A robust MILP and gene expression programming based on heuristic rules for mixed-model multi-manned assembly line balancing

Highlights

• Uncertain demand are first considered into mixed-model multi-manned assembly line balancing problems.

• A novel robust MILP model with cycle time relaxation and robust objective function is developed.

• Two robust heuristic solution generation embedded with evolutionary-generated rules are proposed to obtain robust solutions.

• A gene expression programming with multi-attribute representation to mine efficient dispatching rules.

Abstract

Current dynamic markets require manufacturing industries to organize a robust plan to cope with uncertain demand planning. This work addresses the mixed-model multi-manned assembly line balancing under uncertain demand and aims to optimize the assembly line configuration by a robust mixed-integer linear programming (MILP) model and a robust solution generation mechanism embedded with dispatching rules. The proposed model relaxes the cycle time constraint and designs robust sequencing constraints and objective functions to ensure the line configuration can meet all the demand plans. Furthermore, two solution generation mechanisms, including a task-operator-sequence and an operator-task-sequence, are designed. To quickly find a suitable line configuration, a gene expression programming (GEP) approach with multi-attribute representation is proposed to obtain efficient dispatching rules which are ultimately embedded into the solution generation mechanisms. Experimental results show that solving the proposed MILP model mathematically is effective when tackling small and medium-scale instances. However, for large instances, the dispatching rules generated by the GEP have significant superiority over traditional heuristic rules and those rules mined by a genetic programming algorithm.

Introduction

An assembly line, as one of the flow-oriented production systems, is generally dedicated to process large and complex productions such as cars and electronics due to its high-efficiency and flexible attributes. In an assembly line, products are moved by a transportation system and flows through a set of workstations to perform their tasks [1]. Finding the best configuration of an assembly line is not trivial and the assembly line balancing problem (ALBP) models how to better balance the tasks of the line in workstations. Concretely, the ALBP aims to optimize some specific objectives such as line efficiency and workload while taking task assignment, precedence relation, and cycle time constraints into account. In this problem, each task must be assigned to only one workstation and is executed after all its predecessors complete. Additionally, the time required by the tasks of each workstation cannot exceed the cycle time.

While ALBP has been studied extensively, it is a simplification of the industrial reality and hence, it presents many practical limitations. For instance, ALBP assumes that an assembly line only produces one homogeneous product and is a one-sided serial line layout within single man stations [2]. Consequently, existing research have focused on variants that add realistic characteristics into ALBP, such as worker assignment [3], [4], [5], robot assignment [6], [7], [8], mixed-model [9], [10], [11], ergonomic risks [12], [13], setup times [14], [15] and multi-manned workstations [1], [16].

From the previous family of variants, the multi-manned assembly line balancing problem (MALBP) is dedicated to model large-size industries having a high volume of products such as the automotive industry [17]. The MALBP has four advantages over the traditional ALBP: (1) effective reduction of the production line length, (2) effective use of space, (3) increased yield and (4), reduction of the time required for material handling and its setting [18]. Hence this paper focuses on tackling the MALBP, where each workstation is equipped with multiple operators. Fig. 1 presents an illustrative layout of one multi-manned assembly line. These operators can then accomplish more than one task in the same workstation. The admitted maximum number of operators in each multi-manned workstation is predefined by the system designer according to the real production. If each workstation is assigned to two operators, this problem is also referred as the two-sided assembly line balancing problem.

Existing works on MALBP mainly focus either on a single product or on mixed-model products. However, they neglect that products’ demand is uncertain and can suffer from daily variations. In practice, the products’ demand is usually dynamic and uncertain in many managerial and operational scenarios [19]. In a multi-manned assembly line, designed to assemble mixed-model products where all the tasks are fixed and assigned to a specific operator and workstation, if the demand changes, task times also change, and the original designed line configuration cannot successfully assemble all the required products. This situation will generate scheduling problems and the company could suffer economic losses.

These challenges encourage us to study the mixed-model multi-manned assembly line balancing problem under uncertain demand (r-MMALBP). There is not any existing research investigating this problem. When providing a robust solution to assembly line balancing, current research typically makes use of exact methods and meta-heuristics. In this work, we propose an efficient approach to solve the problem by dispatching efficient heuristic rules, frequently used due to low computational efforts and convenient implementation [20]. Therefore, this work mainly has the following two contributions:

• The proposal of a novel mixed-integer linear programming (MILP) mathematical model to obtain robust line configurations. The proposed MILP model relaxes the cycle time constraint and designs robust sequencing constraints and objective functions to ensure production is not interrupted when product demand changes.

• The design of a gene expression programming (GEP) with multi-attribute representation to mine efficient dispatching rules. The obtained rules are embedded into two new designed solution generation mechanisms to quickly obtain robust efficient line configuration.

We perform an extensive computational study based on a set of benchmark instances to show the benefits of the problem formulation and the solving approach. This benchmark has 30 training instances and 239 test instances. The training instances are used as a training set to evolve different rules by the GEP algorithm. The 239 test instances are used to test the performance of the proposed MILP model, solution generation mechanisms and dispatching rules. Experimental results show that the proposed MILP model is effective when tackling small-scale instances, and the dispatching rules embedded into the task-operator-sequence solution generation have significant superiority over the traditional heuristic rules and the evolutionary rules by genetic programming.

The remainder of this paper is structured as follows. Section 2 reports the literature review. Section 3 defines the new problem and presents a robust MILP model. Section 4 introduces two designed solution generation mechanisms. Section 5 details the proposed GEP algorithm. Section 6 reports the computational study. Finally, Section 7 concludes with the key findings and suggests future work.