Try our new documentation site.


workforce1_c.c


/* Copyright 2019, Gurobi Optimization, LLC */

/* Assign workers to shifts; each worker may or may not be available on a
   particular day. If the problem cannot be solved, use IIS to find a set of
   conflicting constraints. Note that there may be additional conflicts
   besides what is reported via IIS. */

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "gurobi_c.h"


#define xcol(w,s)  nShifts*w+s
#define MAXSTR     128


int
main(int   argc,
     char *argv[])
{
  GRBenv   *env   = NULL;
  GRBmodel *model = NULL;
  int       error = 0, status;
  int       s, w, col;
  int      *cbeg = NULL;
  int      *cind = NULL;
  int       idx;
  double   *cval = NULL;
  char     *sense = NULL;
  char      vname[MAXSTR];
  double    obj;
  int       i, iis, numconstrs;
  char     *cname;

  /* Sample data */
  const int nShifts = 14;
  const int nWorkers = 7;

  /* 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" };

  /* Number of workers required for each shift */
  double shiftRequirements[] =
    { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 };

  /* Amount each worker is paid to work one shift */
  double pay[] = { 10, 12, 10, 8, 8, 9, 11 };

  /* 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 },
      { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };

  /* Create environment */
  error = GRBloadenv(&env, "workforce1.log");
  if (error) goto QUIT;

  /* Create initial model */
  error = GRBnewmodel(env, &model, "workforce1", nWorkers * nShifts,
                      NULL, NULL, NULL, NULL, NULL);
  if (error) goto QUIT;

  /* Initialize assignment decision variables:
     x[w][s] == 1 if worker w is assigned
     to shift s. Since an assignment model always produces integer
     solutions, we use continuous variables and solve as an LP. */
  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 = GRBsetdblattrelement(model, "UB", col, availability[w][s]);
      if (error) goto QUIT;
      error = GRBsetdblattrelement(model, "Obj", col, pay[w]);
      if (error) goto QUIT;
      error = GRBsetstrattrelement(model, "VarName", col, vname);
      if (error) goto QUIT;
    }
  }

  /* The objective is to minimize the total pay costs */
  error = GRBsetintattr(model, "ModelSense", GRB_MINIMIZE);
  if (error) goto QUIT;

  /* Make space for constraint data */
  cbeg = malloc(sizeof(int) * nShifts);
  if (!cbeg) goto QUIT;
  cind = malloc(sizeof(int) * nShifts * nWorkers);
  if (!cind) goto QUIT;
  cval = malloc(sizeof(double) * nShifts * nWorkers);
  if (!cval) goto QUIT;
  sense = malloc(sizeof(char) * nShifts);
  if (!sense) goto QUIT;

  /* Constraint: assign exactly shiftRequirements[s] workers
     to each shift s */
  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;
    }
  }
  error = GRBaddconstrs(model, nShifts, idx, cbeg, cind, cval, sense,
                        shiftRequirements, Shifts);
  if (error) goto QUIT;

  /* Optimize */
  error = GRBoptimize(model);
  if (error) goto QUIT;
  error = GRBgetintattr(model, "Status", &status);
  if (error) goto QUIT;
  if (status == GRB_UNBOUNDED)
  {
    printf("The model cannot be solved because it is unbounded\n");
    goto QUIT;
  }
  if (status == GRB_OPTIMAL)
  {
    error = GRBgetdblattr(model, "ObjVal", &obj);
    if (error) goto QUIT;
    printf("The optimal objective is %f\n", obj);
    goto QUIT;
  }
  if ((status != GRB_INF_OR_UNBD) && (status != GRB_INFEASIBLE))
  {
    printf("Optimization was stopped with status %i\n", status);
    goto QUIT;
  }

  /* do IIS */
  printf("The model is infeasible; computing IIS\n");
  error = GRBcomputeIIS(model);
  if (error) goto QUIT;
  printf("\nThe following constraint(s) cannot be satisfied:\n");
  error = GRBgetintattr(model, "NumConstrs", &numconstrs);
  if (error) goto QUIT;
  for (i = 0; i < numconstrs; ++i)
  {
    error = GRBgetintattrelement(model, "IISConstr", i, &iis);
    if (error) goto QUIT;
    if (iis)
    {
      error = GRBgetstrattrelement(model, "ConstrName", i, &cname);
      if (error) goto QUIT;
      printf("%s\n", cname);
    }
  }



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;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search