Development and Optimization of A Single Stage Multimodal ...Sourav Kumar Ghosh and Md. Mamunur Rashid Department of Industrial and Production Engineering Bangladesh University of

Proceedings of the International Conference on Industrial Engineering and Operations Management Dubai, UAE, March 10-12, 2020

© IEOM Society International

Development and Optimization of A Single Stage Multimodal Fixed-Cost Transportation Problem

Sourav Kumar Ghosh and Md. Mamunur Rashid Department of Industrial and Production Engineering

Bangladesh University of Textiles Dhaka, Bangladesh

[email protected], [email protected]

Naurin Zoha Department of Production and Industrial Engineering

Bangladesh University of Engineering and Technology Dhaka, Bangladesh

[email protected]

Abstract

Transportation plays a vital role in logistics which is an inseparable part of today’s supply chain management. An effective transportation network can optimize the supply chain to a great extent by reducing total cost, total time as well as maximizing profit. In this paper, we deal with one stage (supplier to manufacturer) multimodal fixed cost transportation problem (FCTP) of a local paper mill. Here we have formulated three different models which are road transportation model, rail transportation model and a combination of road and rail transportation models using linear programming to analyze and select the most optimized one for the case. For solving the case, we collected data for keeping the capacity constraints of each source and the demand constraints for each destination. We have used an excel solver to solve the models and the results show that the Rail route is the most cost-effective, but it leaves some of the demands unfulfilled. But the combination of both road and rail routes provide the most cost-effective solution satisfying the demands of the destinations. Henceforth, we compared the results by conducting cost analysis to select the most optimized one for the organization.

Keywords Transportation Problem, FCTP, Multimodal, Excel solver, Optimization.

1. Introduction

The transportation problem is defined by distributing any commodity from any group of suppliers, called sources, to any group of receiving centers, called destinations, in such a way as to minimize the total distribution cost or total time even to maximize profit. It deals with sources where a supply of some commodity is available and destinations where the commodity is demanded. In general, the transportation problem uses a matrix with the rows representing sources and columns representing destinations. The algorithms for solving the problem are based on this matrix representation. The costs of shipping from sources to destinations are indicated by the entries in the matrix. If a shipment is impossible between a given source and destination, a large cost of M is entered. This discourages the solution from using such cells. As in the example, the classic transportation problem has a total supply equal to total demand. Each source has a certain supply of units to distribute to the destinations, and each destination has a certain demand for units to be received from the sources. The transportation cost consists of a fixed cost for a certain destination, independent of the amount transported.

A transportation chain is divided into three segments: pre-haul (or first mile for the pickup process), long-haul (door-to-door transit of containers), and end-haul (or last mile for the delivery process). In most cases, the pre-haul and

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end-haul transportation is carried out via road, but for the long-haul transportation, road, rail, air and water modes can be considered, even multimodal modes can also be applied (SteadieSeifi et al 2014).

T. Van Woensel and his co reviewed the multimodal transportation literature from 2005 onward which discussed three type of planning such as strategic, tactical, and operational levels of planning where Tactical level issues have been studied the most and strategic level problems rank second, followed by the operational level problems (SteadieSeifi et al. 2014). Transportation problems can be considered as a piecewise linear cost model and can be solved using LP relaxation. The piece-wise linear transportation problem has a possibly stronger LP relaxation bound than the standard models considered as it offers a significant reduction in the gap between the LP relaxation of the root node and the optimal solution (Christensen, T. R., & Labbé, M., 2015). Small scale fixed-charge transportation problems can be solved by using a branching method where two novelists are used to find the optimal solutions (Kowalski et al. 2014). Combining Assignments in transportation can reduce computational effort. In this paper, the author shows the comparisons between the general Modi and Hungarian methods with the zero reduction method. In both cases, the author finds a zero reduction method is much better than general ones (Seethalakshmy, A., & Srinivasan, N., 2018). An algorithm is developed by MATLAB 7.7.0 to find the initial feasible solution for the Cost minimization transportation problem (Khan et al. 2015). The genetic algorithm is used to solve the fixed charge transportation problem model by applying mechanisms of all-units discount and incremental discount (Yousefi et al. 2017).

There is a variety of transportation problems such as fixed cost transportation problems, one stage transportation problems, multi-stage, single modal, multi-modal and so on. In our case, a stage multi-modal fixed cost transportation problem was developed. We solved these models using excel solver. Finally, we compared the results and recommended which was the best possible route and the best mode of transportation.

2. Methodology

Suppose, there are m (i=1,2, 3,…m) suppliers and n (j=1,2,3,……n) customers. The capacities for each source and the demands for each destination are denoted as Ai and Bj respectively. The unit costs for transportation of raw materials from the sources to the destination plants by road and by rail are denoted as Cij and Dij respectively. Xij is the number of units shipped by suppliers i to the customer j. The fixed cost transportation problem is formulated (for road route) as below:

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀,𝑍𝑍 = �𝑚𝑚

𝑖𝑖=1

�𝑛𝑛

𝑗𝑗=1

𝑋𝑋𝑖𝑖𝑗𝑗𝐶𝐶𝑖𝑖𝑗𝑗

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑆𝑆𝑆𝑆 𝑆𝑆𝑡𝑡,�𝑛𝑛

𝑗𝑗=1

𝑋𝑋𝑖𝑖𝑗𝑗 = 𝐴𝐴𝑖𝑖, 𝑀𝑀 = 1,2,3 … …𝑀𝑀

�𝑚𝑚

𝑖𝑖=1

𝑋𝑋𝑖𝑖𝑗𝑗 = 𝐵𝐵𝑗𝑗 , 𝑆𝑆 = 1,2,3 … …𝑀𝑀

�𝑛𝑛

𝑗𝑗=1

𝐴𝐴𝑖𝑖 = �𝑚𝑚

𝑖𝑖=1

𝐵𝐵𝑗𝑗

𝐴𝐴𝑖𝑖,𝐵𝐵𝑗𝑗 ,𝑋𝑋𝑖𝑖𝑗𝑗 ,𝐶𝐶𝑖𝑖𝑗𝑗 ≥ 0 The fixed cost transportation problem is formulated (for rail route) as below:


𝑖𝑖=1

�𝑛𝑛

𝑗𝑗=1

𝑋𝑋𝑖𝑖𝑗𝑗𝐷𝐷𝑖𝑖𝑗𝑗


𝑗𝑗=1


�𝑚𝑚

𝑖𝑖=1


�𝑛𝑛

𝑗𝑗=1


𝑖𝑖=1

𝐵𝐵𝑗𝑗

𝐴𝐴𝑖𝑖,𝐵𝐵𝑗𝑗 ,𝑋𝑋𝑖𝑖𝑗𝑗 ,𝐷𝐷𝑖𝑖𝑗𝑗 ≥ 0

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The fixed cost transportation problem is formulated (for rail and road combined) as below:


𝑖𝑖=1

�𝑛𝑛

𝑗𝑗=1

𝑋𝑋𝑖𝑖𝑗𝑗𝐶𝐶𝑖𝑖𝑗𝑗 + �𝑚𝑚

𝑖𝑖=1

�𝑛𝑛

𝑗𝑗=1

𝑋𝑋𝑖𝑖𝑗𝑗𝐷𝐷𝑖𝑖𝑗𝑗


𝑗𝑗=1


�𝑚𝑚

𝑖𝑖=1


�𝑛𝑛

𝑗𝑗=1


𝑖𝑖=1

𝐵𝐵𝑗𝑗

𝐴𝐴𝑖𝑖,𝐵𝐵𝑗𝑗 ,𝑋𝑋𝑖𝑖𝑗𝑗 ,𝐶𝐶𝑖𝑖𝑗𝑗,𝐷𝐷𝑖𝑖𝑗𝑗 ≥ 0

3. Problem Statement

The capacities for each source and the demands for each destination are enlisted as follows: Table 1: Capacity and Demand Table

Sources Capacity Destination Demand

Rangamati 30 Agrabad 15 Bandarban 15 City Gate 12

Khagrachhari 5 Tejgaon 35 Bagerhat 20 Tongi 12 Khulna 8 BSCIC 8

Hobigonj 12 Kadamtoli 13 Moulovibazar 10 Rangpur 5

The unit costs for transportation of raw materials from the sources to the destination plants by road and by rail are obtained. They are enlisted as follows:

Table 2: Data for unit transportation costs (Taka per unit shipments in Thousands)

Destination Source

Agrabad City gate Tejgaon Tongi BSCIC Kadamtoli Rangpur

Rangamati 25 22 37 51 48 72 84 Bandarban 36 26 41 34 43 66 78 Khagrachhari 18 32 50 54 65 78 85 Bagerhat 53 48 28 27 31 56 71 Khulna 49 46 17 33 32 50 65 Hobigonj 62 58 55 59 49 22 28 Moulovibazar 57 63 48 53 23 26 49

Table 3: Data for unit transportation costs (Taka per unit shipments in Thousands)

Destination

Source Agrabad City gate Tejgaon Tongi BSCIC Kadamtoli Rangpur

Rangamati 18 15 31 29 52 67 79 Bandarban 16 18 44 41 49 56 73 Bagerhat 43 54 21 33 16 32 65 Khulna 45 60 33 23 30 70 35

Hobigonj 54 49 52 43 54 31 54 Moulovibazar 51 47 36 51 53 37 56

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3.1 Road Transportation problem summary We use excel solver to solve road transportation problem & the optimum allocations are enlisted as follows:

Table 4: Data table for shipment quantities (Optimum allocation) for road transportation

Destination Source

Agrabad

City gate

Tejgaon

Tongi

BSCIC

Kadamtoli

Rangpur

Capacity

Rangamati 10 12 8 0 0 0 0 30 Bandarban 0 0 0 12 3 0 0 15 Khagrachhari 5 0 0 0 0 0 0 5 Bagerhat 0 0 19 0 1 0 0 20 Khulna 0 0 8 0 0 0 0 8 Hobigonj 0 0 0 0 0 7 5 12 Moulovibazar 0 0 0 0 4 6 0 10 Demand 15 12 35 12 8 13 5

Figure 1: Pie chart for demand covered at each destination for road transportation

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Figure 2: Pie chart for capacity used of each source for road transportation

3.2 Rail Transportation Problem Summary We use excel solver to solve road transportation problem & the optimum allocations are enlisted as follows:

Table 5: Data table for shipment quantities (Optimum allocation) for rail transportation

Destination Source

Agrabad

City gate

Tejgaon

Tongi

BSCIC

Kadamtoli

Rangpur

Capacity

Rangamati 7 0 14 9 0 0 0 30 Bandarban 8 7 0 0 0 0 0 15 Bagerhat 0 0 12 0 8 0 0 20 Khulna 0 0 0 3 0 0 5 8 Hobigonj 0 0 0 0 0 12 0 12 Moulovibazar 0 0 9 0 0 1 0 10 Demand 15 12 35 12 8 13 5

Figure 3: Pie chart for demand covered at each destination for rail transportation

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Figure 4: Pie chart for capacity used of each source for rail transportation

3.3 Combined Transportation Problem Summary We use excel solver to solve combined transportation problem & results are enlisted as follows:

Table 6: Data table for shipment quantities (Optimum allocation) for combined transportation

Destination Source

Agrabad

City gate

Tejgaon

Tongi

BSCIC

Kadamtoli

Rangpur

Capacity

Rangamati 0 7 11 12 0 0 0 30 Bandarban 15 0 0 0 0 0 0 15 Khagrachhari 0 5 0 0 0 0 0 5 Bagerhat 0 0 16 0 4 0 0 20 Khulna 0 0 8 0 0 0 0 8 Hobigonj 0 0 0 0 0 7 5 12 Moulovibazar 0 0 0 0 4 6 0 10 Demand 15 12 35 12 8 13 5

Figure 5: Pie chart for demand covered at each destination for combined transportation

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Figure 6: Pie chart for capacity used of each source for combined transportation

Tanveer Paper Mills has to bear a cost of tk. 22,37,000 if all the resources are supplied by road.

4. Cost Analysis

4.1 Cost Analysis for Road Transportation Tanveer Paper Mills has to bear a cost of tk. 26,78,000 if all the resources are supplied by road. 4.2 Cost Analysis for Rail Transportation Tanveer Paper Mills has to bear a cost of tk. 24,32,000 if all the resources are supplied by rail. But it is to be noted that one of the sources, Khagrachhari, has no direct rail route to the destinations. So, for pure rail transportation analysis, we observed a shortage of 5-unit supplies at the City Gate factory. For this reason, production at this factory deteriorates. 4.3 Cost Analysis to Evaluate the Optimum Transportation Route From our obtained transportation unit cost data, we observed the minimum costs for each destination to receive a shipment and put those in the corresponding source-destination combination cell. From that data, we calculated in excel and found out how much it costs in each route. Finally, we found the optimal mode of transportation for each route. Results are shown in the following table and comparisons are shown in the bar charts:

Table 7: Optimal modals for different routes

Destination Rail Road Combined Agrabad × × Selected City Gate × × Selected Tejgaon × × Selected Tongi Selected × × BSCIC Selected × × Kadamtoli × Selected × Rangpur × Selected ×

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Figure 7: Chart for cost distribution in each route for Agrabad

Figure 8: Chart for cost distribution in each route for City Gate

Figure 9: Chart for cost distribution in each route for Tejgaon

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Figure 10: Chart for cost distribution in each route for Tongi

Figure 11: Chart for cost distribution in each route for BSCIC

Figure 12: Chart for cost distribution in each route for Kadamtoli

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Figure 13: Chart for cost distribution in each route for Rangpur

Figure 14: Chart for combined transportation

5. Conclusion

The transportation problem compares three models that incorporate rail and road transportation systems for single stage transportation network optimization. After a thorough cost analysis, it is evident that the multi-modal network provides the most efficient results for the supply of raw materials for the respective company. This type of optimization network model can also be utilized in varieties of other segments of the logistics network. The problem can also be further worked on by developing multi-stage models that incorporate a broader view of the supply chain network. Further improvement in the accuracy of the results can also be attained by introducing uncertainties in the case.

References SteadieSeifi, M., Dellaert, N. P., Nuijten, W., Van Woensel, T., & Raoufi, R., Multimodal freight transportation

planning: A literature review, European journal of operational research, 233(1), pp. 1-15, 2014. Christensen, T. R., & Labbé, M., A branch-cut-and-price algorithm for the piecewise linear transportation problem,

European journal of operational research, 245(3), pp. 645-655, 2015. Kowalski, K., Lev, B., Shen, W., & Tu, Y., A fast and simple branching algorithm for solving small scale fixed-charge

transportation problem, Operations Research Perspectives, 1(1), pp. 1-5, 2014.

Rangamati

Khagrachhari

Bagerhat

Agrabad

Bandarban City Gate

Tejgaon

Tongi

Khulna BSCIC

For Train route For Road Route

Hobigonj

Moulovibazar Rangpur

Kadamtoli

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Seethalakshmy, A., & Srinivasan, N., A heuristic approach to obtain an optimal solution for transportation problem using assignment, TAGA Journal, 14, pp. 1862-1870, 2018.

Khan, A. R., Vilcu, A., Uddin, M. S., & Ungureanu, F., A competent algorithm to find the initial basic feasible solution of cost minimization transportation problem, Buletinul Institutului Politehnic Din Iasi, Romania, Secţia Automatica si Calculatoare, pp. 71-83, 2015.

Yousefi, K., Afshari, A. J., & Hajiaghaei-Keshteli, M., Genetic algorithm for fixed charge transportation problem with discount models, 13th International Conference on Industrial Engineering, pp. 22-23, 2017.

Biographies Sourav Kumar Ghosh is a lecturer in Industrial and Production Engineering at Bangladesh University of Textiles (BUTEX). He earned B.Sc. in Industrial and Production Engineering from Bangladesh University of Engineering and Technology (BUET) in 2017. He is a former lecturer in textile engineering at Primeasia University. He is currently enrolled in a Master’s program in Industrial and Production Engineering at Bangladesh University of Engineering and Technology, Bangladesh. He has published two journal papers and three conference papers. S. K. Ghosh has completed several research projects under UGC. His research interests include machine learning, supply chain optimization, operation research, parameter optimization of CNC machines, renewable energy, and lean manufacturing. Md Mamunur Rashid is an Assistant Professor in Industrial and Production Engineering at Bangladesh University of Textiles (BUTEX). He received his B.Sc. degree in Industrial and Production Engineering from Bangladesh University of Engineering and Technology (BUET), in 2013. He acted as a corporate professional in both Textile and Garments units of DBL Group to apply Industrial Engineering tools and techniques prior to starting his academic career as a Lecturer at BUTEX in 2015. He has been involved in different research projects in the area of multidisciplinary optimization, CAD/CAM, artificial intelligence application, industry 4.0, supply chain management. He is a Lean Six Sigma Green Belt certified practitioner of lean manufacturing in the Textile and Garments Industries. Mr. Rashid is a life member of the Bangladesh Society for Total Quality Management (BSTQM). Naurin Zoha is a production officer at Nestle Bangladesh Limited which is a renowned multinational company. She completed B.Sc. in Industrial and Production Engineering from Bangladesh University of Engineering and Technology (BUET) in 2017. she ranked 7th out of 36 students of her batch. She is currently enrolled in a Master’s program in Industrial and Production Engineering at Bangladesh University of Engineering and Technology, Bangladesh. She has published a journal paper and three conference papers. She achieved the best performer of the year award at Nestle Bangladesh Limited in 2018-19. She also handled different projects during her journey in Nestle Bangladesh Limited. Her research interests include fuzzy logic, supply chain optimization, large scale linear programming, stochastic modeling, lean manufacturing and transportation problems.

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Development and Optimization of A Single Stage Multimodal ...Sourav Kumar Ghosh and Md. Mamunur Rashid Department of Industrial and Production Engineering Bangladesh University of