Optimal assignment and scheduling of workers and tasks on an assembly line
In this paper the assignment of cross-trained and temporary workers to tasks on an assembly line is investigated. Cross-trained workers are skilled to perform more than one task on the assembly line in the production process. Temporary workers are viewed as either trained or untrained and may be hired or laid oﬀ as required. The solution procedure may be divided into three parts. During the ﬁrst part a model is formulated to determine an optimal assignment of the workers to the production tasks. During the second part the model is extended to determine the eﬀect of the assignment of both trained and untrained temporary workers to the tasks on the assembly line. During the ﬁnal part of the model an optimal sequence of tasks in the assembly line is determined that minimises the resulting execution times of these tasks. During the ﬁrst part the objective is to maximise the total production utility. This is achieved by implementing a two-phase model. The ﬁrst phase maximises the utility of pro-duction by minimising labour shortage in the assembly line. During the second phase the improvement of the workers’ levels of skill is maximised while the eﬀect of the learning and forgetting of skills is taken into consideration. A learn-forget-curve model (LFCM) is implemented to model the eﬀect of this human characteristic on the master model. This approach ensures that the advantageous cross-trained nature of the workers is maintained and optimized, without a large deviation from the solution determined by the ﬁrst phase. The objective of the second part is to minimise the labour cost of production by determin-ing the best type of workers for a certain task as well as the manner in which they should be hired or laid oﬀ. A worker is classiﬁed as either permanently or temporarily employed. Tem-porarily employed workers are further classiﬁed as either untrained or cross-trained workers. The assignment of workers to tasks on the assembly line is achieved by means of a Master Production Scheduling (MPS) model. The MPS has as its objective the minimisation of the total labour cost of performing all the tasks. The labour cost is deﬁned as the sum of the temporary workers’ daily wages, the overtime cost of permanent workers, the overtime cost of temporary workers and the cost of employing and laying oﬀ temporary workers. Finally, during the third part an optimal sequence of tasks is determined in the production process in order to minimise the total production time. This is achieved by means of a two-phase dynamic assembly line balancing model, which is adjusted to incorporate the critical path method. During the ﬁrst phase, an optimal task sequence is determined, while during the second phase, an optimal assignment of tasks to workstations and the timing thereof, is determined. The practical applicability of the model is demonstrated by means of a real life case study. The production of various styles of shoes in a leatherworks factory is considered. The production of each style requires a diﬀerent set of tasks and each task requires a diﬀerent level of skill. The factory under consideration employs both cross-trained and temporary workers and data sets were obtained empirically by observation, interviews and questionnaires. Upon execution of the ﬁrst phase of the assignment model, an optimal utility is found and the second phase is able to maximise the increase of the workers’ skill level without deviation from this optimum. Upon execution of the employment model, it is found that labour costs are minimized by increasing the use of temporary workers and by assigning the maximum allowable number of overtime hours to them. Upon application of the scheduling model, an improved time is obtained compared to the standard execution time of each style. The results obtained from the case study indicate that the application of the model presented in this paper shows a substantial improvement in production, while reducing the cost of labour as well as improving the overall level of workers’ skills. A multi-objective model is thus developed which successfully maximises production utility, maximises skill development of workers, minimises labour costs and the occurrence of idle workers as well as minimises total execution time.