Scheduling problems fundamentally involve allocating limited resources to tasks over time to achieve a specific goal, such as minimizing total completion time or maximizing output. This structure is defined by an objective function (the goal) and a set of constraints (the rules and limitations, like resource availability or task dependencies). Constrained optimization is the mathematical and computational framework designed explicitly to find the best solution (optimum) for an objective function subject to a given set of constraints. Therefore, it is the most appropriate modeling tool for solving scheduling problems.

A. One-armed bandit: This is a reinforcement learning model for balancing exploration and exploitation, not for solving problems with the fixed, complex constraints typical of scheduling.

C. Decision tree: This is a supervised learning model for classification or regression. It predicts an outcome based on input features but does not construct an optimal schedule.

D. Gradient descent: This is an optimization algorithm used to find the minimum of a function, primarily for training machine learning models, not for modeling combinatorial scheduling problems.

1. University Courseware: Bertsimas

D.

& Freund

R. M. (2004). 15.053 Optimization Methods in Business Analytics

Fall 2004. Massachusetts Institute of Technology: MIT OpenCourseWare. In Lecture 5

"Integer Programming Formulations

" scheduling problems (e.g.

the job shop scheduling problem) are presented as classic examples that are modeled and solved using integer programming

a specific class of constrained optimization.

2. University Courseware: Liang

P.

& Sadigh

D. (2021). CS221: Artificial Intelligence: Principles and Techniques

Autumn 2021. Stanford University. Lecture 6

"Constraint Satisfaction Problems

" introduces scheduling as a canonical example of a CSP

where variables (e.g.

start times of tasks) must be assigned values that satisfy a set of constraints. CSPs are a form of constrained optimization.

3. Academic Publication: Pinedo

M. L. (2016). Scheduling: Theory

Algorithms

and Systems (5th ed.). Springer. In Chapter 2

"Framework and Classification

" scheduling problems are formally defined in terms of their objective functions and constraints

which is the core structure of a constrained optimization model.