Topic scheduling problem schedule orders to minimize the total cost of delay in production systems group 09

INTERNATIONAL UNIVERSITY VIETNAM NATIONAL UNIVERSITY - HO CHI MINH CITY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT PROJECT REPORT Deterministic Models in Operations Research _ GO1

INTERNATIONAL UNIVERSITY VIETNAM NATIONAL UNIVERSITY - HO CHI MINH CITY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

PROJECT REPORT Deterministic Models in Operations Research _ GO1

Topic: Scheduling problem - schedule orders to minimize the total cost of delay in production systems _ Group 09

3 Lê Thị Thu Hà IELSIU21194 100%

School of Industrial Engineering and Management Year: 2022-2023

TABLE OF CONTENTS

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School of Industrial Engineering and Management Year: 2022-2023

TABLE OF CONTENTS

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in specific steps using mathematical analysis

In Vietnam, manufacturing plants that manage extensive operations that require assigning people and resources to tasks at specific times must regularly address complex scheduling issues Scheduling is a manufacturing process that involves performing many tasks on a limited set of machines, each of which can perform only one task at a time One common scheduling problem is a job shop concerns the scheduling of tasks on production lines or in warehouse halls The job-shop problem is the most general and universal of scheduling problems It assumes a complete order of tasks and operations and adopts specific guidelines and limitations resulting from technology (e.g no machine can perform more than one operation at the same time) The problem consists in determining the optimal solution that will reduce the resources involved (time, machines, employees) for performing all operations of the considered process

The goal of the job shop problem is to minimize the time interval: the time interval from the earliest job start time to the latest finish time Each job consists

of a sequence of tasks that must be executed in a specified order, and each task must be processed on a specific machine The problem is to schedule the tasks

on the machines in such a way as to minimize the length of the schedule - the time required to complete all the tasks

We apply operations research to the job shop problem to optimize the cost of operation by influencing the tardiness and lateness of each stage of the production process

School of Industrial Engineering and Management Year: 2022-2023

2 Problem Statement

There are still scheduling issues that prevent Vietnam from having an efficient method for producing wooden products In this project, our team will provide an order allocation and integer programming approach to production scheduling to solve the potential delays and lateness that affect the production process from the perspective of make-to-order manufacturing We assume that our company has a total of 28 products such as bed, table, chair, cabinet, with different data Applying some restrictions to see how tardiness and lateness would be influenced led to the cost of operation being optimized

3 Objectives

According to the information given above, we have two core objectives for this case:

Objective 1: Minimizing the cost of operation due to tardiness

Objective 2: Minimizing the tardiness of each process

Moreover, the primary goal of our report's CPLEX model is to have a benchmark for algorithms, hence, the model in our report can only resolve parts of the objectives above

4 Scope and Limitations

1.4.1 Scope:

This project focuses on applying integer linear programming and building the CPLEX model that can minimize the total tardiness of our Company In this model, a group of customer orders are first arranged to be completed, and then without any intermediary inventory, they are sent directly to the customers Finding a combined production and distribution plan that will maximize both customer satisfaction and overall distribution costs is the aim In the study, a mixed integer program was suggested as a use for long-term production schedules in make-to-order manufacturing to determine the ideal value of the maximum earliness

1.4.2 Limitations:

Although our model could make a result and reach the standard target our group expected at the beginning of the project, there still have some limitations in practical application

Firstly, due to the limited information about the database published, we can use this model, we decided to create available data based on relevant information Additionally, as we create the database, we can only force the model to run with limited data to avoid as many inconsistent errors as if we run this model with unlimited data

Secondly, the data we selected is the default information at the same time in the past, and we built the model to improve the profit of the company However, for that reason, this model can not be used immediately if we do not know how many orders and the quantity of each order Moreover, if the list of orders is continuously adjusted will make the accuration of calculating the minimization

O1Set: set of small batches

O2Set: set of large batches

T: set of planning periods

Parameters:

di: due date of order i

Pi: processing time of one unit of each order

N: the limit of processing time in one day

Ai: available date of material of each order

Ci: the cost of tardiness of each order

School of Industrial Engineering and Management Year: 2022-2023

Explanation

according to its assignment

- Constraints (5) indicates the indivisible tardy order is finished after its due date

- Constraints (6) indicates the divisible tardy order is partly assigned after its due date

maximum available time on that day

RESULT ANALYSIS AND DISCUSSION

1 Processing and Result Analysis

1.1 Output data from Cplex:

“Problems © Scripting log :' Solutions = Conflicts =Relaxations “Engine log @ Statistics “Profiler | DOcloud |) CPLEX Servers

| solution ( optimal) with objective 32165000

/ Quali sent solution:

vy MIP Objective 32,165,000 Incumbent 32,165,000 Nodes 0 Remaining nodes 1 Iterations 0

¥ Solution pool Count 1 Mean objective 32,165,000

Figure 2: The statistics of the solution 1.2 Result analysis

After running this model, the number of tardy orders is 4, belonging to order numbers

11, 22, 23, and 25 Meanwhile, the code was able to find an optimal solution with an objective value of 32165000 for a production line with 28 orders The quality of the solution was good, as evidenced by the low norm and error values This suggests that the code can find good solutions to MILP problems in the context of production line scheduling

School of Industrial Engineering and Management Year: 2022-2023

Z=[0000000100 100000000000000000];

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2.3 Case 3: Decreasing limit processing time

In this case, we decrease the limit processing time for 3 units from 16 to 13 After decreasing, we obtain the result with the optimal solution is 4 delays which is order 11,

22, 23, 25 and the objective value is 32165000

Order | Quantity | Price Price of contract Contract value (VND)

School of Industrial Engineering and Management Year: 2022-2023

Table 2: The data input when decreasing contract value by 1%

After decreasing, we obtain the result with the optimal solution is 4 delays which is order 11, 22, 23, 25 and the objective value is 31843350

Z=[(0000000000100000000001101000);

2.4.2 Decrease by 2%

In this case, we decrease 2% of the cost in contract Then we have the input data is:

School of Industrial Engineering and Management Year: 2022-2023

After reducing the time period by 3 units, the optimal value does not change, but

at least we can shorten the production time leading to the decreasing factory operation cost and use time to produce other orders

3.2 Decreasing available date:

It is clear that wnen we decrease the available date by 2 units if the available date

is more than 5 days then the optimal value reduces from 32 165 000 to 375 000 and the number of delays also reduces to 2 delays

Therefore, if the company wants to reduce the available date in order to minimize the cost due to tardiness, it is suggested that they should reduce 2 days for orders that have more than 5 available days, then the optimal value will decrease by 98,8%

3.3 Decreasing the processing time:

Same as the result of decreasing time period, after conducting a sensitivity analysis on decreasing limit processing time by 3 units, the optimal value does not change but it helps to reduce the production process that can optimize the company's operating costs and take advantage of making other orders

3.4 Decreasing cost in contract:

Obviously, The cost in contract is proportional to the optimal value, which means the decreasing cost in contract leads to a reduction in the cost due to tardiness Simply, if the cost in contract decreases by 1% (from 335 460 000 to 109 346 490) and 2% (from 335 460 000 to 108 241 980) then the optimal value will also decrease by the corresponding percentages of 31 843 350 and 31 521 700, respectively

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As the code continues to be developed, it has the potential to solve even larger and more complex problems, including the automation of the scheduling process entirely By doing so, companies can free up valuable human resources to focus

on other critical tasks, such as research and development, which can ultimately lead to further innovations and advancements in the industry

Moreover, the project has the potential to improve the accuracy and reliability of production scheduling, which can lead to increased customer satisfaction With precise scheduling and faster production times, companies can fulfill orders more quickly and efficiently, reducing the risk of delayed deliveries or backlogs, ultimately resulting in happier customers and improved business performance Overall, the sensitivity has the potential to transform the manufacturing industry, optimizing production processes and allowing companies to remain competitive

in an ever-changing market By leveraging this analysis, the company can streamline its operations and achieve greater levels of success, paving the way for a brighter and more efficient future

at peak efficiency, resulting in significant cost savings and increased productivity

V REFERENCES

[1] Wang, C.N., Wei, Y C., So, P ¥., Tinh Nguyen, V., & Nguyen Ky Phuc, P

(2022) Optimization Model in Manufacturing Scheduling for the Garment Industry Computers, Materials & Continua, 71(3), 5875-5889

https://doi.org/10.32604/cmc.2022.023880

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School of Industrial Engineering and Management Year: 2022-2023

int d[O]= ;//The due date of order i

int D[O]= ;/The demand of order i

float P[O]= ;//orocessing time of one unit of each order

int A[O]= ;//available date of material of each order

float C[O]= ;/Ahe cost of tardiness of each order

dvar boolean X[O][T];//binary variable that indicates whether order i is performed in period t

dvar float+ Y[O][T];//fraction of order i to be processed in period t

dvar boolean Z[O];//binary variable that indicates whether order i is completed after due date

minimize sum(i in O)Z[i]*C[i];

subject to {

Constraint_1:

forall (i in O1Set) {//con1; the order assignment constraints

sum (tin T: t>=Ali]) X[i][t] == 1;

}

Constraint_2:

forall (i in O2Set) {//con2; the order assignment constraints

sum (t in 1 numTimeperiod-1: t >= Ali]) X[i][t] == 1;

}

Constraint_3:

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d from SheetRead(consistentOrder,""Customer order'!D2:D29");

D from SheetRead(consistentOrder,"Customer order'!C2:C29");

P from SheetRead(consistentOrder,"Unit processing time day'!F2:F29");

A from SheetRead(consistentOrder,""Customer order'!E2:E29");

C from SheetRead(consistentOrder,"Cost of order delay'!D2:D29");

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School of Industrial Engineering and Management Year: 2022-2023

Table 5: Unit processing time (day)

Table 6: Order division

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School of Industrial Engineering and Management Year: 2022-2023

2 aying 10% of whole contract for delaying 1200000

within 15 days Paying 10% of whol tract f layi

3 aying 0% of whole contract for delaying 850000

within 15 days Paying 10% of whol tract f layi

4 aying 10% of whole contract for delaying 400000

within 15 days

Paying 10% of whole contract for delaying

18 aying 0% of whole contract for delaying 50000

Table 7: Cost of order delay

3 Output data from Cplex:

“Problems © Scripting log :' Solutions = Conflicts = Relaxations “Engine log @ Statistics “Profiler | DOcloud |) CPLEX Servers

Vs solution (optimal) with objective 32165000

// Quality Incumbent solution:

// MIL bjectiv 3.2165000000e+007

// MIL »plution norm |x| (Total, Max) 2.21000e+002 1.00000e+000

//M lution error (Ax=b) (Total, Max) 1 8178e-016

bound error (Total, Max) // MI integrality error (Total, Max) 000e+000 0.00000e+000

// MILP slack bound error (Total, Max) 1.02000e-007 2.30000e-008

// MILP indicator slack bound error (Total, Max) 0.00000e4+000 0.00000e+000