Assignment Instructions

All assignments must be submitted ONLINE via my.wbs by 12pm (midday) UK time on the date displayed against this assessment.

Please ensure that you have inserted a completedassignment coversheet, which must be included as the first page of your script. This should include your Student ID number, but not your name.

Word Limit

1500 word limit.

Word Count Policy

WBS has a school-wide policy on word counts.  This is strictly enforced to ensure consistency across modules and programme. You can find more information about this policy in your Student

Handbook under Academic Practice -7i. Word count policy.

This is a strict limit not a guideline: any piece submitted with more words than the limit will result in the excess not being marked.

Academic Practice

Please ensure you read the full guidelines forAcademic Practicein the Undergraduate Handbook and ensure you understand it. If in doubt, please seek clarification in advance of your submission. This includes important information on:

•    Cheating, plagiarism and collusion

•    Correct referencing

•    Using internet sources in assessments

•    Academic writing

•    English Language support

•    Word count policy

When you submit this assignment online, you will be required to tick a declaration box indicating that the work involved is entirely your own. Each assignment will be put through plagiarism software to identify any collusion or inadequate referencing of materials used from different sources.  Please do not submit images of your typed work unless you have been specifically requested to do so.

We would consider taking action if your work:

1. is too reliant on the words of particular authors (rather than presenting your ideas in your own   words), if the essay uses the ideas or words of an author without referencing them or putting their words into quotations (plagiarism).

2. suggests that you have worked very closely with another student or students (unless explicitly asked to do so by your Module Leader/Tutor) (collusion).

3. includes unreferenced work that you have previously submitted for any accredited course of study (unless explicitly asked to do so by your Module Leader/Tutor) (self-plagiarism).

The Use of Artificial Intelligence (AI)

The University recognises an increasing number of technologies such as Artificial Intelligence and that they maybe applicable in your completing this assessment. The assessment brief sets out

specific requirements or restrictions, and your student handbook has further guidance and advice.

You are reminded that the inappropriate use of such a technology may constitute a breach of

University policy, such as the Proofreading Policy or Regulation 11 (Academic Integrity). If you

breach these policies, it may have significant consequences for your studies. Please make sure you read and understand the assessment brief and how AI mayor may not be used.

If a generative AI or similar is permitted and has been used you MUST make clear why you used such a tool or service, what you used it for and you will be obliged to confirm that you take

sole intellectual ownership of any submitted work. As appendices, and as part of your submitted

work, you must provide screenshots of the question and the AI-generated response, alongside an explanation of how the content has been utilised. You should note the relevant reference alongside each screenshot.

When you submit you must complete (physically or electronically) a declaration. This requires you to explain the use of any AI. Failure to disclose at the point of submission maybe prejudicial in any later investigations should they arise.

For this assessment the use of AI is:

-      Prohibited

You MUST NOT use any generative Artificial Intelligence in this assessment unless specifically authorised for reasonable adjustments. You MAY use non-generative tools such as a spell-check, basic grammar check (non-generative), calculator or similar. If you have any doubts about a tool or service you plan to use please contact the module leader.

Extensions and Self-certification

Late submissions will incura penalty of 5% for every 24 hour period after the due date and time,i.e. this begins one minute after the submission deadline (beginning at 12.01pm).

Requests for specific extensions (of up to 15 days) which are typically for longer and more serious   concerns must be submitted via my.wbs ideally 72 hours BEFORE the deadline. Extensions can only be approved if you clearly detail your circumstances and provide supporting documentation (or a reason as to why you cannot provide the supporting documentation at the time) asset out in the Mitigating Circumstances Policy.

Self-certification is a university-wide policy whereby you are permitted an automatic extension of 5 working days on eligible written assessed work without the need for evidence. WBS permits self-

certification for all types of written, assessed works such as essays and dissertations. It is not permitted for exams, course tests, or presentations.

You can self-certify twice within each year of study, starting from the anniversary of your course

start date. This will coverall eligible written assessments that fall within the self-certification period, as long as they have not previously had an extension applied. To find out further details about the

self-certification policy please see:https://my.wbs.ac.uk/-/academic/20778/item/id/1244460/ .         If you wish to self-certify for an extension of 5 working days, please select 'Self-certification' in the    Extension Type field. If you wish to request a longer extension than 5 working days, please leave the Extension Type as 'Standard'.

Your assignment instructions begin below.

Question 1 [70%]

ABC Company provides a service to its clients. Each client has a job with a processing time of several days. Once the process starts for a client’s job, it must be carried out without any interruption. Each client’s job requires a certain number of operators in each day of its process. ABC must create a plan for the 4 available clients’ jobs for the next 5 days with minimum number of operators needed to satisfy this demand. The processing time of the client’s jobs and the number of operators each of them needs in each day is given below. For instance, client 1 has ajob that lasts for 2 days, and 2 and 3 operators are needed for days 1 and 2 of its execution.

(a)  Formulate an integer  linear  programming  model to minimise the total operators  needed. Describe decision variables, objective function, and constraints properly.

(b)  Solve the ILP formulated in part (a) using Excel Solver. What is the optimal solution and total operators needed?

(c)  Job 2 must start at least one day before job 3. For example, job 2 can start on day 1 and job 2 can start on days 2, 3, 4, or 5. Modify your model and add this condition.

(d)  Solve the  modified  ILP formulated in part (c). Explain how the optimal solution is different from part (b).

(e)  If job 1 is started on day 1 then job 4 also must be started on day  1. Modify your model to accommodate this condition.