The Periodical Vehicle Routing Problem: Research Overview and Practical Application to a South German Fast Food Restaurant

Table of Contents

1. Introduction

2. The Vehicle Routing Problem (VRP)

2.1 The basic developments of the Vehicle Routing Problem

2.1.1 The Bin Packing Problem (BPP)

2.1.2 The Traveling Salesman Problem (TSP)

2.2 The Vehicle Routing Problem (VRP)

2.2.1 The mathematical formulation of the Vehicle Routing Problem

2.2.2 Different kinds of the Vehicle Routing Problem

3. The periodic(al) vehicle routing problem (PVRP)

3.1 The classical PVRP

3.2 Pioneer Work for the PVRP

3.2.1 The concept of Beltrami and Bodin

3.2.2 The concept of Russel and Igo

3.3 Additional work in the 1980s and 1990s

3.3.1 The concept of Christofides and Beasley

3.3.2 The concept of Russel and Gribbin

3.3.3 The concept of Chao, Golden, and Wasil

3.3.4 The concept of Cordeau, Gendreau, and Laporte

3.4 Applied research of today

3.4.1 The concept of Shih and Chang

3.4.2 The concept of Angelelli and Speranza

3.4.3 The concept of Blakeley and Knolmajer

3.4.4 The concept of Alegre, Laguna, and Pacheco

4. The fast food industry and its reasons of success

4.1 McDonald’s

4.1.1 The beginning of McDonald’s

4.1.2 The expansion of McDonald’s

4.2 Burger King

4.2.1 Historical facts

4.2.2 The expansion of Burger King

4.3 Subway

4.3.1 The beginning

4.3.2 The expansion and the principles of shock frosting

4.3.3 The health factor and the German challenge

5. The virtual fast-food chain and the Optimization Programming Language (OPL)

5.1 The virtual fast-food chain

5.1.1 The locations of the virtual fast-food chain

5.1.2 Distances, the resulting fuel costs, and the travel time

5.2 Inventory Costs

5.3 Trucks and driving costs

5.3.1 Trucks

5.3.2 Trucker’s loans

5.4 Opening hours

5.4.1 Different categories of the restaurants

5.4.2 Attendance

5.5 Demand of the restaurants

5.5.1 Range of products

5.5.2 Total delivery quantity

5.6 The Optimization Programming Language (OPL)

5.6.1 The development of the Optimization Programming Language

6. The creation of the mathematical model for the virtual fast-food chain

6.1 Symbols needed for the creation of the mathematical model

6.2 Objective function

6.3 Side conditions

7. Sensitivity analysis

7.1 Basic results

7.2 ILOG’s limit in memory capacity

7.3 Various examples

7.3.1 Five locations, five trucks, and 28 days - normal

7.3.2 Five locations, five trucks, and 28 days – changed demand

7.3.3 Five locations, five trucks, and 28 days – different travel time

7.3.4 Five locations, five trucks, and 28 days – low capacity and different travel time

7.3.5 Five locations, five trucks, and 28 days – changed inventory costs

7.3.6 Five locations, five trucks, and 28 days – changed frequency

7.4 Five locations, five trucks, and 28 days – comparison

8. Conclusion and a perspective of the PVRP in the future

Research Objectives and Topics

This thesis aims to develop a demand-driven scheduling approach for a virtual fast-food chain in South Germany by applying the Periodic(al) Vehicle Routing Problem (PVRP) to optimize delivery logistics and minimize operational costs.

• Review of foundational routing theories including VRP and PVRP.
• Analysis of success factors in the fast-food industry (McDonald's, Burger King, Subway).
• Mathematical modeling of a delivery system for a virtual fast-food chain.
• Implementation and testing of the model using the Optimization Programming Language (OPL/ILOG).
• Conducting a sensitivity analysis to evaluate performance under varying conditions.

Excerpt from the Book

Summary of Chapters

1 Introduction: Provides an overview of the logistics challenges in the fast-food industry and introduces the application of the PVRP as a solution.

2 The Vehicle Routing Problem (VRP): Discusses basic routing problems like the Bin Packing Problem and the Traveling Salesman Problem as foundations for the VRP.

3 The periodic(al) vehicle routing problem (PVRP): Reviews the historical development and various mathematical approaches to the PVRP from the 1970s to present-day research.

4 The fast food industry and its reasons of success: Examines the business models, history, and expansion strategies of major players like McDonald's, Burger King, and Subway.

5 The virtual fast-food chain and the Optimization Programming Language (OPL): Defines the parameters of the virtual chain and introduces the modeling tool OPL.

6 The creation of the mathematical model for the virtual fast-food chain: Details the variables, objective functions, and constraints established for the mathematical delivery model.

7 Sensitivity analysis: Presents test scenarios and the computational performance of the model using different variables and constraints in ILOG.

8 Conclusion and a perspective of the PVRP in the future: Summarizes findings and discusses the future potential of applying PVRP techniques to practical logistics.

Keywords

Periodic(al) Vehicle Routing Problem, PVRP, VRP, Logistics, Fast-Food Industry, Supply Chain Management, Optimization, OPL, ILOG, Bin Packing Problem, Traveling Salesman Problem, Sensitivity Analysis, Route Planning, Delivery Scheduling

Frequently Asked Questions

What is the core focus of this thesis?

The thesis focuses on solving delivery routing problems for a virtual fast-food chain in South Germany using the Periodic(al) Vehicle Routing Problem (PVRP).

Which key industry sectors are analyzed?

The research analyzes the system gastronomy sector, specifically focusing on the business models and logistics requirements of McDonald’s, Burger King, and Subway.

What is the primary research goal?

The primary goal is to minimize transportation costs and logistics inefficiencies by constructing a demand-driven mathematical scheduling model.

What scientific methods are utilized?

The paper utilizes operations research methods, specifically mathematical programming, and implements models using the Optimization Programming Language (OPL) and the ILOG software environment.

What does the main body of the work cover?

It covers the theoretical foundations of VRP/PVRP, the business background of the fast-food industry, the creation of a mathematical logistics model, and a sensitivity analysis of different delivery scenarios.

Which keywords best characterize this work?

Key terms include PVRP, Vehicle Routing, fast-food logistics, mathematical modeling, OPL, and optimization.

Why did the author choose the PVRP over the standard VRP?

Because the logistics requirements of the virtual fast-food chain extend beyond a single day, necessitating a time-horizon generalization that only the PVRP provides.

How does the author handle memory capacity constraints in the software?

The author demonstrates the software's limitations and performs a sensitivity analysis by reducing the number of variables, locations, and trucks to find feasible sub-optimal solutions.