برنامه ریزی در flowshops با عملیات انعطاف پذیر: بهینه سازی خروجی و مزایای انعطاف پذیری

This study considers the throughput optimization in a two-machine flowshop producing identical jobs. Unlike the general trend in the scheduling literature, the machines are assumed to be capable of performing different operations. As a consequence, one of the three operations that a job requires can only be processed by the first and another operation can only be processed by the second machine. These are called fixed operations. The remaining one is called the flexible operation and can be processed by any one of the machines. The machines are assumed to have different technological properties, i.e. non-identical, so that the processing time of the flexible operation has different values on the two machines. We first consider the problem of assigning the flexible operations to the machines for each job in order to maximize the throughput rate. We develop constant time solution algorithms for infinite and zero capacity buffer spaces in between the machines. We then analyze the benefits of flexibility. Managerial insights are provided regarding the changes in the makespan as well as the associated cost with respect to the increase in the level of flexibility.

In order to be successful in today's highly competitive world requiring high levels of productivity and adaptability to changes, firms increase levels of flexibility in their manufacturing systems. Flexibility in manufacturing is defined as the ability to change or react with little penalty in time, effort, cost or performance (Upton, 1994). There are many different types of manufacturing flexibilities such as the machine flexibility defined as the ability of the machines to perform different operations and the operation flexibility defined as the ability to produce a product in different ways (Browne et al., 1984). In order to get the maximum available benefit from flexibility some important problems must be tackled such as the determination of the “optimal” levels of flexibility and the determination of operational rules (e.g. schedules) for such systems. This study considers a flowshop consisting of two workstations which possess machine flexibility. Such situations arise in many different practical settings. For example, if the workstations consist of Computer Numerical Control (CNC) machines which can perform different operations as long as the necessary cutting tools are loaded on their tool magazines or if the workstations consist of manual operators equipped with the necessary tooling and crosstrained to perform different operations. From now on we will refer to the workstations as machines.

In this study we considered machine flexibility as an option to increase the throughput rate in two machine flowshops. As a consequence of this flexibility we assumed that each job has fixed and flexible operations. We first considered the optimization problem where the machines are assumed to be non-identical. For both the no buffer and infinite capacity buffer cases we developed constant time solution procedures. In the second part, we demonstrated the benefits of machine flexibility. We considered the reduction in the makespan corresponding to any flexibility level measured by the processing time of the flexible operations. After this analysis we conclude that most of the benefits in terms of the reduction in the makespan are attained with a relatively small level of flexibility. The cost of increasing the flexibility level need not be directly proportional with the flexibility level as assumed in earlier studies. In such a situation, the optimal flexibility level can be determined through a bicriteria analysis of the makespan and the cost as in Example 2.