A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

This paper develops a new way to help solve difficult linear and nonlinear discrete-optimization decision models more efficiently by introducing a problem-difficulty metric that uses the concept of entropy from information theory. Our entropy metric is employed to devise rules for problem partitioning within an implicit enumeration method, where branching is accomplished based on the subproblem complexity. The only requirement for applying our metric is the availability of (upper) bounds on branching subproblems, which are often computed within most implicit enumeration methods such as branch-and-bound (or cutting-plane-based) methods. Focusing on problems with a relatively small number of constraints, but with a large number of variables, we develop a hybrid partitioning and enumeration solution scheme by combining the entropic approach with the recently developed improved surrogate constraint (ISC) method to produce the new method we call ISCENT. Our computational results indicate that ISCENT can be an order of magnitude more efficient than commercial solvers, such as CPLEX, for convex instances with no more than eight constraints. Furthermore, for nonconvex instances, ISCENT is shown to be significantly more efficient than other standard global solvers