Common due date assignment and scheduling with a rate-modifying activity to minimize the due date,earliness, tardiness,holding, and batch delivery cost

e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the common due date, and scheduling job delivery, we consider the option of performing a rate-modifying activity on the machine. The processing time of a job scheduled after the rate-modifying activity decreases depending on a job-dependent factor. Finished jobs are delivered in batches. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find a common due date for all the jobs, a location of the rate-modifying activity, and a delivery date for each job to minimize the sum of earliness, tardiness, holding, due date, and delivery cost. We provide some properties of the optimal schedule for the problem and present polynomial algorithms for some special cases.     

Single-machine batch delivery scheduling with an assignable common due date and controllable processing times

We consider single-machine batch delivery scheduling with an assignable common due date and controllable processing times, which vary as a convex function of the amounts of a continuously divisible common resource allocated to individual jobs. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. We first provide an O(n⁵) dynamic programming algorithm to find the optimal job sequence, the partition of the job sequence into batches, the assigned common due date, and the resource allocation that minimize a cost function based on earliness, tardiness, job holding, due date assignment, batch delivery, and resource consumption. We show that a special case of the problem can be solved by a lower-order polynomial algorithm. We then study the problem of finding the optimal solution to minimize the total cost of earliness, tardiness, job holding, and due date assignment, subject to limited resource availability, and develop an O(nlog n) algorithm to solve it.     

A branch-and-bound algorithm for single-machine scheduling with batch delivery and job release times

This paper addresses scheduling a set of jobs with specified release times on a single machine for delivery in batches to customers or to other machines for further processing. This problem is a natural extension of minimizing the sum of flow times in the presence of release time by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvement over an existing dynamic programming algorithm.     

Single machine batch scheduling problem with family setup times and release dates to minimize makespan

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an time dynamic programming algorithm and an time dynamic programming algorithm for the problem, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the setup times of all the families and the processing times of all the jobs. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme (PTAS) for the problem.     

A branch-and-bound algorithm to minimize total weighted completion time on identical parallel machines with job release dates

In this paper, we consider an identical parallel machine scheduling problem with release dates. The objective is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose some dominance properties and two lower bounds. We also present an efficient heuristic. A branch-and-bound algorithm, in which the heuristic, the lower bounds and the dominance properties are incorporated, is proposed and tested on a large set of randomly generated instances.     

Bicriteria scheduling problem for unrelated parallel machines with release dates

This research proposes a heuristic and a tabu search algorithm (TSA) to find non-dominated solutions to bicriteria unrelated parallel machine scheduling problems with release dates. The two objective functions considered in this problem are to minimize both makespan and total weighted tardiness. The computational results show that the proposed heuristic is computationally efficient and provides solutions of reasonable quality. The proposed TSA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.     

Scheduling with job release dates, delivery times and preemption penalties

We consider in this paper the single-machine preemptive scheduling problem with job release dates, delivery times and preemption penalties, where each time a job is started, whether initially or after preemption, a job-dependent setup must take place. First, we prove that the problem is strongly NP-hard. Then, we present a dynamic programming algorithm and a polynomial time approximation scheme.     

Minimizing sum of the due date assignment costs,maximum tardiness and distribution costs in a supply chain scheduling problem

In production systems, manufacturers face important decisions that affect system profit. In this paper, three of these decisions are modelled simultaneously: due date assignment, production scheduling, and outbound distribution scheduling. These three decisions are made in the sales, production planning and transportation departments. Recently, many researchers have devoted attention to the problem of integrating due date assignment, production scheduling and outbound distribution scheduling. In the present paper, the problems of minimizing costs associated with maximum tardiness, due date assignment and delivery for a single machine are considered. Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Programming (MIP) are used for the solution. This problem is NP-hard, so two meta-heuristic algorithms, an Adaptive Genetic Algorithm (AGA) and a Parallel Simulated Annealing algorithm (PSA), are used for solution of large-scale instances. The present paper is the first time that crossover and mutation operators in AGA and neighbourhood generation in PSA have been used in the structure of optimal solutions. We used the Taguchi method to set the parameters, design of experiments (DOE) to generate experiments, and analysis of variance, the Friedman, Aligned Friedman, and Quade tests to analyse the results. Also, the robustness of the algorithms was addressed. The computational results showed that AGA performed better than PSA.     

Enhanced grouping league championship and optics inspired optimization algorithms for scheduling a batch processing machine with job conflicts and non-identical job sizes

This research aims to address scheduling of a single batch processing machine, where jobs are in different sizes and have a conflicting nature with each other, in the sense that two conflicting jobs cannot share the same batch and hence, cannot be processed simultaneously by the machine. The problem is referred to as SBMC. After formulating the problem, a strong lower bound procedure is developed by transforming a relaxed version of the scheduling problem to the multiple bottleneck transportation problem (MTP) with conflicts. An efficient Lagrangian relaxation procedure is proposed, which takes advantage of decomposable nature of the relaxed problem, to attain a lower bound for MTP which in essence is a lower bound for SBMC. To solve the problem, two metaheuristic algorithms, namely the League Championship Algorithm (LCA) and Optic Inspired Optimization (OIO), are adapted and fundamentally modified to match the problem unique structure (i.e., the grouping structure) and accordingly the grouping version of these algorithms is developed. The effectiveness of the lower bound procedure, as well as algorithms, are evaluated through extensive computational experiments. To show they perform efficiently in running times and effective in finding near-optimal bounds for most of the problem instances, we generate 20 different classes of problems according to variability in job sizes, number of jobs and density of incompatibility matrix. Then, we make comparison with two of extensively used algorithms from literature, SA and GA. Our proposed algorithms obtain solutions with objective values less than 6% gap from the lower bound and outperform SA and GA algorithms, especially for large instances. Moreover, values of the lower bound procedure lie within less than 4% of objective values provided by CPLEX.