अब तक, हम लागू होने वाले कंस्ट्रेंट के साथ रूटिंग से जुड़ी समस्याओं को देख रहे हैं वाहन यात्रा के दौरान. इसके बाद, हम एक VRPTW प्रज़ेंट करते हैं जिसमें डिपो पर भी कंस्ट्रेंट है: सभी वाहनों को डिपो से रवाना होने और वापस आने पर अनलोड हो गया. सिर्फ़ दो लोडिंग डॉक उपलब्ध हैं. इसलिए, ज़्यादा से ज़्यादा दो वाहन ही लोड हो सकते हैं एक ही समय पर लोड या अनलोड होता है. इस वजह से, कुछ वाहनों को जिनमें डिपो से जाने में देरी हो रही हो. समस्या यह है कि वीआरपीटीडब्ल्यू के लिए, वाहन के सबसे सही रास्ते ढूंढने में मदद मिलती है जो लोडिंग और ट्रैफ़िक को पूरा करते हैं डिपो पर कंस्ट्रेंट को अनलोड करने के लिए इस्तेमाल किया जाता है.
रिसॉर्स कंस्ट्रेंट के साथ VRPTW का उदाहरण
नीचे दिए गए डायग्राम में रिसॉर्स कंस्ट्रेंट वाला वीआरपीटीडब्ल्यू दिखाया गया है.
OR-टूल की मदद से उदाहरण हल करना
नीचे दिए गए सेक्शन में, संसाधन के मुश्किलों की मदद से वीआरपीटीडब्ल्यू को हल करने का तरीका बताया गया है OR-टूल का इस्तेमाल करके. उदाहरण के लिए कुछ कोड पिछले कोड के समान हैं VRPTW उदाहरण, इसलिए हम जो नए हिस्से के बारे में बताता है.
डेटा बनाना
यह कोड, उदाहरण के लिए डेटा बनाता है.
Python
def create_data_model():
"""Stores the data for the problem."""
data = {}
data["time_matrix"] = [
[0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7],
[6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14],
[9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9],
[8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16],
[7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14],
[3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8],
[6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5],
[2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10],
[3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6],
[2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5],
[6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4],
[6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10],
[4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8],
[4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6],
[5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2],
[9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9],
[7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0],
]
data["time_windows"] = [
(0, 5), # depot
(7, 12), # 1
(10, 15), # 2
(5, 14), # 3
(5, 13), # 4
(0, 5), # 5
(5, 10), # 6
(0, 10), # 7
(5, 10), # 8
(0, 5), # 9
(10, 16), # 10
(10, 15), # 11
(0, 5), # 12
(5, 10), # 13
(7, 12), # 14
(10, 15), # 15
(5, 15), # 16
]
data["num_vehicles"] = 4
data["vehicle_load_time"] = 5
data["vehicle_unload_time"] = 5
data["depot_capacity"] = 2
data["depot"] = 0
return data
C++
struct DataModel {
const std::vector<std::vector<int64_t>> time_matrix{
{0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7},
{6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14},
{9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9},
{8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16},
{7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14},
{3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8},
{6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5},
{2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10},
{3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6},
{2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5},
{6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4},
{6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10},
{4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8},
{4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6},
{5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2},
{9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9},
{7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0},
};
const std::vector<std::pair<int64_t, int64_t>> time_windows{
{0, 5}, // depot
{7, 12}, // 1
{10, 15}, // 2
{5, 14}, // 3
{5, 13}, // 4
{0, 5}, // 5
{5, 10}, // 6
{0, 10}, // 7
{5, 10}, // 8
{0, 5}, // 9
{10, 16}, // 10
{10, 15}, // 11
{0, 5}, // 12
{5, 10}, // 13
{7, 12}, // 14
{10, 15}, // 15
{5, 15}, // 16
};
const int num_vehicles = 4;
const int vehicle_load_time = 5;
const int vehicle_unload_time = 5;
const int depot_capacity = 2;
const RoutingIndexManager::NodeIndex depot{0};
};
Java
static class DataModel {
public final long[][] timeMatrix = {
{0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7},
{6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14},
{9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9},
{8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16},
{7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14},
{3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8},
{6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5},
{2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10},
{3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6},
{2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5},
{6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4},
{6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10},
{4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8},
{4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6},
{5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2},
{9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9},
{7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0},
};
public final long[][] timeWindows = {
{0, 5}, // depot
{7, 12}, // 1
{10, 15}, // 2
{5, 14}, // 3
{5, 13}, // 4
{0, 5}, // 5
{5, 10}, // 6
{0, 10}, // 7
{5, 10}, // 8
{0, 5}, // 9
{10, 16}, // 10
{10, 15}, // 11
{0, 5}, // 12
{5, 10}, // 13
{7, 12}, // 14
{10, 15}, // 15
{5, 15}, // 16
};
public final int vehicleNumber = 4;
public final int vehicleLoadTime = 5;
public final int vehicleUnloadTime = 5;
public final int depotCapacity = 2;
public final int depot = 0;
}
C#
class DataModel
{
public long[,] TimeMatrix = {
{ 0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7 },
{ 6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14 },
{ 9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9 },
{ 8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16 },
{ 7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14 },
{ 3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8 },
{ 6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5 },
{ 2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10 },
{ 3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6 },
{ 2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5 },
{ 6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4 },
{ 6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10 },
{ 4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8 },
{ 4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6 },
{ 5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2 },
{ 9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9 },
{ 7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0 },
};
public long[,] TimeWindows = {
{ 0, 5 }, // depot
{ 7, 12 }, // 1
{ 10, 15 }, // 2
{ 5, 14 }, // 3
{ 5, 13 }, // 4
{ 0, 5 }, // 5
{ 5, 10 }, // 6
{ 0, 10 }, // 7
{ 5, 10 }, // 8
{ 0, 5 }, // 9
{ 10, 16 }, // 10
{ 10, 15 }, // 11
{ 0, 5 }, // 12
{ 5, 10 }, // 13
{ 7, 12 }, // 14
{ 10, 15 }, // 15
{ 5, 15 }, // 16
};
public int VehicleNumber = 4;
public int VehicleLoadTime = 5;
public int VehicleUnloadTime = 5;
public int DepotCapacity = 2;
public int Depot = 0;
};
डेटा में ये चीज़ें शामिल होती हैं:
time_matrix: जगहों के बीच यात्रा में लगने वाले समय का कलेक्शन.time_windows: जगहों पर विज़िट का अनुरोध करने के लिए, टाइम विंडो का कलेक्शन.vehicle_load_time: वाहन को लोड करने में लगने वाला समय.vehicle_unload_time: वाहन को अनलोड करने में लगने वाला समय.depot_capacity: यहां पर लोड या अनलोड किए जा सकने वाले वाहनों की ज़्यादा से ज़्यादा संख्या एक साथ.
लोड और अनलोड करने के लिए, टाइम विंडो जोड़ें
यह कोड, वाहनों को लोड और अनलोड करने के लिए टाइम विंडो जोड़ता है
डिपो.
FixedDurationIntervalVar तरीके से बनाई गई ये विंडो,
वैरिएबल टाइम विंडो का मतलब है कि उनके शुरू और खत्म होने का समय तय नहीं है
(जगहों के टाइम विंडो से अलग). विंडो की चौड़ाई इतनी रखें:
vehicle_load_time और vehicle_unload_time ने तय किया है, जो
एक जैसा होगा.
Python
solver = routing.solver()
intervals = []
for i in range(data["num_vehicles"]):
# Add time windows at start of routes
intervals.append(
solver.FixedDurationIntervalVar(
time_dimension.CumulVar(routing.Start(i)),
data["vehicle_load_time"],
"depot_interval",
)
)
# Add time windows at end of routes.
intervals.append(
solver.FixedDurationIntervalVar(
time_dimension.CumulVar(routing.End(i)),
data["vehicle_unload_time"],
"depot_interval",
)
)
C++
Solver* solver = routing.solver();
std::vector<IntervalVar*> intervals;
for (int i = 0; i < data.num_vehicles; ++i) {
// Add load duration at start of routes
intervals.push_back(solver->MakeFixedDurationIntervalVar(
time_dimension.CumulVar(routing.Start(i)), data.vehicle_load_time,
"depot_interval"));
// Add unload duration at end of routes.
intervals.push_back(solver->MakeFixedDurationIntervalVar(
time_dimension.CumulVar(routing.End(i)), data.vehicle_unload_time,
"depot_interval"));
}
Java
Solver solver = routing.solver();
IntervalVar[] intervals = new IntervalVar[data.vehicleNumber * 2];
for (int i = 0; i < data.vehicleNumber; ++i) {
// Add load duration at start of routes
intervals[2 * i] = solver.makeFixedDurationIntervalVar(
timeDimension.cumulVar(routing.start(i)), data.vehicleLoadTime, "depot_interval");
// Add unload duration at end of routes.
intervals[2 * i + 1] = solver.makeFixedDurationIntervalVar(
timeDimension.cumulVar(routing.end(i)), data.vehicleUnloadTime, "depot_interval");
}
C#
Solver solver = routing.solver();
IntervalVar[] intervals = new IntervalVar[data.VehicleNumber * 2];
for (int i = 0; i < data.VehicleNumber; ++i)
{
// Add load duration at start of routes
intervals[2 * i] = solver.MakeFixedDurationIntervalVar(timeDimension.CumulVar(routing.Start(i)),
data.VehicleLoadTime, "depot_interval");
// Add unload duration at end of routes.
intervals[2 * i + 1] = solver.MakeFixedDurationIntervalVar(timeDimension.CumulVar(routing.End(i)),
data.VehicleUnloadTime, "depot_interval");
}
डिपो में संसाधन कंस्ट्रेंट जोड़ें
यह कोड कंस्ट्रेंट बनाता है कि ज़्यादा से ज़्यादा दो वाहन हो सकते हैं एक ही समय पर लोड या अनलोड होता है.
Python
depot_usage = [1 for _ in range(len(intervals))]
solver.Add(
solver.Cumulative(intervals, depot_usage, data["depot_capacity"], "depot")
)
C++
std::vector<int64_t> depot_usage(intervals.size(), 1);
solver->AddConstraint(solver->MakeCumulative(intervals, depot_usage,
data.depot_capacity, "depot"));
Java
long[] depotUsage = new long[intervals.length];
Arrays.fill(depotUsage, 1);
solver.addConstraint(solver.makeCumulative(intervals, depotUsage, data.depotCapacity, "depot"));
C#
long[] depot_usage = Enumerable.Repeat<long>(1, intervals.Length).ToArray();
solver.Add(solver.MakeCumulative(intervals, depot_usage, data.DepotCapacity, "depot"));
ज़्यादा से ज़्यादा depot_capacity वाहन लोड किए जा सकते हैं या
उसी समय अनलोड होता है, जो इस उदाहरण में दो है.
depot_usage एक वेक्टर है जिसमें बैटरी के लिए ज़रूरी स्पेस
लोडिंग (या अनलोडिंग) के दौरान हर वाहन के लिए. इस उदाहरण में, हम मान लेते हैं कि सभी
वाहनों के लिए समान जगह की ज़रूरत होती है. इसलिए, depot_usage में सभी जगह मौजूद है.
इसका मतलब है कि एक ही समय पर, ज़्यादा से ज़्यादा इतने वाहन लोड किए जा सकते हैं
समय 2 है.
प्रोग्राम को चलाने का तरीका
प्रोग्राम का आउटपुट नीचे दिखता है.
Route for vehicle 0: 0 Time(5,5) -> 8 Time(8,8) -> 14 Time(11,11) -> 16 Time(13,13) -> 0 Time(20,20) Time of the route: 20min Route for vehicle 1: 0 Time(0,0) -> 12 Time(4,4) -> 13 Time(6,6) -> 15 Time(11,11) -> 11 Time(14,14) -> 0 Time(20,20) Time of the route: 20min Route for vehicle 2: 0 Time(5,5) -> 7 Time(7,7) -> 1 Time(11,11) -> 4 Time(13,13) -> 3 Time(14,14) -> 0 Time(25,25) Time of the route: 25min Route for vehicle 3: 0 Time(0,0) -> 9 Time(2,3) -> 5 Time(4,5) -> 6 Time(6,9) -> 2 Time(10,12) -> 10 Time(14,16) -> 0 Time(25,25) Time of the route: 25min Total time of all routes: 90min
पिछला VRPTW उदाहरण देखें आउटपुट की जानकारी के लिए.
ध्यान दें कि पहला और तीसरा वाहन, डिपो से समय 0 पर रवाना होते हैं. वाहन 0 और 2, जिसमें
दूसरों के लोड होने की इंतज़ार करना होगा, समय 5 पर निकलेगी, मूल्य
vehicle_load_time.
नीचे दिया गया डायग्राम, समाधान दिखाता है.
प्रोग्राम पूरे करें
संसाधन के साथ कैपेसिटेड व्हीकल रूटिंग की समस्या के लिए सभी प्रोग्राम सीमाएं नीचे दिखाई गई हैं.
Python
"""Vehicles Routing Problem (VRP) with Resource Constraints."""
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model():
"""Stores the data for the problem."""
data = {}
data["time_matrix"] = [
[0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7],
[6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14],
[9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9],
[8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16],
[7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14],
[3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8],
[6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5],
[2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10],
[3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6],
[2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5],
[6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4],
[6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10],
[4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8],
[4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6],
[5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2],
[9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9],
[7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0],
]
data["time_windows"] = [
(0, 5), # depot
(7, 12), # 1
(10, 15), # 2
(5, 14), # 3
(5, 13), # 4
(0, 5), # 5
(5, 10), # 6
(0, 10), # 7
(5, 10), # 8
(0, 5), # 9
(10, 16), # 10
(10, 15), # 11
(0, 5), # 12
(5, 10), # 13
(7, 12), # 14
(10, 15), # 15
(5, 15), # 16
]
data["num_vehicles"] = 4
data["vehicle_load_time"] = 5
data["vehicle_unload_time"] = 5
data["depot_capacity"] = 2
data["depot"] = 0
return data
def print_solution(data, manager, routing, solution):
"""Prints solution on console."""
print(f"Objective: {solution.ObjectiveValue()}")
time_dimension = routing.GetDimensionOrDie("Time")
total_time = 0
for vehicle_id in range(data["num_vehicles"]):
index = routing.Start(vehicle_id)
plan_output = f"Route for vehicle {vehicle_id}:\n"
while not routing.IsEnd(index):
time_var = time_dimension.CumulVar(index)
plan_output += (
f"{manager.IndexToNode(index)}"
f" Time({solution.Min(time_var)}, {solution.Max(time_var)})"
" -> "
)
index = solution.Value(routing.NextVar(index))
time_var = time_dimension.CumulVar(index)
plan_output += (
f"{manager.IndexToNode(index)}"
f" Time({solution.Min(time_var)},{solution.Max(time_var)})\n"
)
plan_output += f"Time of the route: {solution.Min(time_var)}min\n"
print(plan_output)
total_time += solution.Min(time_var)
print(f"Total time of all routes: {total_time}min")
def main():
"""Solve the VRP with time windows."""
# Instantiate the data problem.
data = create_data_model()
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(
len(data["time_matrix"]), data["num_vehicles"], data["depot"]
)
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
# Create and register a transit callback.
def time_callback(from_index, to_index):
"""Returns the travel time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data["time_matrix"][from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(time_callback)
# Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# Add Time Windows constraint.
time = "Time"
routing.AddDimension(
transit_callback_index,
60, # allow waiting time
60, # maximum time per vehicle
False, # Don't force start cumul to zero.
time,
)
time_dimension = routing.GetDimensionOrDie(time)
# Add time window constraints for each location except depot.
for location_idx, time_window in enumerate(data["time_windows"]):
if location_idx == 0:
continue
index = manager.NodeToIndex(location_idx)
time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
# Add time window constraints for each vehicle start node.
for vehicle_id in range(data["num_vehicles"]):
index = routing.Start(vehicle_id)
time_dimension.CumulVar(index).SetRange(
data["time_windows"][0][0], data["time_windows"][0][1]
)
# Add resource constraints at the depot.
solver = routing.solver()
intervals = []
for i in range(data["num_vehicles"]):
# Add time windows at start of routes
intervals.append(
solver.FixedDurationIntervalVar(
time_dimension.CumulVar(routing.Start(i)),
data["vehicle_load_time"],
"depot_interval",
)
)
# Add time windows at end of routes.
intervals.append(
solver.FixedDurationIntervalVar(
time_dimension.CumulVar(routing.End(i)),
data["vehicle_unload_time"],
"depot_interval",
)
)
depot_usage = [1 for _ in range(len(intervals))]
solver.Add(
solver.Cumulative(intervals, depot_usage, data["depot_capacity"], "depot")
)
# Instantiate route start and end times to produce feasible times.
for i in range(data["num_vehicles"]):
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.Start(i))
)
routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.End(i)))
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC
)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data, manager, routing, solution)
else:
print("No solution found !")
if __name__ == "__main__":
main()
C++
#include <cstdint>
#include <sstream>
#include <string>
#include <utility>
#include <vector>
#include "ortools/constraint_solver/routing.h"
#include "ortools/constraint_solver/routing_enums.pb.h"
#include "ortools/constraint_solver/routing_index_manager.h"
#include "ortools/constraint_solver/routing_parameters.h"
namespace operations_research {
struct DataModel {
const std::vector<std::vector<int64_t>> time_matrix{
{0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7},
{6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14},
{9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9},
{8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16},
{7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14},
{3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8},
{6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5},
{2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10},
{3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6},
{2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5},
{6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4},
{6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10},
{4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8},
{4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6},
{5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2},
{9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9},
{7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0},
};
const std::vector<std::pair<int64_t, int64_t>> time_windows{
{0, 5}, // depot
{7, 12}, // 1
{10, 15}, // 2
{5, 14}, // 3
{5, 13}, // 4
{0, 5}, // 5
{5, 10}, // 6
{0, 10}, // 7
{5, 10}, // 8
{0, 5}, // 9
{10, 16}, // 10
{10, 15}, // 11
{0, 5}, // 12
{5, 10}, // 13
{7, 12}, // 14
{10, 15}, // 15
{5, 15}, // 16
};
const int num_vehicles = 4;
const int vehicle_load_time = 5;
const int vehicle_unload_time = 5;
const int depot_capacity = 2;
const RoutingIndexManager::NodeIndex depot{0};
};
//! @brief Print the solution.
//! @param[in] data Data of the problem.
//! @param[in] manager Index manager used.
//! @param[in] routing Routing solver used.
//! @param[in] solution Solution found by the solver.
void PrintSolution(const DataModel& data, const RoutingIndexManager& manager,
const RoutingModel& routing, const Assignment& solution) {
const RoutingDimension& time_dimension = routing.GetDimensionOrDie("Time");
int64_t total_time{0};
for (int vehicle_id = 0; vehicle_id < data.num_vehicles; ++vehicle_id) {
int64_t index = routing.Start(vehicle_id);
LOG(INFO) << "Route for vehicle " << vehicle_id << ":";
std::ostringstream route;
while (!routing.IsEnd(index)) {
auto time_var = time_dimension.CumulVar(index);
route << manager.IndexToNode(index).value() << " Time("
<< solution.Min(time_var) << ", " << solution.Max(time_var)
<< ") -> ";
index = solution.Value(routing.NextVar(index));
}
auto time_var = time_dimension.CumulVar(index);
LOG(INFO) << route.str() << manager.IndexToNode(index).value() << " Time("
<< solution.Min(time_var) << ", " << solution.Max(time_var)
<< ")";
LOG(INFO) << "Time of the route: " << solution.Min(time_var) << "min";
total_time += solution.Min(time_var);
}
LOG(INFO) << "Total time of all routes: " << total_time << "min";
LOG(INFO) << "";
LOG(INFO) << "Advanced usage:";
LOG(INFO) << "Problem solved in " << routing.solver()->wall_time() << "ms";
}
void VrpTimeWindows() {
// Instantiate the data problem.
DataModel data;
// Create Routing Index Manager
RoutingIndexManager manager(data.time_matrix.size(), data.num_vehicles,
data.depot);
// Create Routing Model.
RoutingModel routing(manager);
// Create and register a transit callback.
const int transit_callback_index = routing.RegisterTransitCallback(
[&data, &manager](const int64_t from_index,
const int64_t to_index) -> int64_t {
// Convert from routing variable Index to time matrix NodeIndex.
const int from_node = manager.IndexToNode(from_index).value();
const int to_node = manager.IndexToNode(to_index).value();
return data.time_matrix[from_node][to_node];
});
// Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index);
// Add Time constraint.
const std::string time = "Time";
routing.AddDimension(transit_callback_index, // transit callback index
int64_t{30}, // allow waiting time
int64_t{30}, // maximum time per vehicle
false, // Don't force start cumul to zero
time);
const RoutingDimension& time_dimension = routing.GetDimensionOrDie(time);
// Add time window constraints for each location except depot.
for (int i = 1; i < data.time_windows.size(); ++i) {
const int64_t index =
manager.NodeToIndex(RoutingIndexManager::NodeIndex(i));
time_dimension.CumulVar(index)->SetRange(data.time_windows[i].first,
data.time_windows[i].second);
}
// Add time window constraints for each vehicle start node.
for (int i = 0; i < data.num_vehicles; ++i) {
const int64_t index = routing.Start(i);
time_dimension.CumulVar(index)->SetRange(data.time_windows[0].first,
data.time_windows[0].second);
}
// Add resource constraints at the depot.
Solver* solver = routing.solver();
std::vector<IntervalVar*> intervals;
for (int i = 0; i < data.num_vehicles; ++i) {
// Add load duration at start of routes
intervals.push_back(solver->MakeFixedDurationIntervalVar(
time_dimension.CumulVar(routing.Start(i)), data.vehicle_load_time,
"depot_interval"));
// Add unload duration at end of routes.
intervals.push_back(solver->MakeFixedDurationIntervalVar(
time_dimension.CumulVar(routing.End(i)), data.vehicle_unload_time,
"depot_interval"));
}
std::vector<int64_t> depot_usage(intervals.size(), 1);
solver->AddConstraint(solver->MakeCumulative(intervals, depot_usage,
data.depot_capacity, "depot"));
// Instantiate route start and end times to produce feasible times.
for (int i = 0; i < data.num_vehicles; ++i) {
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.Start(i)));
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.End(i)));
}
// Setting first solution heuristic.
RoutingSearchParameters searchParameters = DefaultRoutingSearchParameters();
searchParameters.set_first_solution_strategy(
FirstSolutionStrategy::PATH_CHEAPEST_ARC);
// Solve the problem.
const Assignment* solution = routing.SolveWithParameters(searchParameters);
// Print solution on console.
PrintSolution(data, manager, routing, *solution);
}
} // namespace operations_research
int main(int /*argc*/, char* /*argv*/[]) {
operations_research::VrpTimeWindows();
return EXIT_SUCCESS;
}
Java
package com.google.ortools.constraintsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.Assignment;
import com.google.ortools.constraintsolver.FirstSolutionStrategy;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.IntervalVar;
import com.google.ortools.constraintsolver.RoutingDimension;
import com.google.ortools.constraintsolver.RoutingIndexManager;
import com.google.ortools.constraintsolver.RoutingModel;
import com.google.ortools.constraintsolver.RoutingSearchParameters;
import com.google.ortools.constraintsolver.Solver;
import com.google.ortools.constraintsolver.main;
import java.util.Arrays;
import java.util.logging.Logger;
/** Minimal VRP with Resource Constraints.*/
public class VrpResources {
private static final Logger logger = Logger.getLogger(VrpResources.class.getName());
static class DataModel {
public final long[][] timeMatrix = {
{0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7},
{6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14},
{9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9},
{8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16},
{7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14},
{3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8},
{6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5},
{2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10},
{3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6},
{2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5},
{6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4},
{6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10},
{4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8},
{4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6},
{5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2},
{9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9},
{7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0},
};
public final long[][] timeWindows = {
{0, 5}, // depot
{7, 12}, // 1
{10, 15}, // 2
{5, 14}, // 3
{5, 13}, // 4
{0, 5}, // 5
{5, 10}, // 6
{0, 10}, // 7
{5, 10}, // 8
{0, 5}, // 9
{10, 16}, // 10
{10, 15}, // 11
{0, 5}, // 12
{5, 10}, // 13
{7, 12}, // 14
{10, 15}, // 15
{5, 15}, // 16
};
public final int vehicleNumber = 4;
public final int vehicleLoadTime = 5;
public final int vehicleUnloadTime = 5;
public final int depotCapacity = 2;
public final int depot = 0;
}
/// @brief Print the solution.
static void printSolution(
DataModel data, RoutingModel routing, RoutingIndexManager manager, Assignment solution) {
// Solution cost.
logger.info("Objective : " + solution.objectiveValue());
// Inspect solution.
RoutingDimension timeDimension = routing.getMutableDimension("Time");
long totalTime = 0;
for (int i = 0; i < data.vehicleNumber; ++i) {
long index = routing.start(i);
logger.info("Route for Vehicle " + i + ":");
String route = "";
while (!routing.isEnd(index)) {
IntVar timeVar = timeDimension.cumulVar(index);
route += manager.indexToNode(index) + " Time(" + solution.min(timeVar) + ","
+ solution.max(timeVar) + ") -> ";
index = solution.value(routing.nextVar(index));
}
IntVar timeVar = timeDimension.cumulVar(index);
route += manager.indexToNode(index) + " Time(" + solution.min(timeVar) + ","
+ solution.max(timeVar) + ")";
logger.info(route);
logger.info("Time of the route: " + solution.min(timeVar) + "min");
totalTime += solution.min(timeVar);
}
logger.info("Total time of all routes: " + totalTime + "min");
}
public static void main(String[] args) throws Exception {
Loader.loadNativeLibraries();
// Instantiate the data problem.
final DataModel data = new DataModel();
// Create Routing Index Manager
RoutingIndexManager manager =
new RoutingIndexManager(data.timeMatrix.length, data.vehicleNumber, data.depot);
// Create Routing Model.
RoutingModel routing = new RoutingModel(manager);
// Create and register a transit callback.
final int transitCallbackIndex =
routing.registerTransitCallback((long fromIndex, long toIndex) -> {
// Convert from routing variable Index to user NodeIndex.
int fromNode = manager.indexToNode(fromIndex);
int toNode = manager.indexToNode(toIndex);
return data.timeMatrix[fromNode][toNode];
});
// Define cost of each arc.
routing.setArcCostEvaluatorOfAllVehicles(transitCallbackIndex);
// Add Time constraint.
routing.addDimension(transitCallbackIndex, // transit callback
30, // allow waiting time
30, // vehicle maximum capacities
false, // start cumul to zero
"Time");
RoutingDimension timeDimension = routing.getMutableDimension("Time");
// Add time window constraints for each location except depot.
for (int i = 1; i < data.timeWindows.length; ++i) {
long index = manager.nodeToIndex(i);
timeDimension.cumulVar(index).setRange(data.timeWindows[i][0], data.timeWindows[i][1]);
}
// Add time window constraints for each vehicle start node.
for (int i = 0; i < data.vehicleNumber; ++i) {
long index = routing.start(i);
timeDimension.cumulVar(index).setRange(data.timeWindows[0][0], data.timeWindows[0][1]);
}
// Add resource constraints at the depot.
Solver solver = routing.solver();
IntervalVar[] intervals = new IntervalVar[data.vehicleNumber * 2];
for (int i = 0; i < data.vehicleNumber; ++i) {
// Add load duration at start of routes
intervals[2 * i] = solver.makeFixedDurationIntervalVar(
timeDimension.cumulVar(routing.start(i)), data.vehicleLoadTime, "depot_interval");
// Add unload duration at end of routes.
intervals[2 * i + 1] = solver.makeFixedDurationIntervalVar(
timeDimension.cumulVar(routing.end(i)), data.vehicleUnloadTime, "depot_interval");
}
long[] depotUsage = new long[intervals.length];
Arrays.fill(depotUsage, 1);
solver.addConstraint(solver.makeCumulative(intervals, depotUsage, data.depotCapacity, "depot"));
// Instantiate route start and end times to produce feasible times.
for (int i = 0; i < data.vehicleNumber; ++i) {
routing.addVariableMinimizedByFinalizer(timeDimension.cumulVar(routing.start(i)));
routing.addVariableMinimizedByFinalizer(timeDimension.cumulVar(routing.end(i)));
}
// Setting first solution heuristic.
RoutingSearchParameters searchParameters =
main.defaultRoutingSearchParameters()
.toBuilder()
.setFirstSolutionStrategy(FirstSolutionStrategy.Value.PATH_CHEAPEST_ARC)
.build();
// Solve the problem.
Assignment solution = routing.solveWithParameters(searchParameters);
// Print solution on console.
printSolution(data, routing, manager, solution);
}
}
C#
using System;
using System.Linq;
using System.Collections.Generic;
using Google.OrTools.ConstraintSolver;
/// <summary>
/// Vehicles Routing Problem (VRP) with Resource Constraints.
/// </summary>
public class VrpResources
{
class DataModel
{
public long[,] TimeMatrix = {
{ 0, 6, 9, 8, 7, 3, 6, 2, 3, 2, 6, 6, 4, 4, 5, 9, 7 },
{ 6, 0, 8, 3, 2, 6, 8, 4, 8, 8, 13, 7, 5, 8, 12, 10, 14 },
{ 9, 8, 0, 11, 10, 6, 3, 9, 5, 8, 4, 15, 14, 13, 9, 18, 9 },
{ 8, 3, 11, 0, 1, 7, 10, 6, 10, 10, 14, 6, 7, 9, 14, 6, 16 },
{ 7, 2, 10, 1, 0, 6, 9, 4, 8, 9, 13, 4, 6, 8, 12, 8, 14 },
{ 3, 6, 6, 7, 6, 0, 2, 3, 2, 2, 7, 9, 7, 7, 6, 12, 8 },
{ 6, 8, 3, 10, 9, 2, 0, 6, 2, 5, 4, 12, 10, 10, 6, 15, 5 },
{ 2, 4, 9, 6, 4, 3, 6, 0, 4, 4, 8, 5, 4, 3, 7, 8, 10 },
{ 3, 8, 5, 10, 8, 2, 2, 4, 0, 3, 4, 9, 8, 7, 3, 13, 6 },
{ 2, 8, 8, 10, 9, 2, 5, 4, 3, 0, 4, 6, 5, 4, 3, 9, 5 },
{ 6, 13, 4, 14, 13, 7, 4, 8, 4, 4, 0, 10, 9, 8, 4, 13, 4 },
{ 6, 7, 15, 6, 4, 9, 12, 5, 9, 6, 10, 0, 1, 3, 7, 3, 10 },
{ 4, 5, 14, 7, 6, 7, 10, 4, 8, 5, 9, 1, 0, 2, 6, 4, 8 },
{ 4, 8, 13, 9, 8, 7, 10, 3, 7, 4, 8, 3, 2, 0, 4, 5, 6 },
{ 5, 12, 9, 14, 12, 6, 6, 7, 3, 3, 4, 7, 6, 4, 0, 9, 2 },
{ 9, 10, 18, 6, 8, 12, 15, 8, 13, 9, 13, 3, 4, 5, 9, 0, 9 },
{ 7, 14, 9, 16, 14, 8, 5, 10, 6, 5, 4, 10, 8, 6, 2, 9, 0 },
};
public long[,] TimeWindows = {
{ 0, 5 }, // depot
{ 7, 12 }, // 1
{ 10, 15 }, // 2
{ 5, 14 }, // 3
{ 5, 13 }, // 4
{ 0, 5 }, // 5
{ 5, 10 }, // 6
{ 0, 10 }, // 7
{ 5, 10 }, // 8
{ 0, 5 }, // 9
{ 10, 16 }, // 10
{ 10, 15 }, // 11
{ 0, 5 }, // 12
{ 5, 10 }, // 13
{ 7, 12 }, // 14
{ 10, 15 }, // 15
{ 5, 15 }, // 16
};
public int VehicleNumber = 4;
public int VehicleLoadTime = 5;
public int VehicleUnloadTime = 5;
public int DepotCapacity = 2;
public int Depot = 0;
};
/// <summary>
/// Print the solution.
/// </summary>
static void PrintSolution(in DataModel data, in RoutingModel routing, in RoutingIndexManager manager,
in Assignment solution)
{
Console.WriteLine($"Objective {solution.ObjectiveValue()}:");
// Inspect solution.
RoutingDimension timeDimension = routing.GetMutableDimension("Time");
long totalTime = 0;
for (int i = 0; i < data.VehicleNumber; ++i)
{
Console.WriteLine("Route for Vehicle {0}:", i);
var index = routing.Start(i);
while (routing.IsEnd(index) == false)
{
var timeVar = timeDimension.CumulVar(index);
Console.Write("{0} Time({1},{2}) -> ", manager.IndexToNode(index), solution.Min(timeVar),
solution.Max(timeVar));
index = solution.Value(routing.NextVar(index));
}
var endTimeVar = timeDimension.CumulVar(index);
Console.WriteLine("{0} Time({1},{2})", manager.IndexToNode(index), solution.Min(endTimeVar),
solution.Max(endTimeVar));
Console.WriteLine("Time of the route: {0}min", solution.Min(endTimeVar));
totalTime += solution.Min(endTimeVar);
}
Console.WriteLine("Total time of all routes: {0}min", totalTime);
}
public static void Main(String[] args)
{
// Instantiate the data problem.
DataModel data = new DataModel();
// Create Routing Index Manager
RoutingIndexManager manager =
new RoutingIndexManager(data.TimeMatrix.GetLength(0), data.VehicleNumber, data.Depot);
// Create Routing Model.
RoutingModel routing = new RoutingModel(manager);
// Create and register a transit callback.
int transitCallbackIndex = routing.RegisterTransitCallback((long fromIndex, long toIndex) =>
{
// Convert from routing variable Index to
// distance matrix NodeIndex.
var fromNode = manager.IndexToNode(fromIndex);
var toNode = manager.IndexToNode(toIndex);
return data.TimeMatrix[fromNode, toNode];
});
// Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transitCallbackIndex);
// Add Distance constraint.
routing.AddDimension(transitCallbackIndex, // transit callback
30, // allow waiting time
30, // vehicle maximum capacities
false, // start cumul to zero
"Time");
RoutingDimension timeDimension = routing.GetMutableDimension("Time");
// Add time window constraints for each location except depot.
for (int i = 1; i < data.TimeWindows.GetLength(0); ++i)
{
long index = manager.NodeToIndex(i);
timeDimension.CumulVar(index).SetRange(data.TimeWindows[i, 0], data.TimeWindows[i, 1]);
}
// Add time window constraints for each vehicle start node.
for (int i = 0; i < data.VehicleNumber; ++i)
{
long index = routing.Start(i);
timeDimension.CumulVar(index).SetRange(data.TimeWindows[0, 0], data.TimeWindows[0, 1]);
}
// Add resource constraints at the depot.
Solver solver = routing.solver();
IntervalVar[] intervals = new IntervalVar[data.VehicleNumber * 2];
for (int i = 0; i < data.VehicleNumber; ++i)
{
// Add load duration at start of routes
intervals[2 * i] = solver.MakeFixedDurationIntervalVar(timeDimension.CumulVar(routing.Start(i)),
data.VehicleLoadTime, "depot_interval");
// Add unload duration at end of routes.
intervals[2 * i + 1] = solver.MakeFixedDurationIntervalVar(timeDimension.CumulVar(routing.End(i)),
data.VehicleUnloadTime, "depot_interval");
}
long[] depot_usage = Enumerable.Repeat<long>(1, intervals.Length).ToArray();
solver.Add(solver.MakeCumulative(intervals, depot_usage, data.DepotCapacity, "depot"));
// Instantiate route start and end times to produce feasible times.
for (int i = 0; i < data.VehicleNumber; ++i)
{
routing.AddVariableMinimizedByFinalizer(timeDimension.CumulVar(routing.Start(i)));
routing.AddVariableMinimizedByFinalizer(timeDimension.CumulVar(routing.End(i)));
}
// Setting first solution heuristic.
RoutingSearchParameters searchParameters =
operations_research_constraint_solver.DefaultRoutingSearchParameters();
searchParameters.FirstSolutionStrategy = FirstSolutionStrategy.Types.Value.PathCheapestArc;
// Solve the problem.
Assignment solution = routing.SolveWithParameters(searchParameters);
// Print solution on console.
PrintSolution(data, routing, manager, solution);
}
}