Question

Step 1: Identify and Solve a Typical Problem
There are a number of typical models in the Operations Research field which can be applied to a wide range of supply chain problems. Select one of the following typical models:
• Travelling Salesperson Problem (TSP)
• Multiple Traveling Salesman Problem (mTSP)
• Knapsack Problem
• Vehicle Routing Problems (VRP)
• Job Shop Scheduling
• Parallel Machine Scheduling
• Christmas lunch problem
• Newsvendor problem
• Pickup and delivery
• Travelling thief problem
• Eight queens problem
• Minimum Spanning Tree
• Hamiltonian path problem

1.1. Background:
• Provide a detailed explanation of the selected problem.

1.2. Model
• Provide typical mathematical model of the selected problem and clearly explain different aspects of the model (e.g. decision variable, objective function, constraints, etc.)

1.3. Solving an Example
• Develop a mathematical model for a workable and reasonable size of the problem.
– For many typical problems, when size of the problem increases, it becomes NP-Hard. In other words, your computer will not be able to solve it mathematically. Therefore, ‘workable and reasonable size’ here means that size of the selected problem should not be too small or too large.
• Solve the problem in Excel and transfer your solution to Word. It is required that details and steps of getting the solution are provided in the Word document.
• Interpret the findings and discuss.

Step 2: LR on Application of Selected Typical Model in Design and Analysis of Supply Chain
• Identify at least 5 peer reviewed articles in which your selected typical problem has been employed to address knowledge gaps in supply chain field.
– At least one of the selected articles should be published after 2010. • Write a comprehensive literature review on the application of “your selected” typical model in design and analysis of supply chain and address the following (but not limited to) points:
- What type of problems in supply chain can be addressed by the selected typical problem?
– Compare similarities and differences of selected articles.
– Discuss the suitability of using the selected typical model in design/analysis of various supply chains. – What are the limitations of your selected typical problem? – Undertaking any additional critical and/or content analysis on the application of selected typical problem in design and analysis of supply chain is highly recommended.

Step 3: Summary of Findings

• A summary of findings regarding the strengths and weaknesses of the selected typical problem in design and analysis of supply chain should be summarised in this section.

Answer 1

Travelling Salesman Problem:

This problem consists of a salesman and a set of cities.The salesman has to visit each one of the cities starting from one city to the another. for example if the salesman start from hometown he/she has to return back to the same city.

EXAMPLE (done in excel):

cities/distance	1	2	3	4	5
1	0	10	8	9	7
2	10	0	10	5	6
3	8	10	0	8	9
4	9	5	8	0	6
5	7	6	9	6	0
optimized route	3	4	2	5	1
respective distance	8	5	6	7	7
	optimized distance travelled by salesman	33

We have 5 cities and the distance is given above :

The minimum distance is covered staring from 3 -- 4 -- 2 -- 5 -- 1.

The total distance is 33.

Procedure we start from a random sequence say 1 to 5 and then use the solver in excel to find the minimum distance. Hence the result.