当时间用作 Pulp 变量中的索引时，如何向 LP 添加优先约束？答案

【问题标题】：How to add precedence constraints to LP when time is used as an index in a Pulp variable?当时间用作 Pulp 变量中的索引时，如何向 LP 添加优先约束？
【发布时间】：2022-02-03 15:48:25
【问题描述】：

亲爱的程序员们，

我想知道如何根据可用性安排活动（请参阅input）。有些人在可用小时数大于零的日子有空。我们希望我们的日程安排尽可能接近于零（高效计划）。这意味着，当我们为一个需要五项活动的客户安排一个新项目时，我们需要我们的算法通过该特定项目日的活动持续时间来减少可用小时数。一些活动需要 0.5 小时才能完成，而另一些活动需要 1 小时才能完成。我试图制定模型的初始版本，其中变量 A、B、C、D 和 E 作为正确顺序的活动（但），只有一名员工（称为“0”，因为我将在未来，但我不想从一开始的太复杂的情况开始）和活动安排的那一天。对于第一个和第五个活动，允许患者给出偏好。对于第二、第三和第四个活动，可以随时安排活动。可用性变量在这里是员工 AW 的可用时间列表（请参阅input）。

days = range(1,32)
preferences = [4,11,18,25]

A = LpVariable.dicts(name = "Intake", indexs = [(0, v) for v in preferences], lowBound = 0, upBound = 1, cat = "Continuous")
B = LpVariable.dicts(name = "Write a transcript of intake", indexs = [(0, d) for d in days], lowBound = 0, upBound = 1, cat =  "Continuous")
C = LpVariable.dicts(name = "Create treatment plan", indexs = [(0, d) for d in days], lowBound = 0, upBound = 0.5, cat = "Continuous")
D = LpVariable.dicts(name = "Schedule a meeting", indexs = [(0, d) for d in days], lowBound = 0, upBound = 0.5, cat = "Continuous")
E = LpVariable.dicts(name = "Discuss treatment plan with patiënt", indexs = [(0, v) for v in preferences], lowBound = 0, upBound = 1, cat = "Continuous")

############################## OBJECTIVE ##############################################


# define the model to maximize the workday
schedule = LpProblem(name="Maximize_Schedule", sense=LpMaximize)

schedule += lpSum(A[(0,v)] for v in preferences) + lpSum(B[(0,d)] for d in days) + lpSum(C[(0,d)] for d in days) + lpSum(D[(0,d)] for d in days) + lpSum(E[(0,v)] for v in preferences)

############################## CONSTRAINTS ############################################

# Less than available hours

for v in preferences:
    schedule += A[0,v] + B[0,v] + C[0,v] + D[0,v] + E[0,v] <= availability[v-1]

for d in days:
    schedule += B[0,d] + C[0,d] + D[0,d] <= availability[d-1]


# There is no more than 4 hours to divide

schedule += lpSum(A[(0,v)] for v in preferences) + lpSum(B[(0,d)] for d in days) + lpSum(C[(0,d)] for d in days) + lpSum(D[(0,d)] for d in days) + lpSum(E[(0,v)] for v in preferences) <= 4

# Every activity must be in the solution

schedule += lpSum(A[(0,v)] for v in preferences) == 1

schedule += lpSum(B[(0,d)] for d in days) == 1

schedule += lpSum(C[(0,d)] for d in days) == 0.5

schedule += lpSum(D[(0,d)] for d in days) == 0.5

schedule += lpSum(E[(0,v)] for v in preferences) == 1


# An activity cannot be less than zero

for v in preferences:
    schedule += A[(0,v)] >= 0
    schedule += E[(0,v)] >= 0

for d in days:
    schedule += B[(0,d)] >= 0
    schedule += C[(0,d)] >= 0
    schedule += D[(0,d)] >= 0


status = schedule.solve()

该模型为我提供了以下输出：

Create_treatment_plan_(0,_4) 0.5
Discuss_treatment_plan_with_patiënt_(0,_11) 1.0
Intake_(0,_11) 1.0
Schedule_a_meeting_(0,_4) 0.5
Write_a_transcript_of_intake_(0,_4) 1.0

已经满足了很多约束条件，但是我们可以看到结果没有优先级（“摄入”计划在“编写摄入记录”之前）。我不知道如何在我的 LP 中实施优先约束，因为我没有使用开始时间和结束时间，而是使用可用性。你能帮我寻找解决方案吗？在此页面的底部，您可以找到我的纸浆中的 LP 配方的完整版本。

亲切的问候，

汤姆

Maximize_Schedule:
MAXIMIZE
1*Create_treatment_plan_(0,_1) + 1*Create_treatment_plan_(0,_10) + 1*Create_treatment_plan_(0,_11) + 1*Create_treatment_plan_(0,_12) + 1*Create_treatment_plan_(0,_13) + 1*Create_treatment_plan_(0,_14) + 1*Create_treatment_plan_(0,_15) + 1*Create_treatment_plan_(0,_16) + 1*Create_treatment_plan_(0,_17) + 1*Create_treatment_plan_(0,_18) + 1*Create_treatment_plan_(0,_19) + 1*Create_treatment_plan_(0,_2) + 1*Create_treatment_plan_(0,_20) + 1*Create_treatment_plan_(0,_21) + 1*Create_treatment_plan_(0,_22) + 1*Create_treatment_plan_(0,_23) + 1*Create_treatment_plan_(0,_24) + 1*Create_treatment_plan_(0,_25) + 1*Create_treatment_plan_(0,_26) + 1*Create_treatment_plan_(0,_27) + 1*Create_treatment_plan_(0,_28) + 1*Create_treatment_plan_(0,_29) + 1*Create_treatment_plan_(0,_3) + 1*Create_treatment_plan_(0,_30) + 1*Create_treatment_plan_(0,_31) + 1*Create_treatment_plan_(0,_4) + 1*Create_treatment_plan_(0,_5) + 1*Create_treatment_plan_(0,_6) + 1*Create_treatment_plan_(0,_7) + 1*Create_treatment_plan_(0,_8) + 1*Create_treatment_plan_(0,_9) + 1*Discuss_treatment_plan_with_patiënt_(0,_11) + 1*Discuss_treatment_plan_with_patiënt_(0,_18) + 1*Discuss_treatment_plan_with_patiënt_(0,_25) + 1*Discuss_treatment_plan_with_patiënt_(0,_4) + 1*Intake_(0,_11) + 1*Intake_(0,_18) + 1*Intake_(0,_25) + 1*Intake_(0,_4) + 1*Schedule_a_meeting_(0,_1) + 1*Schedule_a_meeting_(0,_10) + 1*Schedule_a_meeting_(0,_11) + 1*Schedule_a_meeting_(0,_12) + 1*Schedule_a_meeting_(0,_13) + 1*Schedule_a_meeting_(0,_14) + 1*Schedule_a_meeting_(0,_15) + 1*Schedule_a_meeting_(0,_16) + 1*Schedule_a_meeting_(0,_17) + 1*Schedule_a_meeting_(0,_18) + 1*Schedule_a_meeting_(0,_19) + 1*Schedule_a_meeting_(0,_2) + 1*Schedule_a_meeting_(0,_20) + 1*Schedule_a_meeting_(0,_21) + 1*Schedule_a_meeting_(0,_22) + 1*Schedule_a_meeting_(0,_23) + 1*Schedule_a_meeting_(0,_24) + 1*Schedule_a_meeting_(0,_25) + 1*Schedule_a_meeting_(0,_26) + 1*Schedule_a_meeting_(0,_27) + 1*Schedule_a_meeting_(0,_28) + 1*Schedule_a_meeting_(0,_29) + 1*Schedule_a_meeting_(0,_3) + 1*Schedule_a_meeting_(0,_30) + 1*Schedule_a_meeting_(0,_31) + 1*Schedule_a_meeting_(0,_4) + 1*Schedule_a_meeting_(0,_5) + 1*Schedule_a_meeting_(0,_6) + 1*Schedule_a_meeting_(0,_7) + 1*Schedule_a_meeting_(0,_8) + 1*Schedule_a_meeting_(0,_9) + 1*Write_a_transcript_of_intake_(0,_1) + 1*Write_a_transcript_of_intake_(0,_10) + 1*Write_a_transcript_of_intake_(0,_11) + 1*Write_a_transcript_of_intake_(0,_12) + 1*Write_a_transcript_of_intake_(0,_13) + 1*Write_a_transcript_of_intake_(0,_14) + 1*Write_a_transcript_of_intake_(0,_15) + 1*Write_a_transcript_of_intake_(0,_16) + 1*Write_a_transcript_of_intake_(0,_17) + 1*Write_a_transcript_of_intake_(0,_18) + 1*Write_a_transcript_of_intake_(0,_19) + 1*Write_a_transcript_of_intake_(0,_2) + 1*Write_a_transcript_of_intake_(0,_20) + 1*Write_a_transcript_of_intake_(0,_21) + 1*Write_a_transcript_of_intake_(0,_22) + 1*Write_a_transcript_of_intake_(0,_23) + 1*Write_a_transcript_of_intake_(0,_24) + 1*Write_a_transcript_of_intake_(0,_25) + 1*Write_a_transcript_of_intake_(0,_26) + 1*Write_a_transcript_of_intake_(0,_27) + 1*Write_a_transcript_of_intake_(0,_28) + 1*Write_a_transcript_of_intake_(0,_29) + 1*Write_a_transcript_of_intake_(0,_3) + 1*Write_a_transcript_of_intake_(0,_30) + 1*Write_a_transcript_of_intake_(0,_31) + 1*Write_a_transcript_of_intake_(0,_4) + 1*Write_a_transcript_of_intake_(0,_5) + 1*Write_a_transcript_of_intake_(0,_6) + 1*Write_a_transcript_of_intake_(0,_7) + 1*Write_a_transcript_of_intake_(0,_8) + 1*Write_a_transcript_of_intake_(0,_9) + 0
SUBJECT TO
_C1: Create_treatment_plan_(0,_4) + Discuss_treatment_plan_with_patiënt_(0,_4)
 + Intake_(0,_4) + Schedule_a_meeting_(0,_4)
 + Write_a_transcript_of_intake_(0,_4) <= 3

_C2: Create_treatment_plan_(0,_11)
 + Discuss_treatment_plan_with_patiënt_(0,_11) + Intake_(0,_11)
 + Schedule_a_meeting_(0,_11) + Write_a_transcript_of_intake_(0,_11) <= 4

_C3: Create_treatment_plan_(0,_18)
 + Discuss_treatment_plan_with_patiënt_(0,_18) + Intake_(0,_18)
 + Schedule_a_meeting_(0,_18) + Write_a_transcript_of_intake_(0,_18) <= 5

_C4: Create_treatment_plan_(0,_25)
 + Discuss_treatment_plan_with_patiënt_(0,_25) + Intake_(0,_25)
 + Schedule_a_meeting_(0,_25) + Write_a_transcript_of_intake_(0,_25) <= 6

_C5: Create_treatment_plan_(0,_1) + Schedule_a_meeting_(0,_1)
 + Write_a_transcript_of_intake_(0,_1) <= 0

_C6: Create_treatment_plan_(0,_2) + Schedule_a_meeting_(0,_2)
 + Write_a_transcript_of_intake_(0,_2) <= 5

_C7: Create_treatment_plan_(0,_3) + Schedule_a_meeting_(0,_3)
 + Write_a_transcript_of_intake_(0,_3) <= 7

_C8: Create_treatment_plan_(0,_4) + Schedule_a_meeting_(0,_4)
 + Write_a_transcript_of_intake_(0,_4) <= 3

_C9: Create_treatment_plan_(0,_5) + Schedule_a_meeting_(0,_5)
 + Write_a_transcript_of_intake_(0,_5) <= 0

_C10: Create_treatment_plan_(0,_6) + Schedule_a_meeting_(0,_6)
 + Write_a_transcript_of_intake_(0,_6) <= 0

_C11: Create_treatment_plan_(0,_7) + Schedule_a_meeting_(0,_7)
 + Write_a_transcript_of_intake_(0,_7) <= 6

_C12: Create_treatment_plan_(0,_8) + Schedule_a_meeting_(0,_8)
 + Write_a_transcript_of_intake_(0,_8) <= 0

_C13: Create_treatment_plan_(0,_9) + Schedule_a_meeting_(0,_9)
 + Write_a_transcript_of_intake_(0,_9) <= 6

_C14: Create_treatment_plan_(0,_10) + Schedule_a_meeting_(0,_10)
 + Write_a_transcript_of_intake_(0,_10) <= 1

_C15: Create_treatment_plan_(0,_11) + Schedule_a_meeting_(0,_11)
 + Write_a_transcript_of_intake_(0,_11) <= 4

_C16: Create_treatment_plan_(0,_12) + Schedule_a_meeting_(0,_12)
 + Write_a_transcript_of_intake_(0,_12) <= 0

_C17: Create_treatment_plan_(0,_13) + Schedule_a_meeting_(0,_13)
 + Write_a_transcript_of_intake_(0,_13) <= 0

_C18: Create_treatment_plan_(0,_14) + Schedule_a_meeting_(0,_14)
 + Write_a_transcript_of_intake_(0,_14) <= 4

_C19: Create_treatment_plan_(0,_15) + Schedule_a_meeting_(0,_15)
 + Write_a_transcript_of_intake_(0,_15) <= 0

_C20: Create_treatment_plan_(0,_16) + Schedule_a_meeting_(0,_16)
 + Write_a_transcript_of_intake_(0,_16) <= 4

_C21: Create_treatment_plan_(0,_17) + Schedule_a_meeting_(0,_17)
 + Write_a_transcript_of_intake_(0,_17) <= 7

_C22: Create_treatment_plan_(0,_18) + Schedule_a_meeting_(0,_18)
 + Write_a_transcript_of_intake_(0,_18) <= 5

_C23: Create_treatment_plan_(0,_19) + Schedule_a_meeting_(0,_19)
 + Write_a_transcript_of_intake_(0,_19) <= 0

_C24: Create_treatment_plan_(0,_20) + Schedule_a_meeting_(0,_20)
 + Write_a_transcript_of_intake_(0,_20) <= 0

_C25: Create_treatment_plan_(0,_21) + Schedule_a_meeting_(0,_21)
 + Write_a_transcript_of_intake_(0,_21) <= 4

_C26: Create_treatment_plan_(0,_22) + Schedule_a_meeting_(0,_22)
 + Write_a_transcript_of_intake_(0,_22) <= 0

_C27: Create_treatment_plan_(0,_23) + Schedule_a_meeting_(0,_23)
 + Write_a_transcript_of_intake_(0,_23) <= 4

_C28: Create_treatment_plan_(0,_24) + Schedule_a_meeting_(0,_24)
 + Write_a_transcript_of_intake_(0,_24) <= 7

_C29: Create_treatment_plan_(0,_25) + Schedule_a_meeting_(0,_25)
 + Write_a_transcript_of_intake_(0,_25) <= 6

_C30: Create_treatment_plan_(0,_26) + Schedule_a_meeting_(0,_26)
 + Write_a_transcript_of_intake_(0,_26) <= 0

_C31: Create_treatment_plan_(0,_27) + Schedule_a_meeting_(0,_27)
 + Write_a_transcript_of_intake_(0,_27) <= 0

_C32: Create_treatment_plan_(0,_28) + Schedule_a_meeting_(0,_28)
 + Write_a_transcript_of_intake_(0,_28) <= 4

_C33: Create_treatment_plan_(0,_29) + Schedule_a_meeting_(0,_29)
 + Write_a_transcript_of_intake_(0,_29) <= 0

_C34: Create_treatment_plan_(0,_30) + Schedule_a_meeting_(0,_30)
 + Write_a_transcript_of_intake_(0,_30) <= 5

_C35: Create_treatment_plan_(0,_31) + Schedule_a_meeting_(0,_31)
 + Write_a_transcript_of_intake_(0,_31) <= 7

_C36: Create_treatment_plan_(0,_1) + Create_treatment_plan_(0,_10)
 + Create_treatment_plan_(0,_11) + Create_treatment_plan_(0,_12)
 + Create_treatment_plan_(0,_13) + Create_treatment_plan_(0,_14)
 + Create_treatment_plan_(0,_15) + Create_treatment_plan_(0,_16)
 + Create_treatment_plan_(0,_17) + Create_treatment_plan_(0,_18)
 + Create_treatment_plan_(0,_19) + Create_treatment_plan_(0,_2)
 + Create_treatment_plan_(0,_20) + Create_treatment_plan_(0,_21)
 + Create_treatment_plan_(0,_22) + Create_treatment_plan_(0,_23)
 + Create_treatment_plan_(0,_24) + Create_treatment_plan_(0,_25)
 + Create_treatment_plan_(0,_26) + Create_treatment_plan_(0,_27)
 + Create_treatment_plan_(0,_28) + Create_treatment_plan_(0,_29)
 + Create_treatment_plan_(0,_3) + Create_treatment_plan_(0,_30)
 + Create_treatment_plan_(0,_31) + Create_treatment_plan_(0,_4)
 + Create_treatment_plan_(0,_5) + Create_treatment_plan_(0,_6)
 + Create_treatment_plan_(0,_7) + Create_treatment_plan_(0,_8)
 + Create_treatment_plan_(0,_9) + Discuss_treatment_plan_with_patiënt_(0,_11)
 + Discuss_treatment_plan_with_patiënt_(0,_18)
 + Discuss_treatment_plan_with_patiënt_(0,_25)
 + Discuss_treatment_plan_with_patiënt_(0,_4) + Intake_(0,_11)
 + Intake_(0,_18) + Intake_(0,_25) + Intake_(0,_4) + Schedule_a_meeting_(0,_1)
 + Schedule_a_meeting_(0,_10) + Schedule_a_meeting_(0,_11)
 + Schedule_a_meeting_(0,_12) + Schedule_a_meeting_(0,_13)
 + Schedule_a_meeting_(0,_14) + Schedule_a_meeting_(0,_15)
 + Schedule_a_meeting_(0,_16) + Schedule_a_meeting_(0,_17)
 + Schedule_a_meeting_(0,_18) + Schedule_a_meeting_(0,_19)
 + Schedule_a_meeting_(0,_2) + Schedule_a_meeting_(0,_20)
 + Schedule_a_meeting_(0,_21) + Schedule_a_meeting_(0,_22)
 + Schedule_a_meeting_(0,_23) + Schedule_a_meeting_(0,_24)
 + Schedule_a_meeting_(0,_25) + Schedule_a_meeting_(0,_26)
 + Schedule_a_meeting_(0,_27) + Schedule_a_meeting_(0,_28)
 + Schedule_a_meeting_(0,_29) + Schedule_a_meeting_(0,_3)
 + Schedule_a_meeting_(0,_30) + Schedule_a_meeting_(0,_31)
 + Schedule_a_meeting_(0,_4) + Schedule_a_meeting_(0,_5)
 + Schedule_a_meeting_(0,_6) + Schedule_a_meeting_(0,_7)
 + Schedule_a_meeting_(0,_8) + Schedule_a_meeting_(0,_9)
 + Write_a_transcript_of_intake_(0,_1) + Write_a_transcript_of_intake_(0,_10)
 + Write_a_transcript_of_intake_(0,_11) + Write_a_transcript_of_intake_(0,_12)
 + Write_a_transcript_of_intake_(0,_13) + Write_a_transcript_of_intake_(0,_14)
 + Write_a_transcript_of_intake_(0,_15) + Write_a_transcript_of_intake_(0,_16)
 + Write_a_transcript_of_intake_(0,_17) + Write_a_transcript_of_intake_(0,_18)
 + Write_a_transcript_of_intake_(0,_19) + Write_a_transcript_of_intake_(0,_2)
 + Write_a_transcript_of_intake_(0,_20) + Write_a_transcript_of_intake_(0,_21)
 + Write_a_transcript_of_intake_(0,_22) + Write_a_transcript_of_intake_(0,_23)
 + Write_a_transcript_of_intake_(0,_24) + Write_a_transcript_of_intake_(0,_25)
 + Write_a_transcript_of_intake_(0,_26) + Write_a_transcript_of_intake_(0,_27)
 + Write_a_transcript_of_intake_(0,_28) + Write_a_transcript_of_intake_(0,_29)
 + Write_a_transcript_of_intake_(0,_3) + Write_a_transcript_of_intake_(0,_30)
 + Write_a_transcript_of_intake_(0,_31) + Write_a_transcript_of_intake_(0,_4)
 + Write_a_transcript_of_intake_(0,_5) + Write_a_transcript_of_intake_(0,_6)
 + Write_a_transcript_of_intake_(0,_7) + Write_a_transcript_of_intake_(0,_8)
 + Write_a_transcript_of_intake_(0,_9) <= 4

_C37: Intake_(0,_11) + Intake_(0,_18) + Intake_(0,_25) + Intake_(0,_4) = 1

_C38: Write_a_transcript_of_intake_(0,_1)
 + Write_a_transcript_of_intake_(0,_10) + Write_a_transcript_of_intake_(0,_11)
 + Write_a_transcript_of_intake_(0,_12) + Write_a_transcript_of_intake_(0,_13)
 + Write_a_transcript_of_intake_(0,_14) + Write_a_transcript_of_intake_(0,_15)
 + Write_a_transcript_of_intake_(0,_16) + Write_a_transcript_of_intake_(0,_17)
 + Write_a_transcript_of_intake_(0,_18) + Write_a_transcript_of_intake_(0,_19)
 + Write_a_transcript_of_intake_(0,_2) + Write_a_transcript_of_intake_(0,_20)
 + Write_a_transcript_of_intake_(0,_21) + Write_a_transcript_of_intake_(0,_22)
 + Write_a_transcript_of_intake_(0,_23) + Write_a_transcript_of_intake_(0,_24)
 + Write_a_transcript_of_intake_(0,_25) + Write_a_transcript_of_intake_(0,_26)
 + Write_a_transcript_of_intake_(0,_27) + Write_a_transcript_of_intake_(0,_28)
 + Write_a_transcript_of_intake_(0,_29) + Write_a_transcript_of_intake_(0,_3)
 + Write_a_transcript_of_intake_(0,_30) + Write_a_transcript_of_intake_(0,_31)
 + Write_a_transcript_of_intake_(0,_4) + Write_a_transcript_of_intake_(0,_5)
 + Write_a_transcript_of_intake_(0,_6) + Write_a_transcript_of_intake_(0,_7)
 + Write_a_transcript_of_intake_(0,_8) + Write_a_transcript_of_intake_(0,_9)
 = 1

_C39: Create_treatment_plan_(0,_1) + Create_treatment_plan_(0,_10)
 + Create_treatment_plan_(0,_11) + Create_treatment_plan_(0,_12)
 + Create_treatment_plan_(0,_13) + Create_treatment_plan_(0,_14)
 + Create_treatment_plan_(0,_15) + Create_treatment_plan_(0,_16)
 + Create_treatment_plan_(0,_17) + Create_treatment_plan_(0,_18)
 + Create_treatment_plan_(0,_19) + Create_treatment_plan_(0,_2)
 + Create_treatment_plan_(0,_20) + Create_treatment_plan_(0,_21)
 + Create_treatment_plan_(0,_22) + Create_treatment_plan_(0,_23)
 + Create_treatment_plan_(0,_24) + Create_treatment_plan_(0,_25)
 + Create_treatment_plan_(0,_26) + Create_treatment_plan_(0,_27)
 + Create_treatment_plan_(0,_28) + Create_treatment_plan_(0,_29)
 + Create_treatment_plan_(0,_3) + Create_treatment_plan_(0,_30)
 + Create_treatment_plan_(0,_31) + Create_treatment_plan_(0,_4)
 + Create_treatment_plan_(0,_5) + Create_treatment_plan_(0,_6)
 + Create_treatment_plan_(0,_7) + Create_treatment_plan_(0,_8)
 + Create_treatment_plan_(0,_9) = 0.5

_C40: Schedule_a_meeting_(0,_1) + Schedule_a_meeting_(0,_10)
 + Schedule_a_meeting_(0,_11) + Schedule_a_meeting_(0,_12)
 + Schedule_a_meeting_(0,_13) + Schedule_a_meeting_(0,_14)
 + Schedule_a_meeting_(0,_15) + Schedule_a_meeting_(0,_16)
 + Schedule_a_meeting_(0,_17) + Schedule_a_meeting_(0,_18)
 + Schedule_a_meeting_(0,_19) + Schedule_a_meeting_(0,_2)
 + Schedule_a_meeting_(0,_20) + Schedule_a_meeting_(0,_21)
 + Schedule_a_meeting_(0,_22) + Schedule_a_meeting_(0,_23)
 + Schedule_a_meeting_(0,_24) + Schedule_a_meeting_(0,_25)
 + Schedule_a_meeting_(0,_26) + Schedule_a_meeting_(0,_27)
 + Schedule_a_meeting_(0,_28) + Schedule_a_meeting_(0,_29)
 + Schedule_a_meeting_(0,_3) + Schedule_a_meeting_(0,_30)
 + Schedule_a_meeting_(0,_31) + Schedule_a_meeting_(0,_4)
 + Schedule_a_meeting_(0,_5) + Schedule_a_meeting_(0,_6)
 + Schedule_a_meeting_(0,_7) + Schedule_a_meeting_(0,_8)
 + Schedule_a_meeting_(0,_9) = 0.5

_C41: Discuss_treatment_plan_with_patiënt_(0,_11)
 + Discuss_treatment_plan_with_patiënt_(0,_18)
 + Discuss_treatment_plan_with_patiënt_(0,_25)
 + Discuss_treatment_plan_with_patiënt_(0,_4) = 1

_C42: Intake_(0,_4) >= 0

_C43: Discuss_treatment_plan_with_patiënt_(0,_4) >= 0

_C44: Intake_(0,_11) >= 0

_C45: Discuss_treatment_plan_with_patiënt_(0,_11) >= 0

_C46: Intake_(0,_18) >= 0

_C47: Discuss_treatment_plan_with_patiënt_(0,_18) >= 0

_C48: Intake_(0,_25) >= 0

_C49: Discuss_treatment_plan_with_patiënt_(0,_25) >= 0

_C50: Write_a_transcript_of_intake_(0,_1) >= 0

_C51: Create_treatment_plan_(0,_1) >= 0

_C52: Schedule_a_meeting_(0,_1) >= 0

_C53: Write_a_transcript_of_intake_(0,_2) >= 0

_C54: Create_treatment_plan_(0,_2) >= 0

_C55: Schedule_a_meeting_(0,_2) >= 0

_C56: Write_a_transcript_of_intake_(0,_3) >= 0

_C57: Create_treatment_plan_(0,_3) >= 0

_C58: Schedule_a_meeting_(0,_3) >= 0

_C59: Write_a_transcript_of_intake_(0,_4) >= 0

_C60: Create_treatment_plan_(0,_4) >= 0

_C61: Schedule_a_meeting_(0,_4) >= 0

_C62: Write_a_transcript_of_intake_(0,_5) >= 0

_C63: Create_treatment_plan_(0,_5) >= 0

_C64: Schedule_a_meeting_(0,_5) >= 0

_C65: Write_a_transcript_of_intake_(0,_6) >= 0

_C66: Create_treatment_plan_(0,_6) >= 0

_C67: Schedule_a_meeting_(0,_6) >= 0

_C68: Write_a_transcript_of_intake_(0,_7) >= 0

_C69: Create_treatment_plan_(0,_7) >= 0

_C70: Schedule_a_meeting_(0,_7) >= 0

_C71: Write_a_transcript_of_intake_(0,_8) >= 0

_C72: Create_treatment_plan_(0,_8) >= 0

_C73: Schedule_a_meeting_(0,_8) >= 0

_C74: Write_a_transcript_of_intake_(0,_9) >= 0

_C75: Create_treatment_plan_(0,_9) >= 0

_C76: Schedule_a_meeting_(0,_9) >= 0

_C77: Write_a_transcript_of_intake_(0,_10) >= 0

_C78: Create_treatment_plan_(0,_10) >= 0

_C79: Schedule_a_meeting_(0,_10) >= 0

_C80: Write_a_transcript_of_intake_(0,_11) >= 0

_C81: Create_treatment_plan_(0,_11) >= 0

_C82: Schedule_a_meeting_(0,_11) >= 0

_C83: Write_a_transcript_of_intake_(0,_12) >= 0

_C84: Create_treatment_plan_(0,_12) >= 0

_C85: Schedule_a_meeting_(0,_12) >= 0

_C86: Write_a_transcript_of_intake_(0,_13) >= 0

_C87: Create_treatment_plan_(0,_13) >= 0

_C88: Schedule_a_meeting_(0,_13) >= 0

_C89: Write_a_transcript_of_intake_(0,_14) >= 0

_C90: Create_treatment_plan_(0,_14) >= 0

_C91: Schedule_a_meeting_(0,_14) >= 0

_C92: Write_a_transcript_of_intake_(0,_15) >= 0

_C93: Create_treatment_plan_(0,_15) >= 0

_C94: Schedule_a_meeting_(0,_15) >= 0

_C95: Write_a_transcript_of_intake_(0,_16) >= 0

_C96: Create_treatment_plan_(0,_16) >= 0

_C97: Schedule_a_meeting_(0,_16) >= 0

_C98: Write_a_transcript_of_intake_(0,_17) >= 0

_C99: Create_treatment_plan_(0,_17) >= 0

_C100: Schedule_a_meeting_(0,_17) >= 0

_C101: Write_a_transcript_of_intake_(0,_18) >= 0

_C102: Create_treatment_plan_(0,_18) >= 0

_C103: Schedule_a_meeting_(0,_18) >= 0

_C104: Write_a_transcript_of_intake_(0,_19) >= 0

_C105: Create_treatment_plan_(0,_19) >= 0

_C106: Schedule_a_meeting_(0,_19) >= 0

_C107: Write_a_transcript_of_intake_(0,_20) >= 0

_C108: Create_treatment_plan_(0,_20) >= 0

_C109: Schedule_a_meeting_(0,_20) >= 0

_C110: Write_a_transcript_of_intake_(0,_21) >= 0

_C111: Create_treatment_plan_(0,_21) >= 0

_C112: Schedule_a_meeting_(0,_21) >= 0

_C113: Write_a_transcript_of_intake_(0,_22) >= 0

_C114: Create_treatment_plan_(0,_22) >= 0

_C115: Schedule_a_meeting_(0,_22) >= 0

_C116: Write_a_transcript_of_intake_(0,_23) >= 0

_C117: Create_treatment_plan_(0,_23) >= 0

_C118: Schedule_a_meeting_(0,_23) >= 0

_C119: Write_a_transcript_of_intake_(0,_24) >= 0

_C120: Create_treatment_plan_(0,_24) >= 0

_C121: Schedule_a_meeting_(0,_24) >= 0

_C122: Write_a_transcript_of_intake_(0,_25) >= 0

_C123: Create_treatment_plan_(0,_25) >= 0

_C124: Schedule_a_meeting_(0,_25) >= 0

_C125: Write_a_transcript_of_intake_(0,_26) >= 0

_C126: Create_treatment_plan_(0,_26) >= 0

_C127: Schedule_a_meeting_(0,_26) >= 0

_C128: Write_a_transcript_of_intake_(0,_27) >= 0

_C129: Create_treatment_plan_(0,_27) >= 0

_C130: Schedule_a_meeting_(0,_27) >= 0

_C131: Write_a_transcript_of_intake_(0,_28) >= 0

_C132: Create_treatment_plan_(0,_28) >= 0

_C133: Schedule_a_meeting_(0,_28) >= 0

_C134: Write_a_transcript_of_intake_(0,_29) >= 0

_C135: Create_treatment_plan_(0,_29) >= 0

_C136: Schedule_a_meeting_(0,_29) >= 0

_C137: Write_a_transcript_of_intake_(0,_30) >= 0

_C138: Create_treatment_plan_(0,_30) >= 0

_C139: Schedule_a_meeting_(0,_30) >= 0

_C140: Write_a_transcript_of_intake_(0,_31) >= 0

_C141: Create_treatment_plan_(0,_31) >= 0

_C142: Schedule_a_meeting_(0,_31) >= 0

VARIABLES
Create_treatment_plan_(0,_1) <= 0.5 Continuous
Create_treatment_plan_(0,_10) <= 0.5 Continuous
Create_treatment_plan_(0,_11) <= 0.5 Continuous
Create_treatment_plan_(0,_12) <= 0.5 Continuous
Create_treatment_plan_(0,_13) <= 0.5 Continuous
Create_treatment_plan_(0,_14) <= 0.5 Continuous
Create_treatment_plan_(0,_15) <= 0.5 Continuous
Create_treatment_plan_(0,_16) <= 0.5 Continuous
Create_treatment_plan_(0,_17) <= 0.5 Continuous
Create_treatment_plan_(0,_18) <= 0.5 Continuous
Create_treatment_plan_(0,_19) <= 0.5 Continuous
Create_treatment_plan_(0,_2) <= 0.5 Continuous
Create_treatment_plan_(0,_20) <= 0.5 Continuous
Create_treatment_plan_(0,_21) <= 0.5 Continuous
Create_treatment_plan_(0,_22) <= 0.5 Continuous
Create_treatment_plan_(0,_23) <= 0.5 Continuous
Create_treatment_plan_(0,_24) <= 0.5 Continuous
Create_treatment_plan_(0,_25) <= 0.5 Continuous
Create_treatment_plan_(0,_26) <= 0.5 Continuous
Create_treatment_plan_(0,_27) <= 0.5 Continuous
Create_treatment_plan_(0,_28) <= 0.5 Continuous
Create_treatment_plan_(0,_29) <= 0.5 Continuous
Create_treatment_plan_(0,_3) <= 0.5 Continuous
Create_treatment_plan_(0,_30) <= 0.5 Continuous
Create_treatment_plan_(0,_31) <= 0.5 Continuous
Create_treatment_plan_(0,_4) <= 0.5 Continuous
Create_treatment_plan_(0,_5) <= 0.5 Continuous
Create_treatment_plan_(0,_6) <= 0.5 Continuous
Create_treatment_plan_(0,_7) <= 0.5 Continuous
Create_treatment_plan_(0,_8) <= 0.5 Continuous
Create_treatment_plan_(0,_9) <= 0.5 Continuous
Discuss_treatment_plan_with_patiënt_(0,_11) <= 1 Continuous
Discuss_treatment_plan_with_patiënt_(0,_18) <= 1 Continuous
Discuss_treatment_plan_with_patiënt_(0,_25) <= 1 Continuous
Discuss_treatment_plan_with_patiënt_(0,_4) <= 1 Continuous
Intake_(0,_11) <= 1 Continuous
Intake_(0,_18) <= 1 Continuous
Intake_(0,_25) <= 1 Continuous
Intake_(0,_4) <= 1 Continuous
Schedule_a_meeting_(0,_1) <= 0.5 Continuous
Schedule_a_meeting_(0,_10) <= 0.5 Continuous
Schedule_a_meeting_(0,_11) <= 0.5 Continuous
Schedule_a_meeting_(0,_12) <= 0.5 Continuous
Schedule_a_meeting_(0,_13) <= 0.5 Continuous
Schedule_a_meeting_(0,_14) <= 0.5 Continuous
Schedule_a_meeting_(0,_15) <= 0.5 Continuous
Schedule_a_meeting_(0,_16) <= 0.5 Continuous
Schedule_a_meeting_(0,_17) <= 0.5 Continuous
Schedule_a_meeting_(0,_18) <= 0.5 Continuous
Schedule_a_meeting_(0,_19) <= 0.5 Continuous
Schedule_a_meeting_(0,_2) <= 0.5 Continuous
Schedule_a_meeting_(0,_20) <= 0.5 Continuous
Schedule_a_meeting_(0,_21) <= 0.5 Continuous
Schedule_a_meeting_(0,_22) <= 0.5 Continuous
Schedule_a_meeting_(0,_23) <= 0.5 Continuous
Schedule_a_meeting_(0,_24) <= 0.5 Continuous
Schedule_a_meeting_(0,_25) <= 0.5 Continuous
Schedule_a_meeting_(0,_26) <= 0.5 Continuous
Schedule_a_meeting_(0,_27) <= 0.5 Continuous
Schedule_a_meeting_(0,_28) <= 0.5 Continuous
Schedule_a_meeting_(0,_29) <= 0.5 Continuous
Schedule_a_meeting_(0,_3) <= 0.5 Continuous
Schedule_a_meeting_(0,_30) <= 0.5 Continuous
Schedule_a_meeting_(0,_31) <= 0.5 Continuous
Schedule_a_meeting_(0,_4) <= 0.5 Continuous
Schedule_a_meeting_(0,_5) <= 0.5 Continuous
Schedule_a_meeting_(0,_6) <= 0.5 Continuous
Schedule_a_meeting_(0,_7) <= 0.5 Continuous
Schedule_a_meeting_(0,_8) <= 0.5 Continuous
Schedule_a_meeting_(0,_9) <= 0.5 Continuous
Write_a_transcript_of_intake_(0,_1) <= 1 Continuous
Write_a_transcript_of_intake_(0,_10) <= 1 Continuous
Write_a_transcript_of_intake_(0,_11) <= 1 Continuous
Write_a_transcript_of_intake_(0,_12) <= 1 Continuous
Write_a_transcript_of_intake_(0,_13) <= 1 Continuous
Write_a_transcript_of_intake_(0,_14) <= 1 Continuous
Write_a_transcript_of_intake_(0,_15) <= 1 Continuous
Write_a_transcript_of_intake_(0,_16) <= 1 Continuous
Write_a_transcript_of_intake_(0,_17) <= 1 Continuous
Write_a_transcript_of_intake_(0,_18) <= 1 Continuous
Write_a_transcript_of_intake_(0,_19) <= 1 Continuous
Write_a_transcript_of_intake_(0,_2) <= 1 Continuous
Write_a_transcript_of_intake_(0,_20) <= 1 Continuous
Write_a_transcript_of_intake_(0,_21) <= 1 Continuous
Write_a_transcript_of_intake_(0,_22) <= 1 Continuous
Write_a_transcript_of_intake_(0,_23) <= 1 Continuous
Write_a_transcript_of_intake_(0,_24) <= 1 Continuous
Write_a_transcript_of_intake_(0,_25) <= 1 Continuous
Write_a_transcript_of_intake_(0,_26) <= 1 Continuous
Write_a_transcript_of_intake_(0,_27) <= 1 Continuous
Write_a_transcript_of_intake_(0,_28) <= 1 Continuous
Write_a_transcript_of_intake_(0,_29) <= 1 Continuous
Write_a_transcript_of_intake_(0,_3) <= 1 Continuous
Write_a_transcript_of_intake_(0,_30) <= 1 Continuous
Write_a_transcript_of_intake_(0,_31) <= 1 Continuous
Write_a_transcript_of_intake_(0,_4) <= 1 Continuous
Write_a_transcript_of_intake_(0,_5) <= 1 Continuous
Write_a_transcript_of_intake_(0,_6) <= 1 Continuous
Write_a_transcript_of_intake_(0,_7) <= 1 Continuous
Write_a_transcript_of_intake_(0,_8) <= 1 Continuous
Write_a_transcript_of_intake_(0,_9) <= 1 Continuous

【问题讨论】：

标签： python math optimization mathematical-optimization linear-programming

【解决方案1】：

使用时间索引变量x[t], y[t] ∈ {0,1}，我经常还保留标量变量xt, yt ≥ 0，在其周围保存x,y 的时间：

 xt = sum{ t*x[t] }
 yt = sum{ t*y[t] }

当然这是假设我们有：

 sum{ x[t] } = 1
 sum{ y[t] } = 1

即x,y 恰好发生在一次（只要第一个 t 大于零，它也适用于“最多一次”）。

有了这个，你可以很容易地施加一个优先约束：

 xt ≤ yt-1

【讨论】：

嗨欧文！非常感谢您的帮助！该解决方案确实适用于某些值，例如 A[(0,v)]、B[(0,d)] 和 E[(0,v)]，因为这些值正好需要一个小时，但它还不起作用对于活动 C[(0,d)] 和 D[(0,d)]，因为这些活动需要 0.5 小时。你知道要确保 C[t] ∈ {0,0.5} 在 B[t] ∈ {0,1} 之后吗？ Pulp 只接受整数和连续变量，这使得对浮点数（例如 0.5）进行约束变得更加困难
我认为这里有些混乱。我们处理二进制变量，所以从来没有像C[t] ∈ {0,0.5} 这样的东西。 C[1]=0.5 到底是什么意思？
我们有 5 个变量（A、B、C、D 和 E），其中 C[(m,d)] 是分配给员工 m 的活动 c（我只使用一名员工，称为0 处处使问题不那么复杂）在第 d 天。五项活动中有两项需要每半小时完成，五项活动中有三项每项需要 1 小时才能完成。第三个活动需要半小时才能完成，意思是C[(m,d)] = 0.5 。所以我们有一个带有时间索引天数的时间索引变量，变量本身表示将从输入中的可用小时数中减去的小时数（0.5 或 1）
对不起，这对我来说没有意义。这不是时间索引调度模型的工作方式。