Task 1 (MILP Model + R Implementation) This Section Must Include: Problem Explanation Briefly explain the GI endoscopy capacity planning problem. Identify the goal: minimize total cost while meeting weekly diagnostic

ITAO7104 Assignment Brief 

Instructions

The report must contain two sections only: Section A (Task 1) and Section B (Task 2) in the same report file.

General Requirements

– MSc Business Analytics

• Module: Data-Driven Decision-Making (D3M – ITAO7104) Report must contain ONLY TWO SECTIONS:

○ Section A – Task 1

○ Section B – Task 2

• NO appendix allowed in the report.
• Use 12pt font for body text and 14pt bold for section headings.
• Leave the cover page for me.
• Include page numbers at bottom of pages.
• Word count must be within ±10% of the limit.
• Overall Turnitin similarity must stay below 25%.
• Follow the rubric/marking criteria carefully for scoring.
• Write clearly and professionally with logical explanations and structure.
• Use Harvard referencing style for all citations.
• Visualizations and screenshots must be clear and readable (not too big or too small).

SECTION A – Task 1 (MILP Model + R Implementation) This section must include:

1. Problem Explanation
   • Briefly explain the GI endoscopy capacity planning problem.
   • Identify the goal: minimize total cost while meeting weekly diagnostic and therapeutic demand.
2. Mathematical Model (MILP) Clearly define:

Indices

• Rooms (r) Weeks (w)

Parameters

• Diagnostic demand per week
• Therapeutic demand per week
• Clinician hours available
• Room capacities
• Setup costs Allocation costs

Decision Variables

• Whether room r is:
  • unavailable

○ diagnostic configuration ○ therapeutic configuration Constraints Include:

• Demand satisfaction for diagnostic procedures
• Demand satisfaction for therapeutic procedures
• Room capacity limits
• Clinician hour limits
• Only one configuration per room per week
• Therapeutic procedures only allowed in therapeutic rooms

Objective Function

• Minimize total cost (setup + allocation cost).

Explain why each constraint exists and which part of the problem it represents.

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3. Solve using R
   • Use R with the ompr package and a solver (GLPK / HiGHS / Symphony etc.).
   • Include screenshots of R code and solver output in the report.
   • Code must have short comments explaining key steps.

Also submit the functional R code file separately.

4. Results Explanation

Explain in plain English:

• Which rooms are used each week
• Which configuration each room has
• How diagnostic and therapeutic hours are allocated State clearly:
• Minimum total cost
• MILP optimality gap

5. Visualizations

Include charts such as:

Chart 1 ● Stacked chart showing each room’s configuration over the 26 weeks.

Chart 2

• Weekly aggregated capacity showing:
  • diagnostic hours

○ therapeutic hours

Charts must be clear and properly labeled.

Section B – Task 2 (Essay – max 1250 words)

Choose one healthcare journal article from the QUB library that uses MILP with an exact solution method.

Structure the essay using these headings:

1. Healthcare Problem
   • Explain the healthcare operational problem.
   • Why it matters in practice.
2. MILP Model Outline

Explain in simple terms:

• Decision variables
• Constraints
• Objective

Use bullet points instead of equations.

3. Exact Method Used

Explain the optimization method used in the article (for example branch-and-bound, branchand-price, etc.).

Describe how the method works in the study.

4. Method–Problem Fit

Explain why the chosen method works well for the model.

Discuss aspects like:

• scalability
• structure of the MILP
• computational efficiency

5. Limitations and Practical InsightDiscuss:

• limitations of the model
• real-world challenges
• implementation issues in healthcare

Additional requirements

• Use Harvard references.
• The main article must be bold in the bibliography.
• The article must be recent if possible (preferably after 2023).
• You may include up to 5 additional references.
• Include at least one figure from the article with caption and citation.
• Provide the journal hyperlink in the reference list.

Final Deliverables

1. Assignment Report (Word or PDF) Contains:

• Section A
• Section B

2. R Code File (.R): Must run without errors and produce the same results shown in the report.

3. All screenshots must be clear and readable.

Please ensure the work is clear, well-structured, and written professionally according to the rubric.