مشروع في الأساليب الكمية - Excel and Python

السلام عليكم

1-ارجوا كتابة المشروع باللغة الانجليزية

2- كتابة تقرير محترف ووصف كيف تم المشروع

3- تسليم الملفات التالية:

Deliverables:

-Comprehension of Model

-Sensitivity Analyse

-Model Coding (Excel)

-Model Coding (Python)

العنوان: Blood Transshipment Network Optimization

الوصف:

I. Introduction

Effective blood supply chain management is essential to ensure timely availability of blood across various healthcare facilities, especially in emergency situations. Blood is a unique resource—it is perishable, has specific storage requirements, and must be available in specific types and quantities to meet patient needs. Given these constraints, the challenge is to design a transshipment network that efficiently moves blood from collection points to end users while minimizing waste and costs.

In this project, you will examine a multi-layered blood transshipment network that includes mobile blood donation centers, local and central blood banks, general hospitals, and local clinics. Each layer serves a critical function in maintaining supply continuity and addressing demand in its respective areas. From mobile donation centers collecting blood in the community to clinics and hospitals administering transfusions, the network must operate smoothly and responsively.

The task involves understanding and optimizing the flow of blood between these layers to ensure availability where it’s needed most. By focusing on routing, inventory management, and distribution scheduling, this project aims to balance demand fulfillment with cost efficiency and minimal wastage. This case highlights the complexities of healthcare logistics, specifically in emergency and critical care, where well-coordinated logistics can have life-saving implications.

II. Problem Statement

Blood supply management is crucial in ensuring timely availability at various healthcare facilities. This project focuses on a multi-layered transshipment network that includes several entities, each with a unique role and location:

A.Mobile Blood Donation Centers: These are the frontline collection points where donations are made. There are 6 mobile blood donations, with average daily donations (supply) of 30, 40, 70, 50, 35, and 60 blood bags.

B.Local Blood Banks: These banks receive blood from the mobile centers and serve as local storage facilities. They have limited capacity and serve specific areas, making efficient allocation critical. There are 4 local blood banks, with storage capacities equal to 90, 80, 55, and 50 blood bags.

C.Central Blood Banks: Acting as regional hubs, central blood banks consolidate supplies from multiple local banks and manage redistributions to where demand is high. There are 2 central blood banks, with storage capacities equal to 100, and 130 blood bags.

D.General Hospitals: These facilities have significant demand for blood, often requiring rapid access to varied blood types. They act as primary consumers in the transshipment network. There are 4 general hospitals, with storage capacities equal to 60, 60, 45, and 35 blood bags.

E.Local Clinics: Serving more remote or rural areas, local clinics have lower but still essential demand. They rely on the network to meet periodic needs without the ability to store large supplies. There are 6 local blood banks with average demands equal to 30, 35, 15, 25, 20, and 10 blood bags.

Figure 1 shows a visual representation of the blood network. Assume the cost of transferring blood consist of fixed cost, ??? = 10|? − ?| + 5|???(? ∙ ?)|, that is independent of the amount of blood bags transferred and is in US dollar, and variable cost, ??? = 0.5|? − ?| + 0.25|sin (? ∙ ?)|, that is in US dollar per blood bag transferred. For instance, transporting 123 blood bag through link (1, 7) would cost 10(6)+5cos(7 rad)+123(0.5(6)+0.25sin(7 rad)) which is equal to 452.97 US dollar. Moreover, blood bags are perishable, and some is ruined during transfer. Assume there is a deterioration factor for transfer through link (i, j) equal to ??? = (10? + ?)⁄(? ∙ ? ∙ 40). For instance, if we transfer 100 units from node 11 to node 13, we lose 100(10(11) + 13)⁄((11)(13)40) = 2.15 blood bag in transfer. The objective is to find the optimal routing and allocation of blood bags so that total cost of transfer is minimized, while all meeting all demand.

تسليمات المشروع:

▪Develop the Linear Programming (LP) model for the transshipment problem described in Section II (+15%).

▪Solve the problem using Python (don’t panic, see Section VI) and provide the complete code (+6%). The code must work to get 6%, no partial credit will be given if the code doesn’t work (use PulP solver). Instead, you can provide a clean visually appealing excel dashboard that solves the problem with the click of a button, but you will miss this great opportunity to learn Python and will be given only 5% instead of 6%.

▪Write a report that has the following outline (Mandatory; no report means getting 0% on your project):

1.Introduction (motivation and that this report is part of the requirements of EM520)

2.Problem Statement (explain what the model you provided solves)

3.Model Development (see sample in Section V)

Notations

3.1.1. Sets and Indices (Define your sets correctly!) 3.1.2. Decision Variables

3.1.3. Parameters

3.2. Mathematical Model (number each constraint, and explain each constraint) 4. Results

4.1. Solution Approach

4.1.1. Solver (description of solver used and computer used to run the solver) 4.1.2. Python Code (Excel Dashboard) (provide the code here and explain it) 4.2. Solution

4.3. Sensitivity Analysis

4.3.1. What if Central Blood Bank 12 shuts down.

4.3.2. What if General Hospitals 13, 14 and 15 shuts down.

4.3.3. What if our objective becomes minimization of perished blood instead of cost.

when a facility shuts down, its capacity is transferred evenly toward the other open facilities.

5.Final Remarks (summary + what could have been considered as well to make it more realistic?)

6.Appendices (optional)

Bonuses:

Assume ??? is the time needed to transfer any amount of blood bags from node i to node j. Ensure that any blood bag arrive at any local clinic at most within ? weeks. Provide the updated model (no need to solve it)(+1.5%). (No partial points if you get it wrong)

Hint: Use binary variables similar to the ones in fixed charge models, and use similar logic found in the project crashing case study to formulate the required constraints.

Assume we are considering the different blood types of donors, and patients with different blood types at local clinics. Assume the demand is now represented by ???, and supply by ???. Provide the updated model (no need to solve it) (+1.5%). (No partial points if you get it wrong)

Hint: use variable ???? where ? refers to the blood type transferred between i and j. Note they will be

using the same storage capacity but have distinct flow constraints, and that each patient with different blood type can be satisfied by one or more type of blood donated (lookup blood compatibility).

Python for Optimization

For professionals and academicians, using Python for optimization tasks provides significant benefits over traditional tools like Excel Solver. Python is celebrated for its robust capabilities in handling large datasets and conducting complex calculations with greater efficiency. Unlike Excel, which often falls short due to its limited capacity and rigidity in handling complex optimization scenarios, Python offers remarkable flexibility and scalability. Additionally, Python and its associated libraries, such as the PuLP solver, are open-source and freely available, presenting an economically advantageous option widely accessible to the global academic community.

Figure 2 exemplifies this with a sample code snippet for a product mix problem, illustrating Python's simplicity and straightforward syntax compared to more verbose languages like Java or C++. This example also demonstrates the efficient use of loop functions to apply constraints dynamically within the code, avoiding the tedium of manually entering each constraint. This capability significantly simplifies the development process, making it easier to manage and scale optimization models. Figure 3 shows the code output.

Furthermore, tools such as ChatGPT enhance Python's utility by generating entire code segments and providing robust debugging support. For installation, refer to the accompanying documentation in Blackboard.