transportation problem find the number of trucks to minimize shipping costs from suppliers to manufacturers industry raw milk transportation

VIETNAM NATIONAL UNIVERSITY - HO CHI MINH CITYINTERNATIONAL UNIVERSITYSCHOOL OF INDUSTRIAL ENGINEERING & MANAGEMENT---PROJECT REPORT Course: Deterministic Model in Operation ResearchTopi

VIETNAM NATIONAL UNIVERSITY - HO CHI MINH CITY

INTERNATIONAL UNIVERSITY

SCHOOL OF INDUSTRIAL ENGINEERING & MANAGEMENT

-PROJECT REPORT

Course: Deterministic Model in Operation Research Topic: Transportation problem - Find the number of trucks to minimize shipping costs from suppliers to manufacturers - Industry:

raw milk transportation Lecturer: Ph.D Ha Thi Xuan Chi

Contribution table (Group 03)

Ho Chi Minh City, Vietnam Semester II - 2022

Tables of content

I INTRODUCTION 3

1 Background of Study 3

2 Problem Description and Problem Statement 3

3 Project Scope 5

4 Limitation 6

II MATHEMATICAL MODEL 6

1 Parameters 6

2 Decision Variables 7

3 Objective Function 7

4 Constraints 7

III RESULT ANALYSIS AND DISCUSSION 8

IV CONCLUSION 9

V REFERENCES 9

VI APPENDIX 10

VII FEEDBACK FROM MS THẢO 13

I INTRODUCTION

1 Background of Study

Vehicle routing problems is difficult-to-solve conundrums that lay within but are highly prevalent and well-regarded, due to their potential to minimize transportation costs for industries to convey goods, which deals with moving commodities from sources to destinations The transportation model is critical in ensuring the efficient movement and availability of raw materials and finished goods from their origins to their destinations It is based on a network structure with a finite number of nodes and arcs connected to them The goal of the transportation problem is to find a shipment schedule that minimizes total shipping costs while meeting demand and supply constraints In this research project, an example of a transportation problem is delivering raw milk from the farm to the Vinamilk facility This study proposes an algorithm and a mathematical solution model for finding the smallest possible solution to Vinamilk's milk transportation problem The main purpose of this task is to use Integer Linear Programming to build a mathematical model to find the number of delivering trucks to minimize total transportation costs We can use this challenge

to apply our expertise in Operations Research to solve a complex problem in managing a huge system, as well as support decision-making determination in problem-solving To complete this exercise, we must understand the basic and intermediate knowledge of Operations Research, which means we must be able to apply and practice the linear formula, optimization, algorithms, and data analysis We anticipate that this initiative will solve not only the aforementioned difficulty but also other well-known difficulties in related fields

2 Problem Description and Problem Statement

Delivering raw milk from Vinamilk’s farms to Vinamilk’s factories is an example of a transportation difficulty in this research study Vinamilk requires an estimated total of 400,000 tons of imported milk and fresh milk from 13 farms across Vietnam per year, averaging 2565 tons of milk per local factory per month An estimate of monthly supply and demand of each farm and factory is clearly shown in the two tables below

Farm i Name of farm (tons of milk)Supply

Farm 4 Da Lat cow farm - the third farm 2180

Table 1: The estimated monthly supply capacity of each farm

Factory j Name of factory Demand

(tons of milk) Factory 1 Vietnam powder milk factory 2850

Factory 4 Truong Tho milk factory 2520 Factory 5 Thong Nhat milk factory 2480 Table 2: The estimated monthly total demand of each factory

In terms of the demand of each factory, the above table only shows the total demand which consists of the demand for imported milk and raw milk collected from the local farms

We assume that the demand for raw milk supplied by the domestic farms account for 54% of the total demand

Regarding the fuel traveling costs, each mode of transportation can carry 16,200 liters

of milk (or 16.62 tons of milk) at full capacity, and a 100-kilometer trip will require roughly 16-17 liters of oil (each kilometer consumes 0.165 liters of oil) A liter of oil costs 27,180 VND Also, the following table shows the traveling distances from each farm to each factory:

Distances (km) Vietnam powdermilk factory milk factoryVietnam milk factorySaigon Truong Thomilk factory Thong Nhatmilk factory

Da Lat cow farm

Table 3 The distances between each farm and each factory From the mentioned information, we can compute the fuel traveling costs involved in one trip from each farm to each factory as shown in the following table:

Cij (VND)

Factory 1 Factory 2 Factory 3 Factory 4 Factory 5

Supply (tons of milk) Vietnam

powder milk factory

Vietnam milk factory

Saigon milk factory

Truong Tho milk factory

Thong Nhat milk factory

Farm 1 Tay Ninh cow farm 385235.73 359224.47 331867.8 413937.81 417525.57 2370

Farm 3 Da Lat organic

farm 1210869 1296078.3 1255716 1255716 1264685.4 2040

Farm 4 Da Lat cow farm -the 3rd farm 923848.2 1009057.5 968695.2 973179.9 964210.5 2180

Table 4 The costs involved in one trip from each farm to each factory and

the corresponding monthly demand and supply

Furthermore, we consider the period of 20 days in a month for the Vinamlik to deliver milk, since the information related to truck capacity, supply and demand indicates the period

of only 20-25 days a month is sufficient to supply the demanded milk quantity

The proposed challenge seeks to determine the number of trucks required to minimize the operating costs generated by fuel traveling costs such that the factories’ demands are satisfied without exceeding farms’ supply capacity To solve the problem, we use the CPLEX Optimization Studio tool which is a comprehensive set of tools for modeling and solving optimization problems It includes an integrated development environment, a mathematical optimization engine for planning problems, and a constraint programming tool for scheduling problem solutions

3 Project Scope

Beginning from Re-order Point (ROP) to Enterprise Resources Planning (ERP) and Supply Chain Management (SCM), Operation Research (OR) has experienced far in the wording of scope and techniques which are being utilized It addresses a wide variety of problems in transportation, inventory planning, network design and operation, financial assets, risk management, and many other ones that aim to improve business productivity

Furthermore, OR is embedded in a scientific method, which can solve problems through mathematical models, so its scope is broad There are many fields in which OR can

be applied, such as:

• Production / Manufacturing Management

• Finance Budgeting / Investments

• Purchasing / Procurement / Logistics / Supply Chain Management

• Marketing & Revenue Management

• Telecommunication Networks • Healthcare Management

• Energy / Environment/ Agriculture

• National Plans / Budgets

In this project, we apply OR method to find the optimal solution for Vinamilk company’s problem, which is specifically to find the number of milk delivering trucks to minimize total transportation costs Also, this problem only concerns the milk delivery phenomenon in the southern region of Vietnam Furthermore, we only choose to consider the fuel transporting costs as costs involved in shipping milk

4 Limitation

Whereas the approach below is deemed successful by all members, it also has certain restrictions

Firstly, the primary data in this situation is the supply and demand of milk farms and milk production factories, respectively, which poses difficulties for us to collect since there is

no publication of precise and exact data Therefore, there are a lot of estimates based on the publicized total demand of factories This may lead to a lack of optimality in our solution

Secondly, the data collection of the milk collection centers (the intermediaries between farms and factories) experiences difficulties To be specific, we cannot find the exact information of the coordinates and locations of such collection centers to calculate the distances and travelling fuel costs between each farm/ factory and each milk collection center Therefore, we limit the problem to optimization of direct delivery from farm to factory But this may lead to another problem that the model cannot be applicable in real life However, the formulated model and problem solving can be a base for developing the model involving one more step through the milk collection center

Finally, the problem considered in this case is just a small-scope one, with constraints and parameters only concerning the supply and demand of farms and factories, while other possible constraints such as time windows and the number of tanks of milk types in a truck have not been put into consideration Therefore, our solution might not be appropriate if being applied to larger problems As extended problems in real life require more specific data, more applied methods, and more expert knowledge, any companies or enterprises facing similar situations are recommended to revise the model, develop and enlarge the scope to receive better solutions, and enhance the operating performance

II MATHEMATICAL MODEL

1 Parameters

i,j – the indices of farm and factory, respectively (i = 1,2,3,4; j =1,2,3,4,5)

Parameter Name Parameter expression Interpretation

farm i and factory j

2 Decision Variables

from farm i to factory j

3 Objective Function

With assumption that the truck always carries milk at its full capacity for a 20-day delivery period in a month, the objective is to find the number of milk delivering trucks to minimize the total fuel travelling cost

MinZ=20x4�=1�=15 ���Cij

4 Constraints

Assumption:the truck always carries milk at its full capacity (=16.62 tons) for a 20-day delivery period in a month Also, the demand for milk collected from the local farms account for 54% of the total demand of factories

1 20 × 16.62 ×

�=1

5

�1�

2 20 × 16.62 ×

�=1

5

�2�

3 20 × 16.62 ×

�=1

5

�3�

4 20 × 16.62 ×

�=1

5

�4�

5 2850 ∗ 54% ≤ 20 × 16.62 ×

�=1

4

��1

 ≤ 2850 Demand constraint of factory 1

6 3060 ∗ 54% ≤ 20 × 16.62 ×

�=1

4

��2

 ≤ 3060 Demand constraint of factory 2

7 2530 ∗ 54% ≤ 20 × 16.62 ×

�=1

4

��3

 ≤ 2530 Demand constraint of factory 3

8 2520 ∗ 54% ≤ 20 × 16.62 ×

�=1

4

��4

 ≤ 2520 Demand constraint of factory 4

9 2480 ∗ 54% ≤ 20 × 16.62 ×

�=1

4

��5≤ 2480

III RESULT ANALYSIS AND DISCUSSION

The objective is to minimize transportation costs while still meeting factory demand and farm supply for milk To do so, the number of vehicles going between factories is one of the variables that must be optimized The following is the outcome of running CPLEX with the given data:

x[i][j] is the variable showing the optimal number of trucks travelling from farm i to factory j for the minimized total shipping costs while still meeting the demand and supply constraints For example, x[1][2] is the number of trucks delivering milk from farm 1 to factory 2, which totals 5 trucks; x[1][5] is the number of trucks delivering milk from farm 1

to factory 5, which totals 0 Therefore, from the report result from the CPLEX, we can develop the table showing the values of each x[i][j] as below

Xij (trucks)

Factory 1 Factory 2 Factory 3 Factory 4 Factory 5

Supply (tons of milk)

Vietnam powder milk factory

Vietnam milk factory

Saigon milk factory

Truong Tho milk factory

Thong Nhat milk factory

Farm

Farm

3 Da Lat organic farm 0 0 1 5 0 2040 Farm

Table 5 The number of trucks is optimally divided

As mentioned in Part II, the following function calculates the company's minimum cost:

MinZ=20x4�=1�=15 ���Cij= 461,879,253 (VND per month)

Because it is dependent on the amount of milk required monthly, the data must be updated on

a frequent basis to produce the greatest outcomes

IV CONCLUSION

In conclusion, after collecting data, formulating the model, and coding, the optimal solutions are obtained as shown above Despite the mentioned limitations in problem-solving,

we believe that although the model formulation is not good and large-scale enough for enterprises or individuals to apply in the real-life milk delivering problem, this can serve as a foundation for the development of algorithms and heuristics to solve larger-scale problems

In addition, the study gives a greater understanding of the ideas and aims of Operations Research, which uses advanced mathematical approaches to help businesses, transportation, and product decision-makers make better judgments

1 Hillier, Frederick S Introduction to operations research / Frederick S Hillier, Gerald J Lieberman - 9th ed

2 Hyundai MPC (n.d) 02 loại xe bồn chở sữa tươi 16 khối của Huyndai giá tốt nhất [brochure], Hyundai MPC, https://hyundai-mpc.vn/

3 (2021) Báo cáo thường niên 2021, vinamilk.com.vn, accessed 5 May

2022, <https://static2.vietstock.vn/data/HOSE/2021/BCTN/VN/VNM_Baocaothuong nien_2021.pdf?fbclid=IwAR3RWoxvl7BaN8xbJqIUiA1L3mGV3Mzm4ogS0QcTUY XzHwSnrPTeaChzzfA>

4 PVOIL (11 May 2022) 'Bảng giá xăng dầu', accessed 15 May

2022, <https://www.pvoil.com.vn/truyen-thong/tin-gia-xang-dau>

VI APPENDIX

1 CPLEX code.

1.1 Data file

1.2 Model file

2 Input data (Excel/Table) used to run models.

Cij (VND)

Factory 1 Factory 2 Factory 3 Factory 4 Factory 5

Supply (tons of milk)

Vietnam powder milk factory

Vietnam milk factory

Saigon milk factory

Truong Tho milk factory

Thong Nhat milk factory

Farm 1 Tay Ninh cow farm 385235.73 359224.47 331867.8 413937.81 417525.57 2370

Farm 2 Da Lat cow farm 1210869 1296078.3 1255716 1264685.4 1255716 2190

Farm 3 Da Lat organicfarm 1210869 1296078.3 1255716 1255716 1264685.4 2040

Farm 4 Da Lat cow farm

-the 3rd farm 923848.2 1009057.5 968695.2 973179.9 964210.5 2180

Demand (tons of milk) 2850 3060 2530 2520 2480

3 Output data obtained from CPLEX.

3.1 Text file

3.2 Excel file

Xij (trucks)

Factory 1 Factory 2 Factory 3 Factory 4 Factory 5

Supply (tons of milk) Vietnam

powder milk factory

Vietnam milk factory

Saigon milk factory

Truong Tho milk factory

Thong Nhat milk factory

Farm 4 Da Lat cow farm

VII FEEDBACK FROM MS THẢO

Firstly, the direct milk transportation from the farm to the factory may encounter problems such as high costs and interlaced transport network Therefore, one suggestion to solve such problems is to consider adding milk collection centers to the model, which serve

as an intermediary between suppliers (farms) and manufacturers (factories) However, during the information searching process, our team has not found the exact data related to the coordinates and locations of the milk collection centers to formulate model; therefore, our team chose to develop the model that optimizes the direct transportation from farms to factories only However, in the future study or in the real-life logistics, this problem should

be considered more in detail, to increase the applicability of the formulated model Secondly, the model seems simple with few types of constraints, which reduces the applicability of the model in real-life problems Hence, more constraints such as the time windows, the delivery route, the number of tanks of milk types that a truck can carry, and more consideration such as adding milk collection centers should be analyzed more to solve the larger-scale problems Also, CPLEX is insufficient and inappropriate to solve the large-scale problems in real life, so some other algorithms and heuristics (metaheuristics and hybrid heuristics, for example) should be developed and used for real-life problem solving