计算调度问题中的雇用天数

在调度问题中，我还想最小化总雇用天数。

如果雇员在该天之前和该天之后工作，则该雇员在该天被雇用。

这是一个小工作示例：

import random
from ortools.sat.python import cp_model

model = cp_model.CpModel()
solver = cp_model.CpSolver()

employees = range(3)
days = range(10)

works_day = {(e, d): model.NewBoolVar(f'{e}_works_{d}')
             for e in employees for d in days}
hired_day = {(e, d): model.NewBoolVar(f'{e}_employed_{d}')
             for e in employees for d in days}

# random example
for boolean in works_day.values():
    model.Add(boolean == random.choice([0, 1]))

# give value to hired_day
add_hired_days()

# solve
print('Variables:', len(model.Proto().variables))
print('Constraints:', len(model.Proto().constraints))
status = solver.Solve(model)

for e in employees:
    print()
    print('Employee', e)
    for d in days:
        print('Works', solver.Value(works_day[e, d]),
              'Hired', solver.Value(hired_day[e, d]))

Where add_hired_days is:

def add_hired_days():
    for idx, d in enumerate(days):
        for e in employees:
            model.AddImplication(works_day[e, d], hired_day[e, d])
            previous = [works_day[e, d] for d in days[:idx + 1]]
            following = [works_day[e, d] for d in days[idx:]]

            # too many variables
            works_previous = model.NewBoolVar('')
            works_following = model.NewBoolVar('')

            model.AddBoolOr(previous).OnlyEnforceIf(works_previous)
            model.AddBoolAnd([d.Not() for d in previous
                              ]).OnlyEnforceIf(works_previous.Not())

            model.AddBoolOr(following).OnlyEnforceIf(works_following)
            model.AddBoolAnd([d.Not() for d in following
                              ]).OnlyEnforceIf(works_following.Not())

            model.AddBoolAnd([works_previous, works_following
                              ]).OnlyEnforceIf(hired_day[e, d])
            model.AddBoolOr([works_previous.Not(),
                             works_following.Not()
                             ]).OnlyEnforceIf(hired_day[e, d].Not())

有没有办法在不创建这么多变量和约束的情况下做到这一点？

如果一名员工一个月工作 n 天，则需要雇用 n - 2 次。