کنترل فازی با فرصت های محدود و کنترل تاخیر پاسخ - یک سناریوی کنترل تولید موجودی

This paper examines the utility of fuzzy control over crisp in situations where the control opportunities are limited and the system response to control actions is delayed. Such situations are often encountered in production systems where limited resources restrict the control opportunities and the operation time delays the response. The performance of a real-time production-inventory control system is studied with fuzzy control strategy and compared with a corresponding crisp control and no-control strategy. The system consists of a production shop having a number of identical processing machines which produce two products. The output goes into two bins whose inventory is required to be controlled at desired level by varying the number of machines allocated to the products. Real-time inventory variation, output, average inventory and machine usage, number of setups and stock-outs are used as performance measures. The simulation results of the system with various configurations show that the capability of fuzzy control is seriously inhibited by limited opportunities and response delay although fuzzy has distinct advantage over crisp. As control opportunities increase fuzzy control becomes increasingly efficient with diminishing effect of response delay.

Fuzzy logic has been successfully used for designing and building industrial sys- tems with two main purposes––rapid control and low cost, although the quality of control is not necessarily better than the corresponding crisp control. This can be seen in [1], where the capabilities of fuzzy controllers for complex systems are pre- sented including an example of a controller for an inverted pendulum. In most applications of fuzzy control the opportunities for control in terms of manipulations of control parameters are quite large along with almost immediate setting of parameters at levels desired by the control system. However, there exists a class of problems where either the scope for parameter manipulation is limited or there is a delay in setting of parameters to new values or both. Such situations are found in control of production systems due to its fixed capacity (limited resources) and a delay in resetting the machines and getting re- sponses on signal parameters. It is interesting to investigate the usefulness of fuzzy controller in comparison to the simple crisp controller in such situations. We choose real-time control of a discrete production-inventory system to investigate this effect. Fuzzy logic has been used by other researchers in production systems for various kinds of problems. Chan et al. [2] have shown the benefit of using fuzzy approach to operation and routing selection over other conventional rules like WINQ (work in queue) and SNQ (shortest number of jobs in queue). Details of the use of fuzzy logic in production planning, scheduling, process and quality monitoring, group tech- nology etc. can be found in [3,4]. Other studies using fuzzy logic in production management in general can be seen in [5–7]. Studies closer to our study are Sudiarso and Labib [8] who use maintenance data to determine optimal batch size for production control. Grabot et al. [9] convert various objectives to a fuzzy based multi-objective optimization problem for a decision support system for production activity control. Tsourveloudis et al. [10] develop fuzzy systems for work-in-process inventory control of unreliable machines in three different modules––a transfer line module, an assembly module, and a dis- assembly module. They attempt to control WIP by varying machines’ processing rates. They demonstrate the performance of the control system through continuous flow simulator and took averages of the simulation runs, which may not show a typical response of a discrete production system in real-time. Moreover, they show comparisons of their system with full capacity production and, in one case, with hedging point control. The paper does not show a comparison with a crisp control strategy with similar reasoning as fuzzy. Another paper of interest is by Samanta and Al-Araimi [11] who use fuzzy logic for inventory control with varying demands by varying monthly production quota. They compare three strategies, fuzzy PID (proportional-integral-derivative) with resetting, fuzzy PID without resetting, and PID without fuzzy. Their last case may be thought of as crisp control. Their results show only slight advantage of using fuzzy approach. Since they used monthly setting of production levels, the study does not bring out the behavior of the system in real-time control. To investigate the effect of using fuzzy approach over crisp in real-time produc- tion-inventory control, we choose a simple production shop where a number of reliable machines produce two products. Each machine is capable of producing both products with equal efficiency. The items produced go into separate bins from where they depart according to demand. The goal is to control inventory of both products at the bins at a preset level by manipulating the number of machines assigned for production of each product. Thus machines switch from producing one product to another or stop working altogether. We present various cases where the system is balanced at full or part capacity. The limited opportunity of control comes from the capacity of the shop and the availability of machines for switchover while the re- sponse delay comes from the fact that the effect of adding or deleting a machine on the inventory of the relevant product is not immediate. Various performance mea- sures are used to compare fuzzy and crisp control strategies with the help of discrete event simulations.

The benefits of using fuzzy control over crisp and no-control were examined in a situation with limited control opportunities and response delay. A few cases of the real-time control of production-inventory systems were considered. The sim- ulation results confirm that the benefits of using fuzzy are grossly restricted when fewer opportunities for control exist and the response delay degrades the performance significantly in such situations. This is seen in cases where full capacity is required for system balance. One would be tempted not to use any control strategy in full capacity cases looking at the averages alone. However, in case a control strategy is used for leveling out the inventory, the fuzzy control has distinct advantage over crisp in reducing the number of setups and stock- outs. As soon as the system is used at partial capacity and some extra capacity becomes available, the fuzzy control strategy becomes superior in all performance measures. The extra capacity increases the control opportunities and the effect of response delay diminishes. More the extra capacity more is the benefit. With ample oppor- tunities fuzzy control produces more output, controls the inventory in a desired range, reduces the number of setups and prevents stock-outs. Two different membership functions for machine assignments were examined. The results gave somewhat confusing picture. To clarify the situation, more simulations were performed with systems balanced at 80% and 70% capacity. The number of setups required for crisp, fuzzy-1 and fuzzy-2 are shown in Fig. 8. Two things can be seen from this figure. First, fewer setups are required in both crisp and fuzzy at 100% capacity because there are less opportunities for changing setup. As opportunities increase to some extent setups increase, but decrease again with additional opportunities because wider allocations become possible requiring less frequent setup changes. Second, setups in fuzzy-2 are generally more than fuzzy-1 except in a short range near full capacity and that too by a very little difference. Hence, it can be safely concluded that fuzzy-1 is better than fuzzy-2 in general. This is a serious result for it calls for not putting medium or the centre of the middle predicate at the average level of system balance but at the middle of the total capacity (opportunity). This may become understandable in the sense that, this way, the extra capacity is distributed to all the predicates of the fuzzy variable.Thus care is needed in designing membership functions so that control oppor- tunities are evenly divided over the universe of discourse rather than put on a side. Finally, then, it can be said with confidence that while fuzzy control strategy has benefits over crisp even with limited opportunities, its real benefit is unleashed only when large opportunities for manipulation of control parameters are available. Any kind of control would become restricted if there is a delay in system response to control actions; fuzzy control is less affected by such delay if enough control opportunities exist. It is the opinion of the authors that less than expected performance of fuzzy control in most of the reported studies in production control, including those cited above, can be explained by the above reasoning.