এখন পর্যন্ত, আমরা যানবাহন ভ্রমণের সময় প্রযোজ্য বাধাগুলির সাথে রাউটিং সমস্যাগুলি দেখছি। এর পরে, আমরা একটি VRPTW উপস্থাপন করি যার ডিপোতেও সীমাবদ্ধতা রয়েছে: সমস্ত যানবাহন ডিপো ছেড়ে যাওয়ার আগে লোড করতে হবে এবং ফেরার সময় আনলোড করতে হবে। যেহেতু শুধুমাত্র দুটি উপলব্ধ লোডিং ডক রয়েছে, তাই একই সময়ে সর্বাধিক দুটি যানবাহন লোড বা আনলোড করা যেতে পারে। ফলস্বরূপ, কিছু যানবাহন অন্যদের লোড হওয়ার জন্য অপেক্ষা করতে হবে, ডিপো থেকে তাদের প্রস্থান বিলম্বিত করে। সমস্যাটি হল VRPTW-এর জন্য সর্বোত্তম যানবাহন রুটগুলি খুঁজে বের করা যা ডিপোতে লোডিং এবং আনলোডিং সীমাবদ্ধতাগুলিও পূরণ করে৷
সম্পদের সীমাবদ্ধতা সহ VRPTW উদাহরণ
নীচের চিত্রটি সম্পদের সীমাবদ্ধতা সহ একটি VRPTW দেখায়।
OR-Tools দিয়ে উদাহরণ সমাধান করা
নিম্নলিখিত বিভাগগুলি দেখায় কিভাবে OR-Tools ব্যবহার করে সম্পদের সীমাবদ্ধতার সাথে VRPTW সমাধান করা যায়। উদাহরণের জন্য কিছু কোড আগের VRPTW উদাহরণের মতোই, তাই আমরা শুধু নতুন অংশগুলি বর্ণনা করব৷
ডেটা তৈরি করুন
নিম্নলিখিত কোড উদাহরণের জন্য ডেটা তৈরি করে।
পাইথন
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
সি++
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}; };
জাভা
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; }
সি#
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; };
তথ্য নিম্নলিখিত অন্তর্ভুক্ত:
-
time_matrix: অবস্থানের মধ্যে ভ্রমণ সময়ের একটি অ্যারে। -
time_windows: অবস্থানগুলিতে অনুরোধ করা ভিজিটের জন্য সময় উইন্ডোগুলির একটি অ্যারে। -
vehicle_load_time: একটি যানবাহন লোড করার জন্য প্রয়োজনীয় সময়। -
vehicle_unload_time: একটি যানবাহন আনলোড করার জন্য প্রয়োজনীয় সময়। -
depot_capacity: সর্বোচ্চ সংখ্যক যানবাহন যা একই সময়ে লোড বা আনলোড করতে পারে।
লোড এবং আনলোড করার জন্য সময় উইন্ডো যোগ করুন
নিম্নলিখিত কোড ডিপোতে যানবাহন লোড এবং আনলোড করার জন্য সময় উইন্ডো যোগ করে। FixedDurationIntervalVar পদ্ধতির দ্বারা তৈরি এই উইন্ডোগুলি হল পরিবর্তনশীল টাইম উইন্ডো , যার অর্থ তাদের নির্দিষ্ট শুরু এবং শেষের সময় নেই (স্থানের সময় উইন্ডোগুলির বিপরীতে)। জানালার প্রস্থ vehicle_load_time এবং vehicle_unload_time দ্বারা নির্দিষ্ট করা হয়েছে, যা এই উদাহরণে একই রকম।
পাইথন
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", ) )
সি++
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")); }
জাভা
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"); }
সি#
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"); }
ডিপোতে সম্পদের সীমাবদ্ধতা যোগ করুন
নিম্নলিখিত কোডটি এই সীমাবদ্ধতা তৈরি করে যে একই সময়ে সর্বাধিক দুটি যানবাহন লোড বা আনলোড করা যেতে পারে।
পাইথন
depot_usage = [1 for _ in range(len(intervals))] solver.Add( solver.Cumulative(intervals, depot_usage, data["depot_capacity"], "depot") )
সি++
std::vector<int64_t> depot_usage(intervals.size(), 1); solver->AddConstraint(solver->MakeCumulative(intervals, depot_usage, data.depot_capacity, "depot"));
জাভা
long[] depotUsage = new long[intervals.length];
Arrays.fill(depotUsage, 1);
solver.addConstraint(solver.makeCumulative(intervals, depotUsage, data.depotCapacity, "depot"));সি#
long[] depot_usage = Enumerable.Repeat<long>(1, intervals.Length).ToArray();
solver.Add(solver.MakeCumulative(intervals, depot_usage, data.DepotCapacity, "depot")); depot_capacity হল সর্বাধিক সংখ্যক যানবাহন যা একই সময়ে লোড বা আনলোড করা যায়, যা এই উদাহরণে 2।
depot_usage হল একটি ভেক্টর যাতে লোড করার (বা আনলোডিং) সময় প্রতিটি গাড়ির প্রয়োজনীয় স্থানের আপেক্ষিক পরিমাণ থাকে। এই উদাহরণে, আমরা অনুমান করি যে সমস্ত যানবাহনের জন্য একই পরিমাণ স্থান প্রয়োজন, তাই depot_usage সবগুলি রয়েছে। এর মানে হল যে একই সময়ে সর্বোচ্চ 2টি গাড়ি লোড করা যায়।
কার্যক্রম পরিচালনা করছেন
নিম্নলিখিত প্রোগ্রামের আউটপুট দেখায়.
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
আউটপুট ব্যাখ্যার জন্য পূর্ববর্তী VRPTW উদাহরণ দেখুন।
মনে রাখবেন যে যানবাহন 1 এবং 3 ডিপো থেকে 0 সময়ে প্রস্থান করে। যানবাহন 0 এবং 2, যেগুলিকে অন্যগুলি লোড হওয়ার জন্য অপেক্ষা করতে হবে, 5 টায় ছাড়বে, vehicle_load_time মান।
নীচের চিত্রটি সমাধানটি দেখায়।
সম্পূর্ণ প্রোগ্রাম
সম্পদের সীমাবদ্ধতা সহ ক্যাপাসিটেটেড গাড়ির রাউটিং সমস্যার জন্য সম্পূর্ণ প্রোগ্রামগুলি নীচে দেখানো হয়েছে।
পাইথন
"""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()
সি++
#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; }
জাভা
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); } }
সি#
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); } }