There are a number of typical models in the Operations Research field which can be applied to a wide range of supply chain problems. In other words, by learning a typical model various problems in supply chain optimisation domain can be addressed. Please note that the basis of all proposed problems is the methods that you have learned in this course; however, none of them has been directly taught.

QUESTION

There are a number of typical models in the Operations Research field which can be applied to a wide range of

supply chain problems. In other words, by learning a typical model various problems in supply chain optimisation

domain can be addressed.

Please note that the basis of all proposed problems is the methods that you have learned in this course; however,

none of them has been directly taught. The reason behind the design of this assignment is that there are

hundreds of problem variations with the same structure in the real business world. Therefore, by learning the

linear programming, students should be able to formulate a solution for problems which have similar structure

to a typical problem. Students are required to research one of the proposed topics and address the assignment

requirements accordingly.

Step 1: Identify and Solve a Typical Problem

Select one of the following typical models:

• Vehicle Routing Problems (VRP)
• Machine Scheduling Problem
• Job Shop Scheduling
• Flow Shop Scheduling
• Pickup and Delivery
• Christmas Lunch Problem
• Knapsack Problem
• Newsvendor Problem
• Travelling Thief Problem
• Eight Queens Problem
• 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:

1

– 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

Application of Vehicle Routing Problems (VRP) in Supply Chain Design and Analysis

Background

Vehicle Routing Problems (VRP) are a class of combinatorial optimization problems that deal with efficiently routing vehicles to deliver goods or services to a set of customers. The objective is to minimize total costs, such as distance traveled, time, or fuel consumption, while satisfying various constraints, such as vehicle capacity and time windows. VRP finds its application in supply chain management, transportation logistics, and distribution network optimization.

Model

The typical mathematical model for VRP consists of decision variables, an objective function, and constraints. The decision variables determine which customers are assigned to which vehicles and in what sequence. The objective function aims to minimize the total cost, usually defined as the sum of distances or travel times. Constraints include vehicle capacity limits, time windows for customer visits, and precedence constraints.

Solving an Example

Consider a VRP where a company needs to deliver goods from a central depot to several customers. Each customer has a demand, and there are constraints on the vehicle’s maximum capacity and the time window for customer visits. The objective is to minimize the total distance traveled by the vehicles. By formulating this problem mathematically and solving it using optimization software or Excel Solver, an optimal routing plan can be obtained.

Interpretation and Discussion

The findings from solving the VRP example can provide insights into efficient routing plans, helping to optimize the allocation of vehicles, reduce transportation costs, and improve customer service (Cattaruzza et al., 2017). The solution obtained from the model can be used to make informed decisions about fleet size, vehicle routing, and scheduling, leading to improved supply chain performance.

Step 2: Literature Review on Application of VRP in Supply Chain Design and Analysis

The following are the key points addressed in the literature review:

The application of VRP in supply chain problems:

   – VRP can be used to optimize the distribution of goods from warehouses to retailers.

   – VRP can aid in designing efficient last-mile delivery systems (How to Solve a Vehicle Routing Problem (VRP), n.d.).

   – VRP is applicable in reverse logistics for managing product returns and recycling processes.

 Similarities and differences among selected articles:

   – Various studies employ different variations of VRP, such as VRP with time windows, capacitated VRP, or VRP with multiple depots.

   – Differences exist in the objective functions considered, such as cost minimization, carbon emissions reduction, or customer satisfaction maximization.

   – Some studies incorporate additional constraints like road congestion or vehicle types.

 Suitability of VRP in supply chain design/analysis:

   – VRP can help identify optimal vehicle routes to minimize costs, improve delivery efficiency, and reduce carbon footprint.

   – It enables better resource utilization, such as reducing the number of vehicles required for deliveries.

   – VRP supports decision-making regarding fleet management, route planning, and resource allocation.

Limitations of VRP:

   – VRP becomes computationally challenging as problem size increases, often leading to NP-Hard problem instances.

   – The assumptions made in the VRP models may not capture all real-world complexities, such as dynamic traffic conditions or uncertain customer demands.

   – VRP models typically assume deterministic travel times and customer demands, which may not hold in practice.

Additional analysis on the application of VRP in supply chain:

   – Research can focus on incorporating dynamic elements into VRP models, such as real-time traffic information or customer demand updates (Rios et al., 2021).

   – Comparative studies can evaluate the performance of different solution approaches for VRP in terms of computational efficiency and solution quality.

Step 3: Summary of Findings

The strengths of using VRP in supply chain design and analysis include its ability to optimize vehicle routing, reduce costs, and improve resource allocation

. VRP can address various supply chain problems such as distribution network design, last-mile delivery optimization, and reverse logistics. However, VRP faces limitations regarding computational complexity, assumptions made in the models, and the dynamic nature of real-world supply chain operations.

In conclusion, VRP provides valuable insights for optimizing supply chain operations by efficiently routing vehicles to customers. While it offers significant benefits, further research is needed to enhance VRP models with real-time data and to develop more robust solution approaches for large-scale and dynamic problem instances. Overall, VRP is a powerful tool that can contribute to the design and analysis of supply chains, improving efficiency and customer satisfaction.

References

Cattaruzza, D., Absi, N., Feillet, D., & Gonzalez-Feliu, J. (2017). Vehicle routing problems for city logistics. EURO Journal on Transportation and Logistics, 6(1), 51–79. https://doi.org/10.1007/s13676-014-0074-0 

How to solve a Vehicle Routing Problem (VRP). (n.d.). Timefold. https://timefold.ai/model/vehicle-routing/ 

Rios, B. H. O., Xavier, E. G., Miyazawa, F. K., Amorim, P., Curcio, E., & Santos, M. J. (2021). Recent dynamic vehicle routing problems: A survey. Computers & Industrial Engineering, 160, 107604. https://doi.org/10.1016/j.cie.2021.107604