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护士排班之线性算法
发表时间：2024-03-19 11:53浏览量：354
护士排班问题可以转化为一个线性规划问题，我们可以使用C#语言中的线性规划库来求解。以下是一个简单的示例代码：
csharp
using System;using System.Collections.Generic;using System.Linq;using System.Text;using System.Threading.Tasks;using Microsoft.SolverFoundation.Common;using Microsoft.SolverFoundation.Services;
namespace NurseScheduling
{
class Program
{
static void Main(string[] args)
{
// 定义问题
SolverContext context = SolverContext.GetContext();
Model model = context.CreateModel();
// 定义变量
Decision[,] schedule = new Decision[7, 3];
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
schedule[i, j] = new Decision(Domain.IntegerNonnegative, "schedule[" + i + "," + j + "]");
model.AddDecision(schedule[i, j]);
}
}
// 定义约束条件
for (int i = 0; i < 7; i++)
{
model.AddConstraint("shifts_per_day[" + i + "]", schedule[i, 0] + schedule[i, 1] + schedule[i, 2] == 2);
}
for (int j = 0; j < 3; j++)
{
model.AddConstraint("shifts_per_nurse[" + j + "]", schedule[0, j] + schedule[1, j] + schedule[2, j] + schedule[3, j] + schedule[4, j] + schedule[5, j] + schedule[6, j] == 2);
}
// 定义目标函数
Term objective = 0;
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
objective += schedule[i, j];
}
}
model.AddObjective("objective", ObjectiveKind.Maximize, objective);
// 求解问题
Solution solution = context.Solve(new SimplexDirective());
Report report = solution.GetReport();
// 输出结果
Console.WriteLine("Solution:");
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
Console.Write(schedule[i, j].GetDouble() + " ");
}
Console.WriteLine();
}
Console.WriteLine("Objective: " + objective.GetDouble());
Console.ReadLine();
}
}
}
在上面的代码中，我们使用了Microsoft Solver Foundation 库来定义问题、变量、约束条件和目标函数，并使用线性规划算法求解问题。具体来说，我们定义了一个 7x3 的决策变量数组 schedule ，表示每个护士在每天的班次安排。然后，我们定义了两个约束条件，分别表示每天需要有两个班次，每个护士每周需要工作两天。最后，我们定义了一个目标函数，表示最大化所有班次的总数。通过调用 SolverContext 的 Solve 方法，我们可以得到最优解，并输出结果。 需要注意的是，上面的代码只是一个简单的示例，实际的护士排班问题可能会更加复杂，需要根据具体情况进行调整。
能否在深入些，提供更复杂的demo
当然可以。以下是一个更复杂的护士排班问题的示例代码，其中包含了更多的约束条件和变量：
csharp
using System;using System.Collections.Generic;using System.Linq;using System.Text;using System.Threading.Tasks;using Microsoft.SolverFoundation.Common;using Microsoft.SolverFoundation.Services;
namespace NurseScheduling
{
class Program
{
static void Main(string[] args)
{
// 定义问题
SolverContext context = SolverContext.GetContext();
Model model = context.CreateModel();
// 定义变量
Decision[,] schedule = new Decision[7, 3];
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
schedule[i, j] = new Decision(Domain.IntegerNonnegative, "schedule[" + i + "," + j + "]");
model.AddDecision(schedule[i, j]);
}
}
// 定义约束条件
for (int i = 0; i < 7; i++)
{
model.AddConstraint("shifts_per_day[" + i + "]", schedule[i, 0] + schedule[i, 1] + schedule[i, 2] == 2);
}
for (int j = 0; j < 3; j++)
{
model.AddConstraint("shifts_per_nurse[" + j + "]", schedule[0, j] + schedule[1, j] + schedule[2, j] + schedule[3, j] + schedule[4, j] + schedule[5, j] + schedule[6, j] == 2);
}
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
model.AddConstraint("max_consecutive_shifts[" + i + "," + j + "]", schedule[i, j] + schedule[(i + 1) % 7, j] + schedule[(i + 2) % 7, j] <= 2);
}
}
for (int j = 0; j < 3; j++)
{
model.AddConstraint("max_consecutive_days[" + j + "]", schedule[0, j] + schedule[1, j] + schedule[2, j] <= 1);
model.AddConstraint("max_consecutive_days[" + j + "]", schedule[1, j] + schedule[2, j] + schedule[3, j] <= 1);
model.AddConstraint("max_consecutive_days[" + j + "]", schedule[2, j] + schedule[3, j] + schedule[4, j] <= 1);
model.AddConstraint("max_consecutive_days[" + j + "]", schedule[3, j] + schedule[4, j] + schedule[5, j] <= 1);
model.AddConstraint("max_consecutive_days[" + j + "]", schedule[4, j] + schedule[5, j] + schedule[6, j] <= 1);
}
for (int j = 0; j < 3; j++)
{
model.AddConstraint("min_consecutive_days[" + j + "]", schedule[0, j] + schedule[1, j] + schedule[2, j] + schedule[3, j] >= 1);
model.AddConstraint("min_consecutive_days[" + j + "]", schedule[1, j] + schedule[2, j] + schedule[3, j] + schedule[4, j] >= 1);
model.AddConstraint("min_consecutive_days[" + j + "]", schedule[2, j] + schedule[3, j] + schedule[4, j] + schedule[5, j] >= 1);
model.AddConstraint("min_consecutive_days[" + j + "]", schedule[3, j] + schedule[4, j] + schedule[5, j] + schedule[6, j] >= 1);
}
for (int j = 0; j < 3; j++)
{
model.AddConstraint("max_weekend_shifts[" + j + "]", schedule[5, j] + schedule[6, j] <= 1);
}
// 定义目标函数
Term objective = 0;
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
objective += schedule[i, j];
}
}
model.AddObjective("objective", ObjectiveKind.Maximize, objective);
// 求解问题
Solution solution = context.Solve(new SimplexDirective());
Report report = solution.GetReport();
// 输出结果
Console.WriteLine("Solution:");
for (int i = 0; i < 7; i++)
{
for (int j = 0; j < 3; j++)
{
Console.Write(schedule[i, j].GetDouble() + " ");
}
Console.WriteLine();
}
Console.WriteLine("Objective: " + objective.GetDouble());
Console.ReadLine();
}
}
}
在上面的代码中，我们增加了更多的约束条件，包括：
每个护士每天最多工作两个班次；
每个护士每周需要工作两天；
每个护士连续工作的天数不能超过两天；
每个护士连续工作的班次不能超过两个；
每个护士每周最多工作一个周末班次。
通过增加这些约束条件，我们可以更好地控制护士的工作时间和工作负荷，从而更好地满足医院的需求。