval, GRB_EQUAL, 0.0, cname); if (error) goto QUIT; } /* Constraint: set minShift/maxShift variable to less <=/>= to the * number of shifts among all workers */ for (w = 0; w < nWorkers; w++) { cind[w] = totShiftscol(w); } error = GRBaddgenconstrMin(model, NULL, minShiftcol, nWorkers, cind, GRB_INFINITY); if (error) goto QUIT; error = GRBaddgenconstrMax(model, NULL, maxShiftcol, nWorkers, cind, -GRB_INFINITY); if (error) goto QUIT; /* Set global sense for ALL objectives */ error = GRBsetintattr(model, GRB_INT_ATTR_MODELSENSE, GRB_MINIMIZE); if (error) goto QUIT; /* Set primary objective */ cind[0] = totSlackcol; cval[0] = 1.0; error = GRBsetobjectiven(model, 0, 2, 1.0, 2.0, 0.10, "TotalSlack", 0.0, 1, cind, cval); if (error) goto QUIT; /* Set secondary objective */ cind[0] = maxShiftcol; cval[0] = 1.0; cind[1] = minShiftcol; cval[1] = -1.0; error = GRBsetobjectiven(model, 1, 1, 1.0, 0, 0, "Fairness", 0.0, 2, cind, cval); if (error) goto QUIT; /* Save problem */ error = GRBwrite(model, "workforce5.lp"); if (error) goto QUIT; error = GRBwrite(model, "workforce5.mps"); if (error) goto QUIT; /* Optimize */ error = solveAndPrint(model, nShifts, nWorkers, Workers, &status); if (error) goto QUIT; if (status != GRB_OPTIMAL) goto QUIT; QUIT: /* Error reporting */ if (error) { printf("ERROR: %s\n", GRBgeterrormsg(env)); exit(1); } /* Free data */ free(cbeg); free(cind); free(cval); free(sense); /* Free model */ GRBfreemodel(model); /* Free environment */ GRBfreeenv(env); return 0; } int solveAndPrint(GRBmodel* model, int nShifts, int nWorkers, char** Workers, int* status) { int error, w; double val; error = GRBoptimize(model); if (error) return error; error = GRBgetintattr(model, "Status", status); if (error) return error; if ((*status == GRB_INF_OR_UNBD) || (*status == GRB_INFEASIBLE) || (*status == GRB_UNBOUNDED)) { printf("The model cannot be solved " "because it is infeasible or unbounded\n"); return 0; } if (*status != GRB_OPTIMAL) { printf("Optimization was stopped with status %i\n", *status); return 0; } /* Print total slack and the number of shifts worked for each worker */ error = GRBgetdblattrelement(model, "X", totSlackcol, &val); if (error) return error; printf("\nTotal slack required: %f\n", val); for (w = 0; w < nWorkers; ++w) { error = GRBgetdblattrelement(model, "X", totShiftscol(w), &val); if (error) return error; printf("%s worked %f shifts\n", Workers[w], val); } printf("\n"); return 0; }
