辅导CI423、讲解Mathematical Programming、辅导Matlab编程、Matlab程序设计辅导

CI423 – Mathematical Programming Assessment

You should submit your answer through blackboard – please refer to the instructions at the end of this document.

Problem Description

EDP Construction, a small contractor that provides a portfolio of services

to the construction sector, is preparing a bid for the provision of logistics

support services for a major residential development in the centre of

London. EDP has a fleet of three trucks, each with a different capacity and

operating cost (Table 1). Only one vehicle will be used in the project, but

it is expected to make several deliveries. To simplify operations, EDP has

identified a supplier that can provide the required materials in bagged

form, therefore allowing a combination of different products to be delivered to the site with each delivery.

To secure a planning permission for the development, the lead contractor has agreed to implement a strict operational

efficiency plan, imposed by the local borough. As such, EDP has to make the best possible use of available truck capacity

and will be charged with an efficiency penalty of ￡0.10 per kg of unused truck capacity for each delivery.

As a recently hired Graduate Engineer with brilliant optimisation skills, you have

been asked to develop a mathematical model (based on the knapsack problem)

that will help determine various aspects of the bid proposal. In the first instance,

the model will be used to obtain the optimal loading plan for deliveries to the

site. The weight of bag units of each type are provided in the table nearby.

Each delivery is required to satisfy a strict product weight ratio imposed by the lead contractor, to ensure the uniform

consumption of resources during construction and reduce wastage. The dictated weight ratio should be 1:3:3 for

cement, sand and aggregate respectively, or in other words 300kg of sand and 300kg of aggregate to be delivered for

every 100kg of cement. The objective of the loading plan should be to minimize any potential efficiency penalty that

may be charged for each delivery.

Task 1 – Write the mathematical formulation for the model. In your report discuss the purpose of every variable and

constraint in the formulation.

[20 marks]

Task 2 – Solve the model using the Matlab code provided in class to solve the above model using a genetic algorithm.

[50 marks]

Task 3 – For each vehicle type, identify an optimal loading plan and estimate the resulting efficiency penalties.

[10 marks]

Task 4 – Implement an alternative algorithm termination logic, which would end the search once if the fitness value has

not been improved for more than 1000 generations.

[30 marks]

Submission Instructions

You can submit your answers through the CPLEX Lab Assessment area on Blackboard, by clicking the Submission Area

link. You are expected to upload the following files:

A word document with your answers/discussion, entitled YOURCID-YOURSURNAME-Report.docx.

A matlab file with your code for Tasks 2 and 4, entitled YOURCID-YOURSURNAME-Code.m

Truck

Type

Truck

Capacity

Delivery

Cost

Small Truck 5940 kg ￡250

Medium Truck 7240 kg ￡300

Large Truck 11100 kg ￡350

Table 1 – Vehicle Characteristics

Product Type Unit Weight

Cement Bag 160 kg

Packed Sand 240 kg

Packed Aggregate 320 kg

Table 2 – Product Characteristics

Marking Scheme

For Task 1, full marks will be awarded for a correct and valid mathematical formulation, with full discussion of the

purpose of every variable, parameter and constraint.

For Tasks 2 and 4, full marks will be awarded for properly commented code files that run without errors.

For Task 4, full marks will be awarded for well-supported discussions that correctly cite appropriate sources.

In addition to the specific marks allocated to each question, 10 marks have been reserved to reward good standards

of presentation, and a further 10 to reward proper grammar and syntax.

Plagiarism Warning

In addition to the standard TurnItIn check, all submitted code files will be scanned using a specialised Matlab

plagiarism checker.

GOOD LUCK