322 lines
10 KiB
C#
322 lines
10 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using System.Linq;
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using System.Diagnostics;
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using Google.OrTools.ConstraintSolver;
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public class NurseRostering
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{
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/*
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* Global constraint regular
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*
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* This is a translation of MiniZinc's regular constraint (defined in
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* lib/zinc/globals.mzn), via the Comet code refered above.
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* All comments are from the MiniZinc code.
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* """
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* The sequence of values in array 'x' (which must all be in the range 1..S)
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* is accepted by the DFA of 'Q' states with input 1..S and transition
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* function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
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* (which must be in 1..Q) and accepting states 'F' (which all must be in
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* 1..Q). We reserve state 0 to be an always failing state.
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* """
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*
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* x : IntVar array
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* Q : number of states
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* S : input_max
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* d : transition matrix
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* q0: initial state
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* F : accepting states
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*
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*/
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static void MyRegular(Solver solver, IntVar[] x, int Q, int S, int[,] d, int q0, int[] F)
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{
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Debug.Assert(Q > 0, "regular: 'Q' must be greater than zero");
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Debug.Assert(S > 0, "regular: 'S' must be greater than zero");
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// d2 is the same as d, except we add one extra transition for
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// each possible input; each extra transition is from state zero
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// to state zero. This allows us to continue even if we hit a
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// non-accepted input.
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int[][] d2 = new int [Q + 1][];
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for (int i = 0; i <= Q; i++)
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{
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int[] row = new int[S];
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for (int j = 0; j < S; j++)
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{
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if (i == 0)
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{
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row[j] = 0;
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}
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else
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{
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row[j] = d[i - 1, j];
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}
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}
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d2[i] = row;
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}
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int[] d2_flatten =
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(from i in Enumerable.Range(0, Q + 1) from j in Enumerable.Range(0, S) select d2[i][j]).ToArray();
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// If x has index set m..n, then a[m-1] holds the initial state
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// (q0), and a[i+1] holds the state we're in after processing
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// x[i]. If a[n] is in F, then we succeed (ie. accept the
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// string).
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int m = 0;
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int n = x.Length;
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IntVar[] a = solver.MakeIntVarArray(n + 1 - m, 0, Q + 1, "a");
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// Check that the final state is in F
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solver.Add(a[a.Length - 1].Member(F));
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// First state is q0
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solver.Add(a[m] == q0);
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for (int i = 0; i < n; i++)
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{
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solver.Add(x[i] >= 1);
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solver.Add(x[i] <= S);
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// Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
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solver.Add(a[i + 1] == d2_flatten.Element(((a[i]) * S) + (x[i] - 1)));
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}
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}
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/**
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*
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* Nurse rostering
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*
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* This is a simple nurse rostering model using a DFA and
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* my decomposition of regular constraint.
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*
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* The DFA is from MiniZinc Tutorial, Nurse Rostering example:
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* - one day off every 4 days
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* - no 3 nights in a row.
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*
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* Also see http://www.hakank.org/or-tools/nurse_rostering.py
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*
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*/
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private static void Solve()
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{
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Solver solver = new Solver("NurseRostering");
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//
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// Data
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//
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// Note: If you change num_nurses or num_days,
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// please also change the constraints
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// on nurse_stat and/or day_stat.
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int num_nurses = 7;
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int num_days = 14;
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// Note: I had to add a dummy shift.
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int dummy_shift = 0;
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int day_shift = 1;
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int night_shift = 2;
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int off_shift = 3;
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int[] shifts = { dummy_shift, day_shift, night_shift, off_shift };
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int[] valid_shifts = { day_shift, night_shift, off_shift };
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// the DFA (for regular)
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int n_states = 6;
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int input_max = 3;
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int initial_state = 1; // 0 is for the failing state
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int[] accepting_states = { 1, 2, 3, 4, 5, 6 };
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int[,] transition_fn = {
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// d,n,o
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{ 2, 3, 1 }, // state 1
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{ 4, 4, 1 }, // state 2
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{ 4, 5, 1 }, // state 3
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{ 6, 6, 1 }, // state 4
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{ 6, 0, 1 }, // state 5
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{ 0, 0, 1 } // state 6
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};
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string[] days = { "d", "n", "o" }; // for presentation
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//
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// Decision variables
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//
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// For regular
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IntVar[,] x = solver.MakeIntVarMatrix(num_nurses, num_days, valid_shifts, "x");
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IntVar[] x_flat = x.Flatten();
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// summary of the nurses
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IntVar[] nurse_stat = solver.MakeIntVarArray(num_nurses, 0, num_days, "nurse_stat");
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// summary of the shifts per day
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int num_shifts = shifts.Length;
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IntVar[,] day_stat = new IntVar[num_days, num_shifts];
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for (int i = 0; i < num_days; i++)
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{
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for (int j = 0; j < num_shifts; j++)
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{
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day_stat[i, j] = solver.MakeIntVar(0, num_nurses, "day_stat");
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}
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}
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//
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// Constraints
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//
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for (int i = 0; i < num_nurses; i++)
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{
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IntVar[] reg_input = new IntVar[num_days];
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for (int j = 0; j < num_days; j++)
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{
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reg_input[j] = x[i, j];
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}
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MyRegular(solver, reg_input, n_states, input_max, transition_fn, initial_state, accepting_states);
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}
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//
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// Statistics and constraints for each nurse
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//
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for (int i = 0; i < num_nurses; i++)
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{
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// Number of worked days (either day or night shift)
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IntVar[] b = new IntVar[num_days];
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for (int j = 0; j < num_days; j++)
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{
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b[j] = ((x[i, j] == day_shift) + (x[i, j] == night_shift)).Var();
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}
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solver.Add(b.Sum() == nurse_stat[i]);
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// Each nurse must work between 7 and 10
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// days/nights during this period
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solver.Add(nurse_stat[i] >= 7);
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solver.Add(nurse_stat[i] <= 10);
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}
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//
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// Statistics and constraints for each day
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//
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for (int j = 0; j < num_days; j++)
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{
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for (int t = 0; t < num_shifts; t++)
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{
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IntVar[] b = new IntVar[num_nurses];
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for (int i = 0; i < num_nurses; i++)
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{
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b[i] = x[i, j] == t;
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}
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solver.Add(b.Sum() == day_stat[j, t]);
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}
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//
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// Some constraints for each day:
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//
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// Note: We have a strict requirements of
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// the number of shifts.
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// Using atleast constraints is harder
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// in this model.
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//
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if (j % 7 == 5 || j % 7 == 6)
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{
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// special constraints for the weekends
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solver.Add(day_stat[j, day_shift] == 2);
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solver.Add(day_stat[j, night_shift] == 1);
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solver.Add(day_stat[j, off_shift] == 4);
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}
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else
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{
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// for workdays:
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// - exactly 3 on day shift
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solver.Add(day_stat[j, day_shift] == 3);
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// - exactly 2 on night
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solver.Add(day_stat[j, night_shift] == 2);
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// - exactly 2 off duty
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solver.Add(day_stat[j, off_shift] == 2);
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}
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}
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(x_flat, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
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solver.NewSearch(db);
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int num_solutions = 0;
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while (solver.NextSolution())
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{
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num_solutions++;
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for (int i = 0; i < num_nurses; i++)
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{
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Console.Write("Nurse #{0,-2}: ", i);
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var occ = new Dictionary<int, int>();
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for (int j = 0; j < num_days; j++)
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{
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int v = (int)x[i, j].Value() - 1;
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if (!occ.ContainsKey(v))
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{
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occ[v] = 0;
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}
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occ[v]++;
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Console.Write(days[v] + " ");
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}
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Console.Write(" #workdays: {0,2}", nurse_stat[i].Value());
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foreach (int s in valid_shifts)
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{
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int v = 0;
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if (occ.ContainsKey(s - 1))
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{
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v = occ[s - 1];
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}
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Console.Write(" {0}:{1}", days[s - 1], v);
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}
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Console.WriteLine();
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}
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Console.WriteLine();
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Console.WriteLine("Statistics per day:\nDay d n o");
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for (int j = 0; j < num_days; j++)
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{
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Console.Write("Day #{0,2}: ", j);
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foreach (int t in valid_shifts)
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{
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Console.Write(day_stat[j, t].Value() + " ");
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}
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Console.WriteLine();
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}
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Console.WriteLine();
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// We just show 2 solutions
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if (num_solutions > 1)
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{
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break;
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}
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}
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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solver.EndSearch();
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}
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public static void Main(String[] args)
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{
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Solve();
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}
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}
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