DETERMINATION OF TRANSPORTATION DELIVERY ROUTE AT PT. XYZ USES VEHICLE ROUTING PROBLEMS HETEROGENOUS FLEET AND TIME WINDOWS WITH INTEGER LINEAR PROGRAMMING (ILP) TO MINIMIZE TRANSPORTATION COSTS
- 1. DETERMINATION OF TRANSPORTATION DELIVERY ROUTE AT PT. XYZ USES VEHICLE ROUTING PROBLEMS HETEROGENOUS FLEET AND TIME WINDOWS WITH INTEGER LINEAR PROGRAMMING (ILP) TO MINIMIZE TRANSPORTATION COSTS Genta Yusuf Madhani (1201174352)
- 2. ADVISORS M. Nashir Ardiansyah, S.T., M.T., Ph.D. Dr. Mohammad Deni Akbar, S.T., M.Math 1 2
- 4. INTRODUCTION PT. XYZ is one of the leading, largest, and most trusted companies in the concrete works division in Indonesia and located in Kab. Bandung. PT.XYZ sees the fragility of buildings in Indonesia against earthquakes which always take lives and depend on air conditioning which can exacerbate global warming. PT. XYZ makes product innovations that are strong and lightweight, a construction materials with styrofoam as the base in the construction process, which can be used as walls, roofs, floors, or stairs with the sizes and specifications desired by customers.
- 5. Products
- 6. RESEARCH BACKGROUND Frequencies PT. XYZ experienced delays in some of their delivery process. The delays that occurs is when the product arrives at the customer exceeds the time closes. Januari Februari Maret 0 20 40 60 80 100 120 140 160 180 148 140 155 16 16 17 Deliveries (Customer) Deliveries Lateness
- 7. RESEARCH BACKGROUND The incident of delivery delays was analyzed to find out the cause of the delay that occurred in January 2021 Causes of Delays 63% 13% 25% Delivery Delays Causes Route Determination Integrated System Product Availability
- 8. RESEARCH BACKGROUND Man Method Machine Jenis kendaraan yang digunakan Penjadwalan pengiriman Pemahaman karakteristik rute Peramalan produksi dan pengiriman Keterlambatan pengiriman produk pesanan Keterbatasan pada kendaraan Environment Kepadatan lalu lintas
- 9. 2 1 2 1 PROBLEM FORMULATION How to determine route planning that can reduce delays? How to determine route planning that can reduce deliveries operational costs? Find out route planning that can reduce delays Find out route planning that can reduce deliveries operational costs RESEARCH PURPOSES
- 10. PROBLEM LIMITATIONS Research data for deliveries only use that exists in January 2021 Doesn’t consider natural disasters that can detain deliveries Doesn’t consider traffic jam condition Research data for deliveries that use company’s fleet only in Java Consider average velocity for each type of transportation that owned by the company Unloading processes target is 20 minutes at every customer
- 12. LITERATURE STUDIES Supply Chain Management Distribution Transportation is an approach for stakeholders at factory to delivers products in a right amount, time, and place to minimize overall costs. (Hugos, 2006) is a process that concerned fulfilling demand and cost to deliver products to customers. (Chopra & Meindl, 2014) is a tool that helps interaction between people and to facilitate the movement of goods. (Fatimah, 2019)
- 13. LITERATURE STUDIES Vehicle Routing Problem Linear Programming MILP is an optimization problem for determining vehicle optimal route with one or more depots to serve several customers. (Toth & Vigo, 2002) is a mathematical method to solve problems that has limitation and a non- negative linear objective and constraints. (Luenberger, 2016) is a simplex and branch- and-bound method to solve a linear programming that has a combination between integer and decimals. (Hadi, 2010)
- 14. LITERATURE STUDIES Previous Final Projects Methods Literature Author Mohammed, Mazin Abed (2017) Lai, David S.W. (2015) Ahkamiirad, Azadeh (2018) Jeong, Ho Young (2019) Method Genetic Algorithm Tabu Search Genetic & Particle swamp Hybrid Mixed Integer Linear Programmin g Heterogene ous Fleet √ Time Windows √ Nodes 35 20 38 15 Distance Min. √ √ √ √ Costs min. √ √ √ √ Travel Time Min. √ Author Research Arini Nourma (2018) Prafajar Suksesanno (2016) R. Fauzi Novianda (2016) Penelitian ini (2020) Objects PT. ABC (Food Industry) PT. XYZ (Investments Company) PT. XYZ (F&B Distributor) PT. XYZ (Concrete works) Methods Branch and Bound Algoritma Tabu Search Algoritma Tabu Search Algoritma MILP Heterogeneous Fleet √ √ √ Time Window √ √ √ √ Distance Min. √ √ √ √ Costs Min. √ √ Time Travel Min. √ Delivery Scheduling √
- 16. METHODOLOGY Conclusions and Suggestion Preliminary Study Data Processing 02 01 02 03 02 04 Gathering Data
- 17. METHODOLOGY Preliminary Study 02 01 02 03 02 04 1. PT. XYZ Study Case 2. Literature Study 3. Problem Formulation 4. Research Purposes
- 18. METHODOLOGY 02 02 03 02 04 Gathering Data 2. Customer’s Data • Customer’s Location • Customer’s Demand • Operational Hours 1. Company’s Data • Fleet’s type and capacity • Product Deliveries • Operational Hours
- 19. METHODOLOGY Data Processing 02 02 03 02 04 1. Existing Routes Analysis 2. Influence Diagram 3. Programming Solving 4. Proposed Routes Analysis
- 20. METHODOLOGY Conclusions and Suggestion 02 02 04 1. Lateness Analysis 2. Cost Analysis 3. Conclusions 4. Suggestions
- 21. SECTION 4 Gathering and Data Processing
- 22. Transportatio n Fleet PT.XYZ transportation fleet only used for deliveries within Java island. The transportation fleet that owned by the company has different types and capacities. N o Types Capaci ty (dm3 ) Fixed Cost Variable Cost Avg. Velocity (meter/minute) 1 XL 3600 Rp. 50.000,- Rp. 1358,- / km 666,67 2 XV 14400 Rp. 50.000,- Rp. 970,- / km 583,33 3 XQ 18000 Rp. 50.000,- Rp. 1492,- / km 500 4 XW 28800 Rp. 50.000,- Rp. 1552,- / km 416,67 5 XM 36000 Rp. 60.000,- Rp. 3234,- /km 333,33
- 23. Customer’s Identification Deliveries that occurs in January 2021 only has 32 consumers with different demands within days and locations. Consumers Latitude Longitude Q1 -6.8985 107.5835 Q2 -6.90894 107.6841 Q3 -6.9271 107.6034 Q4 -6.92593 107.5936 Q5 -7.03913 107.5933 Q6 -6.91947 107.6075 Date Customer Demand (dm3 ) 4 Q1 36000 Q2 2700 Q3 900 Q4 17400 Q5 1800 Q6 450 Q8 900 5 Q6 2250 Q7 36000 Q10 10400 Q11 3900 Q14 17800 Q15 3600 Q28 1350 6 Q1 16800 Q4 26500 Q6 3300 Q8 1200 Q13 1200 Q30 36000 Q31 3000 Q32 600 Consumers Time Window Opening hours Closes hours Service Time Q1 8:00 17:00 20 Q2 8:00 17:00 20 Q3 8:00 17:00 20 Q4 8:00 17:00 20 Q5 8:00 17:00 20 Q6 8:00 17:00 20
- 24. INFLUENCE DIAGRAM Biaya Transportasi Biaya Tetap Biaya Variabel Perutean Konsumen Jenis Kendaraan Waktu Tempuh Rute Pengiriman Konsumsi BBM (L/M) Ongkos Jalan Setiap Kendaraan Matriks Jarak per Node Jam Buka Tutup Tiap Node Kecepatan Kendaraan Harga Bahan Bakar per Liter Kapasitas tiap Kendaraan Jumlah Pelanggan Demand Pelanggan Pemilihan Kendaraan
- 25. MATHEMATICAL MODEL Objective Function: min∑ 𝑖=0 𝑛 ∑ 𝑗=0 𝑛 ∑ 𝑣=1 𝑣 𝑋𝑖𝑗𝑣 𝐷𝑖𝑗(𝐶𝑉𝑣 1000 )+∑ 𝑗=0 𝑛 ∑ 𝑣=1 𝑣 𝑋0 𝑗𝑣𝐶 𝐹𝑣 Subject to: ∑ 𝑗=0 𝑛 ∑ 𝑣=1 𝑣 𝑋𝑖𝑗𝑣 =1 ∑ 𝑖=0 𝑛 ∑ 𝑣=1 𝑣 𝑋𝑖𝑗𝑣=1 ∑ 𝑖=0 𝑛 𝑋𝑖𝑘𝑣 −∑ 𝑗=0 𝑛 𝑋𝑘𝑗𝑣=0 ∑ 𝑖= 0 𝑛 𝑋0𝑖𝑣 ≤1 𝑔𝑗𝑣 ≥𝑔𝑖𝑣+𝐺𝑗+((𝑋𝑖𝑗𝑣 −1)𝑥 𝑍) (2) (3) (4) (5) (6) (1) 𝐺𝑖𝑣 ≤ 𝑄𝑣 𝑎 𝑗𝑣 ≥ 𝑎𝑖𝑣 + ( 𝐷𝑖𝑗 𝐴𝑐𝑣 )+𝑆𝑡 +(( 𝑋𝑖𝑗𝑣 − 1)𝑥 𝑍) 𝑎𝑖𝑣 +( 𝐷𝑖 0 𝐴𝑐𝑣 )≤ 𝐿 𝑎𝑖𝑣 ≥𝐸 𝑇𝑖 𝑎𝑗𝑣 ≤ 𝐿𝑇𝑖 𝑑𝑗𝑣 ≥ 𝑑𝑖𝑣+𝐷𝑖𝑗+((𝑋𝑖𝑗𝑣−1)𝑥 𝑍) (7) (8) (9) (10) (11) (12)
- 26. MATHEMATICAL MODEL Sets: N = Sets of customer Nd = Sets of customer includes company V = Sets of vehicles 0 = Company index i = Origin index j = Destination Index k = Node Index v = Fleet Index Index: Variable: = Distance between node i to j = Routes decision (binary) to visit node i and j. = Accumulated load of vehicle v at node j = Accumulated time travel of vehicle v at node j = Accumulated distance of vehicle v at node j Parameter: D = Distance between nodes G = Customer demand Q = Vehicle capacity Cf = Vehicle fixed cost Cv = Vehicle variable cost Ac = Vehicle average velocity Z = Big number E = Company opening hours L = Company closing hours Et = Customer opening hours Lt = Customer closing hours St = Unloading time for customer
- 27. DELIVERY ROUTES Existing routes are obtained when gathering information processes. The data that shown is a sample for 3 days in January 2021 deliveries. EXISTING ROUTES Date Vehicles Routes Distances (m) Cost 4 XL 0-2-3-0 193000 Rp533,520 XQ 0-6-4-0 XL 0-5-8-0 XM 0-1-0 5 XV 0-11-10-0 402500 Rp812,202 XL 0-6-28-0 XL 0-15-0 XQ 0-14-0 XM 0-7-0 6 XQ 0-1-13-0 369100 Rp1,074,012 XV 0-6-8-0 XL 0-31-32-0 XW 0-4-0 XM 0-30-0
- 28. DELIVERY ROUTES Proposed routes are obtained from MILP programming using Gurobi Optimization with Python. The data that shown is a sample for 3 days in January 2021 deliveries. PROPOSED ROUTES Date Vehicles Routes Distanc e (m) Cost 4 XW 0-4-3-6-2-0 156800 Rp440,512 XL 0-5-8-0 XM 0-1-0 5 XW 0-7-28-6-0 381900 Rp760,383 XV 0-11-14-0 XM 0-10-0 XL 0-15-0 6 XV 0-32-13-6- 31-0 303200 Rp916,429 XQ 0-8-1-0 XW 0-4-0 XM 0-30-0
- 29. SECTION 5 Research Results Evaluation and Analysis
- 30. LATENESS ANALYSIS Date Existing (minutes) Lateness Proposed (minutes) Lateness Gap 4 352,6 1 331,17 0 6,08% 5 710,3 0 728,2 0 -2,53% 6 866 2 764,81 0 11,69% 7 641,24 0 655,53 0 -2,23% 8 974,06 1 929,02 0 4,62% 11 991,49 2 772,37 0 22,1% 12 1390,7 1 1279,2 0 8,02% 13 647,13 1 532,66 0 17,69% 14 1163,4 2 1039,5 0 10,65% 15 1017,5 1 994,7 0 2,24% 18 910,27 0 913,19 0 -0,32% 19 950,28 1 922,53 0 2,92% 20 2123,2 2 1898,6 0 10,58% 21 822,35 0 806,15 0 1,97% 22 446,73 1 376,88 0 15,64% 25 1062,6 0 1118,9 0 -5,3% 26 623,3 0 620,72 0 0,41% 27 1734,5 1 1541,4 0 11,13% 28 960,12 1 848,97 0 11,58% 29 923,18 0 874,11 0 5,32% Total 19311 17 17949 0 6,61% Average
- 31. COST ANALYSIS The gap between existing and proposed routes are obtained from MILP algorithm with Gurobi Optimization. The table shown the gap within days in January 2021. Date Existing Proposed Gap Distance (m) Cost Distance (m) Cost Distance (m) Cost 4 193 Rp533,520 156.8 Rp440,512 36.2 Rp93007.8 5 402.5 Rp812,202 381.9 Rp760,383 20.6 Rp51818.4 6 369.1 Rp1,074,012 303.2 Rp916,429 65.9 Rp157583 7 255 Rp818,735 254.15 Rp769,965 0.85 Rp48769.4 8 446.8 Rp1,139,827 404.7 Rp997,466 42.1 Rp142361 11 430.5 Rp733,911 360.3 Rp676,222 70.2 Rp57689.6 12 1095.4 Rp3,249,658 1027.5 Rp3,079,649 67.9 Rp170010 13 299.95 Rp662,796 260.55 Rp582,910 39.4 Rp79885.7 14 589.9 Rp1,041,651 481 Rp858,769 108.9 Rp182882 15 514.9 Rp1,006,927 494.7 Rp931,323 20.2 Rp75604.4 18 375.65 Rp973,039 369.85 Rp966,604 5.8 Rp6435.1 19 1119.4 Rp1,813,489 1090.2 Rp1,744,599 29.2 Rp68889.4 20 1010.1 Rp2,122,344 996.5 Rp1,730,006 13.6 Rp392338 21 428.7 Rp866,402 420.6 Rp854,317 8.1 Rp12085.2 22 206.9 Rp648,406 177.1 Rp486,387 29.8 Rp162019 25 463.5 Rp1,086,431 428.5 Rp1,028,846 35 Rp57584.8 26 337.65 Rp764,768 336.15 Rp763,313 1.5 Rp1455 27 685.4 Rp1,726,880 637.2 Rp1,522,430 48.2 Rp204450 28 399.9 Rp1,006,140 368.4 Rp853,999 31.5 Rp152141 29 409.45 Rp880,957 366.2 Rp780,551 43.25 Rp100406
- 32. COST ANALYSIS From the previous table, it all summed up to discover the gap percentage for January 2021 cost. Jan 2021 Existing Proposed Gap Distance (m) Cost Distance (m) Cost Distance (m) Cost Total 10033.7 Rp22,962,094 9315.5 Rp20,744,679 7.16% 9.66%
- 33. VELOCITY DECREASING SENSITIVITYVelocity This sensitivity analysis represents traffic jam that affects average velocity when delivering products. Graphic shown is an average velocity decreasing to sustain the routes that proposed. XL XV XQ XW XM 0% 10% 20% 30% 40% 50% 60% 48% 38% 38% 39% 41% Average Velocity Decreasing
- 34. VARIABLE COST SENSITIVITY Variable Cost This sensitivity analysis represents if there are any changes for the fuel costs that determined by the government. Graphic shown is an average costs when decreased 25% until increased into 25% - 25 % - 20 % - 15 % - 10 % -5% 0% 5% 10 % 15 % 20 % 25 % Rp0 Rp200,000 Rp400,000 Rp600,000 Rp800,000 Rp1,000,000 Rp1,200,000 Rp1,400,000 Delivery Cost Average
- 36. 01 02 03 04 CONCLUSIO NS Proposed routes travel time is 17949 minutes, or optimized by 6,61% from existing routes. Proposed routes cost is Rp. 20.744.679, or optimized by 9,66% from existing routes. Average increases variable costs is 15% that makes proposed routes infeasible. Average decreasing velocity to maintain routes is 48% for XL, 38% for XV and XQ, 39% for XW, and 41% for XM.
- 37. 01 02 SUGGESTIO NS Futured search is expected to obtain more detailed data and obtain routes without Google Maps for travel distances. A developed program that integrates between data obtained and processing to ease company uses proposed projects.
- 38. THANK YOU