Bi-objective optimization algorithms for joint production and maintenance scheduling under a global resource constraint: Application to the permutation flow shop problem

Highlights

• A methodology for addressing a bi-objective, resource constrained permutation flow shop scheduling problem is proposed

• Makespan and Total Production Cost (comprised of maintenance and resource related costs) are simultaneously optimized

• NSGA-II, a proposed Bi-Objective PSO (BOPSO) algorithm and a novel Bi-Objective Randomized Local Search (BORLS) heuristic are developed to solve the problem and compared for their performances

• Initializing the algorithms with purely random populations, BOPSO algorithm outperforms NSGA-II in most of the comparison criteria when large size problems are considered

• The proposed BORLS shows high effectiveness both when used to enhance the performances of the two metaheuristics by generating a small proportion of the initial populations, and when used as an independent search algorithm.

Abstract

Production scheduling and maintenance planning are two of the most important tasks that managers face before implementing their decisions on the shop floor. Another issue managers have to keep in mind is the proper allocation of various resources for production. These issues create difficulties in the planning process. In this paper, we propose a bi-objective model that integrates the three aforementioned issues and determines production scheduling, maintenance planning and resource supply rate decisions in order to minimize the make span and total production costs, which include total maintenance, resource consumption and resource inventory costs. Two meta heuristic methods were employed to find approximations of the Pareto optimal front in a permutation flow shop environment: The well-known non-dominated sorting genetic algorithm (NSGA-II) and a bi-objective adaptation of the particle swarm optimization (BOPSO). Additionally, a bi-objective randomized local search (BORLS) heuristic was developed in order to generate multiple non-dominated solutions along its search path. Two sets of computational experiments were conducted. In the first set, the performances of the two meta heuristics with purely random initial populations were compared, with results showing the superiority of BOPSO over NSGA-II. In the second set, the initial populations were enhanced with heuristically generated solutions from BORLS and the performances of BOPSO, NSGA-II and BORLS used as an independent search algorithm, were compared. In this instance, the algorithms performed evenly for large problems, with the BORLS method generating better solutions when total production cost is emphasized.

Introduction

Modern manufacturing companies are confronted with daily challenges in managing production systems and efficiently exploiting scarce resources the moment these resources become available. Moreover, the current industrial context imposes the maintenance of consistent systems that are able to meet consumer requirements, such as providing high quality products, adherence to deadline restrictions and the reduction of production costs in order to survive global competition. In order to tackle these challenges, enterprises have adapted new methodologies and philosophies into their facilities, such as Lean, Just-In-Time manufacturing and Theory of Constraints methodologies that can help industrial companies achieve their goals by improving their processes and reinforcing the efficient utilization of resources by eliminating waste, lowering inventory and breaking bottlenecks constraining system performance. The adaptation of these ideas have drastically changed operations management and given rise to new kinds of problems to be solved by operational and tactical decision makers.

Operations scheduling and planning is unquestionably one of the key-elements that lead to the success or failure of a manufacturing organization. Well-conceived and flexible schedules can increase throughput and the availability of resources as well as reduce costs. Resources implied in a typical process can be of two types, renewable (e.g., machines and operators) and nonrenewable (e.g., raw materials and fuel), which are needed to support or complement the operations in progress. Production scheduling primarily concerns allocating a set of resources to a set of tasks that have to be performed according to a defined timing plan so that a single or multiple performance measures are optimized (e.g., completion time, total production costs and tardiness in deliveries). Despite their importance, most scheduling problems are hard (Garey & Johnson, 1979). Even classical problems with simple configurations and small instances are handled with difficulty and there are hardly any efficient methods capable of generating optimal solutions within reasonable computational time. As production environments become more complex and as the magnitude of problems increase, obtaining optimal schedules through exact solution methods becomes intractable. Conflicting objectives set by different services brings-in another level of complication to the models. Actually, production scheduling and maintenance planning are two main sources of these conflicts.

Within an industrial enterprise, production and maintenance services are major contributors to the success of business management, although the two activities target separate goals. The first is mainly motivated by maximizing the utilization of resources and equipment in order to meet demand and the delivery dates agreed upon by the customer and the producer. However, this full exploitation may decrease the availability of machinery due to the higher risks of machine breakdown. On the other hand, maintenance emphasizes the maximization of equipment availability by assigning scheduled inspections and other preventive actions (e.g., filter replacements, adjustments and lubrication) that also may disrupt production plans. Therefore, in order to reduce conflicts, communication and synchronized cooperation between the two services is vital.

Another issue related to production is the allocation of consumable resources required by different machines to carry out jobs. Inappropriate assignments of these consumable resources may cause the unavailability and the idleness of the system, where an operation needs to wait for the arrival of resources before beginning the process. This may also increase levels of waste and as a result, lead to higher costs. In addition, management of such resources should bear in mind various maintenance responsibilities and vice-versa (Wang & Liu, 2015).

Flow shop scheduling is a very common problem in various types of industries dealing with semi-conductor devices, steel-rolling and many pharmaceutical and chemical processes where raw materials need to undergo a stage-by-stage transformation throughout the system. Additionally, each job requires a certain quantity of resources at each stage (e.g., heat, water and chemical additives) for its treatment. Processors may also suffer from degradation, which increases overtime. Therefore, an optimal maintenance policy should be implemented (Segawa et al., 1992). Motivated by the previously described settings, this paper explores the integration of production scheduling and maintenance planning in a flow shop environment that takes into account the scarcity of a global resource, supplied from outside the production system and shared by all production machines at any given moment during the planning horizon with the objective to minimize the makes pan and total production costs.

The main contributions of this study are as follows:

• Proposing an integrated model that accounts for production, maintenance and global resource constraint decisions all at once.

• Developing a fast computing method for constructing and evaluating a production plan.

• Developing an efficient bi-objective meta heuristic algorithm to find an approximation of the Pareto frontier.

• Proposing a novel bi-objective randomized local search procedure in order to generate multiple non dominated solutions in a single run that can be used as an enhancement of the initial population of a meta heuristic or as an independent search algorithm.

The remainder of the paper is structured as follows:

First, a literature review is presented in section 2 In section 3, the definition of the problem and a detailed model formulation are described, followed by an explanation of the solution approach in section 4 Samples of results obtained from the computational experiments are analyzed in section 5 Finally, concluding remarks and future research scopes are provided.