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日期：2025-03-12 10:18

Coursework: Optimizing Inventory Management with 1D Bin

Packing

1 Overview

This coursework focuses on the application of the 1D bin packing problem to inventory management in

a retail or manufacturing setting. Students will be tasked with developing an algorithm to efficiently

allocate items of various sizes into fixed-size bins (representing storage units or shipping containers) to

minimize space wastage and optimize inventory storage or distribution costs. This real-world applica tion helps in understanding how computational algorithms can solve operational challenges in inventory

management.

This coursework carries 45% of the module marks. The rest of the module marks come from the final

written exam and lab quizs.

2 Background

In inventory management, space optimization is crucial for reducing storage and transportation costs.

The 1D bin packing problem, a classic problem in artificial intelligence and management, involves packing

objects of different volumes into a finite number of bins with a certain capacity in the most space-efficient

way. Applying this concept to inventory management can significantly enhance operational efficiency and

cost-effectiveness.

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3 Bin Packing Problem (BPP)

Given a set of n items, each item j has a volume of aj

, BPP aims to pack all items in the minimum number

of identical-sized bins without violating the capacity of bins (V ). The problem can be mathematically

formulated as follows:

This mathematical formulation is generally NOT solvable by existing integer programming solvers like

CPlex, Gurobi, and LPSolve, especially when the number of items n is large. To consistently solve the

problem with good quality solutions, metaheuristics and hyper-heuristics are used, which is the task of

this coursework.

4 Objectives

• To understand the principles and applications of the 1D bin packing problem in inventory manage ment.

• To develop and implement an algorithm that optimizes the packing of items into bins.

• To evaluate the algorithm’s efficiency and effectiveness in reducing unused space and potential cost

savings.

5 Materials

Students will be provided materials that include:

• A list of items to be stored or shipped, each with its volume.

• The volume capacity of the bins (assumed to be uniform for simplicity)

• An example python code can output the solution file.

JSON File: https://moodle.nottingham.ac.uk/pluginfile.php/11653384/mod_folder/

content/0/CW_ins.json?forcedownload=1

Example Code: https://moodle.nottingham.ac.uk/pluginfile.php/11653384/mod_folder/

content/0/CW_exp.py?forcedownload=1

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6 Tasks

• Literature Review:

Study the 1D bin packing problem and existing algorithms used to solve it, such as Next-Fit First-Fit,

Analysis and Reporting:

Analyze the algorithm’s performance, comparing it with other strategies studied during the literature

review. Prepare a detailed report documenting the project’s methodology, implementation, results,

and conclusions.

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Best-Fit, and other advanced methods.

• Algorithm Selection and Development:

Choose an appropriate algorithm or develop a new strategy for solving the 1D bin packing problem

in the context of inventory management. Implement the algorithm using a programming language

of choice (e.g., Python, Java).

• Simulation and Optimization:

Run simulations using the provided dataset to allocate items into bins based on the developed

algorithm. Optimize the algorithm to improve the space utilization ratio.

•

Deliverables

• A no more 3 pages report includes a declaration of AI usage, introduction, description of the

chosen algorithm, implementation details, results, analysis (compare with other algorithms), and

conclusions (a PDF file).

• Source code for the implemented algorithm (a Python/C/Cpp/Java file program, program should

take no more than 5 mins on the CS Linux to produce output). Hint: Using delta evaluation or

other methods to save evaulation time, and adapt your approach based on dataset size.

• Solutions for the provided problem sets (a JSON file output by example code).

Note:

• Submit your lab report via the dedicated Moodle coursework link (https://moodle.nottingham.

ac.uk/mod/assign/view.php?id=8081091).

• Essay only accepts .pdf format.

• Code only accepts .py/.c/.cpp/.java format.

• Solution only accepts .json format.

• Please name your submission file as ID FirstName LastName.xxx (e.g., 1234567 Xinan Chen.pdf).

• Late submission is subject to normal late submission penalties. Three extra hours are provided on

the moodle submission portal in case of internet connection issues. The extra hours should not be

relied on for submission. Submitting your essay a few hours before the deadline would always be

good practice.

• You can ask your classmates for help, but you cannot completely copy their code, solutions, or

essays.

• The CS Linux is used to test your program. If your runtime exceeds 5 minutes, it may result in

penalties, or you may even receive a 0 for the results part.

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• Your solution should match your program. If your program does not match your solution, you may

receive a 0 mark in the results part.

8 Mark Criteria

1. The quality of the experimental results (30%). Your algorithm shall be tested for a file containing

10 instances. The performance of your algorithm is evaluated by computing the absolute gap with

the best-known results using. If your result is better than the best-known result, you will receive a

3-mark bonus perinstance, but the total marks for this coursework cannot exceed 100:

abs gap = your bin used − best known bin used (1)

Criteria

abs gap < 0

abs gap = 0

0 < abs gap <= 1

1 < abs gap <= 2

2 < abs gap <= 3

abs gap > 4 or errors

Mark

3marks + 3 marks bonus per instance

3marks per instance

2marks per instance

3marks per instance

0.5 marks per instance

0marks

Best-known results for all instances:

• Instance: instance 1 Best known of bins used: 52

• Instance: instance 2 Best known of bins used: 59

• Instance: instance 3 Best known of bins used: 24

• Instance: instance 4 Best known of bins used: 27

• Instance: instance 5 Best known of bins used: 47

• Instance: instance 6 Best known of bins used: 49

• Instance: instance 7 Best known of bins used: 36

• Instance: instance 8 Best known of bins used: 52

• Instance: instance large 9 Best known of bins used: 417

• Instance: instance large 10 Best known of bins used: 375

• Total: 1138

Note: Use the solution marker to check the mark and feasibility for your solution.

https://moodle.nottingham.ac.uk/pluginfile.php/11653384/mod_folder/content/0/

CW_marker.py?forcedownload=1

2. The quality of codes (30%) The code quality evaluation will be based on the following criteria, each

contributing to the total mark of 30. The objective is to assess not only the functionality of the

code but also its efficiency, readability, and adherence to good programming practices.

(a) Readability (10 Marks)

• Clarity: Code is easy to read and understand (5 Marks).

• Comments: Adequate comments are provided to explain the logic and functionality (5

Marks).

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(b) Structure and Organization (10 Marks)

• Modularity: Code is well-structured and divided into functions or modules where appro-

priate (6 Marks).

• Consistency: Consistent naming conventions and code layout (4 Marks).

(c) Efficiency and Performance (10 Marks)

• Algorithm Efficiency: The chosen algorithm or approach efficiently solves the problem (6

Marks).

• Resource Management: Efficient use of computational resources, minimizing unnecessary

computations (4 Marks).

3. Report (40%) The report submitted for evaluation will be assessed based on the following criteria,

totaling 40 marks:

(a) Introduction and Background (7 Marks)

• Clarity of Problem Statement (4 Marks): Clear presentation of the problem being ad dressed.

• Context and Relevance (3 Marks): Explanation of the importance and applications of the

problem.

(b) Methodology (10 Marks)

• Approach and Justification (5 Marks): Detailed description of the approach taken to solve

the problem, including justification for the chosen methods.

• Implementation Details (5 Marks): Comprehensive explanation of how the solution was

implemented, including any algorithms, models, or frameworks used.

(c) Results and Analysis (16 Marks)

• Presentation of Results (6 Marks): Clear and accurate presentation of the findings, sup ported by appropriate figures, tables, or graphs.

• Critical Analysis (10 Marks): In-depth analysis of the results, including comparing their

performance with other methods and the pros and cons of each method.

(d) Conclusion and Recommendations (7 Marks)

• Summary of Key Findings (4 Marks): Concise summary of the main outcomes of the

project.

• Future Work and Recommendations (3 Marks): Insightful suggestions for future research

or improvements to the project based on the findings.

9 AI Usage

This coursework permits using AI to assist in programming or essay writing. However, you must declare

the use of AI at the beginning of your essay (e.g., used AI for programming). Failure to do so may

result in a loss of marks for any part where AI assistance is detected.

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10 Repetition Check

If a repetition rate higher than 20% is found (or 5% from a single source), your submission will be

checked by lecturers. You may lose a certain number of marks for improper citations, plagiarism, etc.

Severe cases will be reported to the exam officer for further action.

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