Parallel-batching Scheduling Problem Research Articles

A parallel machine batch scheduling problem in a brewing company

This work introduces a scheduling problem which is motivated from a real situation faced by one of the largest brewing companies in Mexico. Several products must follow a brewing process which is composed by three main stages: coction, fermentation, and conditioning. In the coction stage, there are multiple unrelated parallel machines, and in the fermentation and conditioning stages, there are several heterogeneous tanks. Additionally, during the production process, some maintenance operations must be scheduled. The problem can be seen as a parallel machine batch scheduling problem with sequence-dependent setup times. Due to the complex structure of the problem, we propose a Greedy Randomized Adaptive Search Procedure to generate good quality solutions in a short computation time. Computational experiments are conducted with real and artificial instances. The solutions obtained for the real instances show that the proposed algorithm reaches better solutions than the current solutions generated by the decision maker at the brewery, and the computation time required by our algorithm is dramatically shorter than the one required by the company.

Single machine parallel-batching scheduling problem with fuzzy due-date and fuzzy precedence relation

A problem of single machine parallel-batching problem with fuzzy due-date and fuzzy precedence relation is investigated. Each job has a positive processing time. Set-up times are assumed to be identical for all batches. All batch sizes cannot exceed a common upper bound. The length of a batch is equal to the largest processing time among all jobs in the batch. Fuzzy due-date denotes the degree of satisfaction with respect to completion times of jobs. Fuzzy precedence constraint expresses the satisfaction level about precedence between two jobs. The objective is to minimise maximum completion time, maximise the minimum value of desirability of the fuzzy due-date and the minimum value of desirability of the fuzzy precedence. First, we propose a fuzzy due-date and ordinary precedence model, which maximises the minimum satisfaction degree of fuzzy due-date. An efficient iterative algorithm based on Procedure HL is designed. On that basis, another efficient algorithm to seek non-dominated solution is presented for the main problem in this paper. The non-dominated solution is defined to be consists of batch size, batch number and allocation of jobs to batches. The whole solution procedure needs at most computational time. Finally, we illustrate the procedure with a numerical example.

Parallel-batch scheduling and transportation coordination with waiting time constraint.

This paper addresses a parallel-batch scheduling problem that incorporates transportation of raw materials or semifinished products before processing with waiting time constraint. The orders located at the different suppliers are transported by some vehicles to a manufacturing facility for further processing. One vehicle can load only one order in one shipment. Each order arriving at the facility must be processed in the limited waiting time. The orders are processed in batches on a parallel-batch machine, where a batch contains several orders and the processing time of the batch is the largest processing time of the orders in it. The goal is to find a schedule to minimize the sum of the total flow time and the production cost. We prove that the general problem is NP-hard in the strong sense. We also demonstrate that the problem with equal processing times on the machine is NP-hard. Furthermore, a dynamic programming algorithm in pseudopolynomial time is provided to prove its ordinarily NP-hardness. An optimal algorithm in polynomial time is presented to solve a special case with equal processing times and equal transportation times for each order.

A note on two-agent scheduling on an unbounded parallel-batching machine with makespan and maximum lateness objectives

This paper studies the two-agent scheduling on an unbounded parallel-batching machine. In the problem, there are two agents A and B with each having their own job sets. The jobs of a common agent can be processed in a common batch. Moreover, each agent has an objective function to be minimized. The objective function of agent A is the makespan of his jobs and the objective function of agent B is maximum lateness of his jobs. Yazdani Sabouni and Jolai [M.T. Yazdani Sabouni, F. Jolai, Optimal methods for batch processing problem with makespan and maximum lateness objectives, Appl. Math. Model. 34 (2010) 314–324] presented a polynomial-time algorithm for the problem to minimize a positive combination of the two agents’ objective functions. Unfortunately, their algorithm is incorrect. We then dwell on the problem and present a polynomial-time algorithm for finding all Pareto optimal solutions of this two-agent parallel-batching scheduling problem.

Approximability results for the resource-constrained project scheduling problem with a single type of resources

In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for the non-preemptive and the preemptive problems have a ratio of O(logn), where n is the number of jobs. This means that there exist instances for which the lower bound of Mingozzi et al. has a bad relative error of O(logn), and the calculation of this bound is an NP-hard problem. In addition, we give a proof that there exists a type of instances for which known approximation algorithms with polynomial time complexity have an approximation ratio of at least equal to \(O(\sqrt{n})\), and known lower bounds have a relative error of at least equal to O(logn). This type of instances corresponds to the single machine parallel-batch scheduling problem 1|p−batch,b=∞|Cmax.

Bounded parallel-batch scheduling on single and multi machines for deteriorating jobs

We consider the bounded parallel-batch scheduling problem in which the processing time of a job is a simple linear function of its starting time. The objective is to minimize the makespan. When the jobs have identical release dates, we present an optimal algorithm for the single-machine problem and an fully polynomial-time approximation scheme for the parallel-machine problem. When the jobs have distinct release dates, we show that the single-machine problem is NP-hard and present an optimal algorithm for one special case.

Bounded single-machine parallel-batch scheduling with release dates and rejection

We consider the bounded single-machine parallel-batch scheduling problem with release dates and rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and then processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. When the jobs have identical release dates, we present a polynomial-time algorithm. When the jobs have a constant number of release dates, we give a pseudo-polynomial-time algorithm. For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.

The bounded single-machine parallel-batching scheduling problem with family jobs and release dates to minimize makespan

We consider the problem of scheduling family jobs with release dates on a bounded batching machine to minimize the makespan. A polynomial-time approximation scheme for the identical job size model and an approximation algorithm with a worst-case ratio of 5 2 for the non-identical job size model will be derived.

The single-machine parallel-batching on-line scheduling problem with family jobs to minimize makespan

In this paper we consider the single-machine parallel-batching scheduling problem with family jobs under on-line setting in the sense that we construct our schedule irrevocably as time proceeds and do not know of the existence of any job until its arrival. Our objective is to minimize the maximum completion time of the jobs (makespan). We deal with two variants of the problem: the unbounded model in which the machine can handle infinite number of jobs simultaneously and the bounded model. For the unbounded case, we provide an on-line algorithm with a worst-case ratio of 2 and prove that there exists no on-line algorithm with a worst-case ratio less than 2. For the bounded case, we also present an on-line algorithm with a worst-case ratio of 2.

Single machine parallel batch scheduling problem with release dates and three hierarchical criteria to minimize makespan, machine occupation time and stocking cost

In this paper we consider an unbounded model of the single machine parallel batch scheduling problem with release dates and three hierarchical criteria. The first criterion is to minimize makespan, the second criterion is to minimize machine occupation time and the third criterion is to minimize stocking cost. We solve this problem by an O ( n 2 ) time dynamic programming algorithm.

The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan

In this paper we consider the unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an O( n ( n / m +1) m ) time dynamic programming algorithm and an O( mk k +1 P 2 k −1 ) time dynamic programming algorithm, 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 processing times of all families. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme for the problem.

The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan

In this paper we consider the unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an O( n( n/ m+1) m ) time dynamic programming algorithm and an O( mk k+1 P 2 k−1 ) time dynamic programming algorithm, 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 processing times of all families. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme for the problem.

Scheduling a batch-processing machine subject to precedence constraints, release dates and identical processing times

We consider the single machine parallel-batching scheduling problem with precedence relations, release dates and identical processing times to minimize a regular objective function. When the processing times are unit, we give an O( n 2) time optimal algorithm. When there are no precedence relations, we solve this problem by dynamic programming in O( n 3) time. When the precedence relations are “layerly complete”, we solve this problem by a dynamic programming algorithm that runs in O( n 7) time. For the total weighted completion time minimization problem, we give an O( n 2) time 3 2 -approximation algorithm. For the makespan minimization problem, we give an O( n 2) time optimal algorithm and an expression of the minimum makespan.