رویکرد مبتنی بر LP-برای بارگیری و مسیریابی در یک خط مونتاژ انعطاف پذیر

The paper presents integer programming formulations and a heuristic solution procedure for a bicriterion loading and assembly plan selection problem in a flexible assembly line. The problem objective is to simultaneously determine an allocation of assembly tasks among the stations and select assembly sequences and assembly routes for a mix of products so as to balance station workloads and to minimize total transportation time in a unidirectional flow system. In the approach proposed, first the station workloads are balanced using a linear relaxation-based heuristic and then assembly sequences and assembly routes are selected for all products, based on a network flow model. An illustrative example is provided and some computational results are reported.

A flexible assembly line (FAL) is a unidirectional flow system made up of a set of assembly stations in series and a loading/unloading (L/U) station, linked with an automated material handling system. The flexible assembly stations (e.g., assembly robots or automatic insertion machines) have a finite work space due to their physical configuration. The component feeding mechanism associated with each assembly task uses some of the finite work space. Therefore only a limited number of tasks can be assigned to a station. When components are all of relatively similar sizes one may assume that each task uses the same amount of the station work space, Under this assumption the finite work space of a station can be refined as its flexibility capacity which specifies the maximum number of tasks that can be assigned to the station. There are negligible setup times between task changes among the tasks assigned to a station, e.g., [1] and [2]. In a FAL different product types are assembled simultaneously. A typical assembly process proceeds as follows. A base part of a product is loaded on a pallet and enters the line at the L/U station. As the pallet is carried by a conveyor or an automated guided vehicle through a series of assembly stations, components are assembled with the base part. A product may bypass some stations but does not revisit any station. When all the required components are assembled with the base part, it is carried back to the L/U station and the complete product leaves the system.

Flexibility in the short-term planning is an important issue in enhancing productivity of a flexible assembly system. An efficient utilization of the system capabilities requires alternative assembly plans for each product to be considered at the loading level. In order to achieve the best results, allocation of assembly tasks should be determined along with the selection of the assembly plans and assembly routes for all the products. The LP-based heuristic for loading and the network flow model for routing and assembly plan selection seems to be applicable in practice for such a short-term allocation of the system resources. The two-level approach proposed for the bi-objective loading, routing and assembly plan selection enables a network flow structure of the routing and sequence selection subproblem to be efficiently exploited. However, it is a pure top down approach and the solution obtained at the lower level has no effect on the upper level problem. To avoid that disadvantage, an improved hierarchical approach shown in Fig. 5 can be considered as an alternative optimization scheme. In the hierarchical framework proposed in Fig. 5 the solution value obtained at one level generates a cut constraint for the other level. The cuts are based on the current upper bounds on the value of each objective function, which may further improve performance of the lexicographic approach proposed for the multiobjective optimization. The new framework can be incorporated into an interactive optimization scheme where the most preferred final solution can be selected based on the decision maker's preferences, e.g., [13].