Flexible open-shop problem for minimizing weighted total completion time

In this article, scheduling flexible open shops with identical machines in each station is studied. A new mathematical model is offered to describe the overall performance of the system. Since the problem enjoys an NP-hard complexity structure, we used two distinct metaheuristic methods to achieve acceptable solutions for minimizing weighted total completion time as the objective function. The first method is customary memetic algorithm (MA). The second one, MPA, is a modified version of memetic algorithm in which the new permutating operation is replaced with the mutation. Furthermore, some predefined feasible solutions were imposed in the initial population of both MA and MPA. According to the results, the latter action caused a remarkable improvement in the performance of algorithms.

Multistage Open-Shop-Problem: Schedules for N Tasks on K Machines with Different Technical Characteristics for an Arbitrary order of Tasks

The statements and mathematical models of the open — shop-problem are considered: performing N tasks on K machines with an arbitrary order of processing each task on all machines. Unlike most publications on solving this problem, the task posed is solved in a multi-stage formulation under the conditions of a sequential chain of sections and workshops of the enterprise, as well as in the presence of restrictions on the start and end times of tasks and the permissible operating times of machines. In addition, for scheduling systems of enterprises, it is extremely important to consider this task in a multi-stage setting, i.e. in a sequential chain of plots and workshops. The properties of admissible and optimal schedules, as well as algorithms of exact and approximate methods for solving these problems by successive optimization algorithms are investigated. At the early stages of solving the problem, the fact of incompatibility of the system of constraints of the task and the definition of a subset of tasks or resources, the time range of which should be expanded, is established. The described algorithms for solving the problem are illustrated by numerical examples.

NO-WAIT OPEN SHOP WITH WORKER FLEXIBILITY

The Open Shop Problem is a Production Scheduling problem where jobs do not have predestined processing routes, which increases the solution space and, therefore, the complexity of the problem. This work proposes a novel mathematical model that addresses the Open Shop theme with worker flexibility and no-wait. We consider the resource constraint of flexible and multiskilled labor. That is, the workers can execute their activities in more than one workstation. Simultaneously, the latter the continued production is contemplated, which hinders the reachability of feasible solutions and therefore increases the problem complexity. To validate the model, we generate several benchmarks, and the results obtained highlight the importance of worker flexibility in achieving greater problem feasibility.