In a dimensional model used for data warehousing, what type of relationship typically exists within a standard hierarchy inside a single dimension table, for example between level and sub level members?

Introduction / Context:
Dimensional modeling for data warehousing frequently uses hierarchies within dimensions, such as year to quarter to month to day in a time dimension, or region to country to state to city in a geography dimension. Understanding the relationship type inside such hierarchies is important for correct aggregation and drill down behavior. This question asks about the typical relationship between parent and child members in a standard dimension hierarchy.

Given Data / Assumptions:

• We are dealing with a single dimension hierarchy, such as a time or geography hierarchy.
• Each child member belongs to exactly one parent at a given level of the hierarchy.
• A parent can group multiple child members.
• We are not modeling complex many to many relationships in this basic hierarchy example.

Concept / Approach:
In a classic star schema hierarchy, the relationship between a parent level and its child level is usually one to many. For example, one year contains many quarters, one quarter contains many months, and one month contains many days. At each step, a parent has multiple children, but each child belongs to exactly one parent. This one to many relationship ensures that aggregate measures can roll up cleanly from the child to the parent level without ambiguity. Many to many relationships are handled differently and are not typical within a basic dimension hierarchy path.

Step-by-Step Solution:
Step 1: Think of common hierarchies: one region to many countries, one category to many products, one manager to many employees. Step 2: Observe that in these examples each child member appears under exactly one parent at the hierarchy level in question. Step 3: This pattern corresponds to a one to many relationship between parent and child. Step 4: Option b explicitly states one to many, with each parent having many children and each child having one parent, which matches the pattern. Step 5: The other options describe one to one, many to many, or no relationship, which do not reflect standard hierarchy semantics.

Verification / Alternative check:
If you design a time dimension in a data warehouse, you normally assign each day to exactly one month, one quarter, and one year. This assignment allows you to sum sales by month or year without double counting. If a day could belong to many months, aggregation would become ambiguous. This illustrates why one to many relationships are used in hierarchies and supports the choice of option b.

Why Other Options Are Wrong:
Option a, one to one, would imply each parent has exactly one child, which fails to represent realistic hierarchies where, for example, one year has multiple months. Option c, many to many, would allow a child to belong to multiple parents, complicating rollup logic. Option d contradicts the definition of a hierarchy by claiming there is no relationship. Option e suggests that only self referencing many to many relationships are allowed, which does not match dimensional modeling practice.

Common Pitfalls:
A common modeling error is to ignore hierarchy structure and treat dimension attributes as unrelated columns, which makes drill down and rollup harder. Another pitfall is to introduce many to many relationships inside dimensions without understanding their impact on aggregation. Starting from clear one to many parent child relationships keeps the model intuitive and the Business Intelligence engine easier to configure.

Final Answer:
Within a standard dimension hierarchy, the relationship between parent and child members is one to many, where each parent can have many children and each child has one parent at that level, as in option b.