Discrete Optimisation

Topic: Discrete Optimization

The well-known capacitated vehicle routing problem (CVRP) and its numerous variations have been widely studied by the OR community for decades. The variants, including but not limited to the incorporations of time windows, multiple depots, a mix of pickups and deliveries, and different or multiple objective functions, also take a substantial part in the “Rich Vehicle Routing Problem” family.

Recently, the branch-price-cut (or branch-cut-price) method has been proposed to efficiently solve several variations of CVRPs. Your task is to conduct a literature review of the branch-price-cut method proposed in the existing literature for solving CVRPs. Limit your scope to only two CVRP variants of your choice. In your report, you are to:
1. For each selected problem, identify and describe the model formulation (master and pricing), the pricing algorithm, and other key components (such as cuts, cut generation, and branching) of the branch-price-cut method. (35%)
2. Between the two branch-price-cut methods, analyze and discuss the similarities and differences of the models, algorithms, and the components of the methods. (15%)
3. For each selected problem, show your understandings of the solution method by providing sufficient numerical examples to illustrate how the method and algorithm are applied in each step/component as described in (1). (50%)

The aim of the report is primarily to achieve the following objectives:
• producing an independent, systematic, and clear treatment of a given topic
• Independently analyze specific issues
• conducting a ​literature search on a chosen topic
• Independently acquire and use study of relevant literature, including the ability to evaluate and summarize central elements found in a larger context.