تجزیه و تحلیل عملکرد سیستم های تولید به صورت سفارشی تحت رژیم های مختلف کنترل حجم کار

This paper firstly discusses the make-to-order (MTO) manufacturing sector to show the different types of queuing network that may exist and need to be covered. The workload control (WLC) production planning method is modelled as a queuing network with limited buffer capacities in front of each workstation. Exact solutions for a general network with more than 3 or 4 workstations are not possible. An approximation algorithm, as an extension of earlier work on simple tandem queuing networks, has been developed to cope with any number of workstations and to allow flows forwards and backwards between the workstations. The essentials of the model and solution algorithm are briefly described. The second half of the paper presents the results of using the model and algorithm to analyse four issues in WLC in MTO. The first set of experiments examines the relative value of two WLC mechanisms for controlling manufacturing lead times, job release and order acceptance. The second set of experiments is to gain insight into how increased complexity in production layouts and the product variety impact on manufacturing performance measures. The third set of experiments examines the differential effects of extra buffer capacity at earlier or later workstations in the main path flow; whilst the final set of experiments examines the impact of having groups of high- and low-priority jobs.

Manufacturing companies differ in the way they meet their demand. Some deliver products to their clients from finished goods inventories as their production anticipates customers’ orders; others, however, manufacture only in response to customers’ orders. Orders for the products tend to be on a make-to-order, make-to-print or engineer-to-order basis (MTO), often being specific to a particular customer with intermittent or no repetition of demands for the same product. The typical company in the produce-to-order manufacturing sector has to supply a wide variety of products, usually in small quantities, ranging from a range of standard products to all orders requiring a customised product. The arrival of customer enquiries is a stochastic process over time. Each potential order from the enquiry tends to be for a differing number of units and requires varying routings and processing times through the production facilities. Each order requires processing (transformation work) on a series of workstations. Jobs enter the production system and go to the first workstation in their routing sequence. They typically join a queue of other jobs waiting their turn for their processing work to be carried out. Once the work on a job at a workstation is completed, the job is transported to the next workstation in its routing sequence, where it again joins a queue of jobs awaiting processing. The manufacturing lead time is thus the sum of the set-up and processing times at each of the workstations in the job's routing sequence plus all of the time spent waiting in queues in front of the workstations. It is well known that in the produce-to-order sector an order can spend up to 90% of the total time in production waiting in front of or between workstations. It is reported that manufacturing lead times are often long and unreliable almost entirely due to the large proportion of time spent in the queues, see Stommel (1976) and Stalk and Hout (1992). A general model of the shop floor is a network of workstations each with a set of orders (jobs) queuing waiting their turn to be processed. Clearly, the production process can be viewed as a network of queues, of different types as illustrated in Fig. 1. MTO companies differ in the degree of product customisation, covering pure customisation, tailored customisation, standard customisation and non-customisation, and the amount of product variety. Some companies offer standard products that are expensive to produce to meet intermittent low demands. So in such cases they would not be kept in stock but only produced to order. As there is repetitive production, albeit on an intermittent basis, the products are likely to be manufactured on a single production line (Fig. 1a) or on assembly lines. The assembly line is better known as a flow shop. In a flow shop, the products move in one direction only with only one operation at each workstation, as illustrated in Fig. 1b. There may be multiple entry and leaving points in the system. A purely customised product is one that is developed from scratch for each customer. Since almost every product is unique and produced in a different way, production tends to be via a job shop layout, see Fig. 1c. Most of the literature on the production planning problems of produce-to-order companies has focused on the individual workstation level. The bulk of this has concentrated on priority dispatching; the order in which jobs should be scheduled through each workstation. Surveys show that hundreds of such priority rules have been devised for application on the shop floor. However, experience has demonstrated that priority dispatching is a relatively weak mechanism for the control of queues. If used alone, it has little effect in reducing the long lengths and high variability of the queues of jobs in front of machines. A stronger instrument, controlled job release, entails maintaining a ‘pool’ of unreleased jobs in the production planner's office, which are only released onto the shop floor if doing so would not cause the planned queues to exceed some pre-determined norms. This in turn reduces the work-in-process and the task of priority dispatching is made easier. However, planning needs to be extended even further backwards to ensure the company only takes on work that it can profitably produce and deliver to the customer's satisfaction. If we are going to assist in the management and planning activities of MTO manufacturers at the more aggregate job release and order acceptance levels, we need to know how the different queuing networks behave under alternative types of planning processes and methods. We can try to tackle this problem by applying analytical models or by the use of simulation. The only analytical models that exist are based on the work of Jackson (1957) and Jackson (1963). He argued that a fairly general class of networks can be exactly analysed as individual queues, and each queue can be formulated as M/M/1 or M/M/c1 when the arrivals occur as Poisson processes and service times are exponentially distributed. A closed-form solution, known as the product-form solution, exists which means that the steady-state joint probabilities can be expressed as the product of the marginal probabilities of each independent queue. Hence, formulae to calculate important manufacturing performance measures such as the manufacturing lead times (using Little's Law) and the work-in-progress can be derived. All of this assumes that there is infinite storage capacity in front of any workstation. However, in practice storage is usually limited, either by restricted physical space for storage or by management policy. The classical example of this is the use of Kanbans in just-in-time production of standard products on assembly lines. Once the queue of jobs in front of a workstation reaches some value, production at earlier stations is stopped until the queue is reduced. This is known as blocking. Blocking means that the individual workstations and queues cannot be treated as independent. Their behaviour depends upon what is happening to previous and subsequent workstations. There are thus significant interactions between the different work stages (workstations). Queuing networks with finite buffers are generally difficult to analyse owing to blocking and product-form solutions cannot in general be obtained. The number of states for exact numerical analysis grows combinatorially with the number of nodes (workstations) and buffer capacities (limit on jobs in the queue). Hence, most analyses are based on analytical approximations using decomposition methods or simulation techniques. As discussed in Haskose et al. (2002a), most of this work has been for tandem queuing networks, i.e. a single production line, as in Fig. 1a. Clearly, this is of limited practical application. Research on the analysis of arbitrary queuing networks is much less frequent. Most approximation methods for arbitrary networks decompose the system into individual queues with revised capacities, arrival and service processes and tend to assume that external arrivals occur at only one queue. Virtually all methods assume feed-forward topologies of networks; i.e. jobs cannot go back to nodes previously visited. In all cases, the size of network that can be analysed is very limited except where much simpler or special networks are considered. Haskose et al. (2002a) presented an exact model for an arbitrary queuing network with blocking for a triangle configuration of workstations. This modelled the production system as a Markov Process. Practically it is only computationally feasible to solve the model exactly if the number of workstations is less than three or four. The results presented in the paper and in Haskose (2001) indicated that the traditional M/M/1 and M/M/1/K2 formulae, based on the Jackson network which treats each workstation as independent, can lead to serious errors when used to estimate manufacturing lead times, jobs turned away and work in process (WIP), see e.g. Table 1 and Table 2. These give example results for three workstations as a flow shop or as a job shop where the workload rate is 90%. The workload rate is the ratio of the arrival rate of work per unit time to the system processing rate per unit time. Furthermore, the M/M/1 model cannot produce a solution if the arrival rate of work exceeds the processing rate. The alternative and more usual approach in research on the behaviour of MTO production systems is simulation. Simulation experiments are used to evaluate the relationships between the workload norms, the arrival rate of jobs, the capacity provided and important performance parameters such as WIP, lead time and capacity. The large literature on priority dispatching rules for individual workstations is based on extensive simulation experiments. There are problems with a simulation approach. One issue is how one deals with a new situation and a new production layout or a different demand generation process. A very large number of simulation experiments may need to be run. Whilst in theory simulation allows a large number of scenarios to be investigated in practice, the large number of experiments required for any one of them often limits the usefulness of the approach. It is complex and time consuming to find the queuing time norms to use for each workstation for day to day planning using simulation methods. The planning norms selected will lead to some average manufacturing lead time value, which includes the average time spent waiting at each workstation. One will need to keep iterating to ensure that these average waiting times per workstation are the same as the planning norms put into the simulation.

This paper has shown how MTO manufacturing in its widest sense can be modelled as an arbitrary queuing network with limited buffer capacities to store jobs in front of each workstation. This makes it immediately apparent that WLC ideas are an obvious way to plan and manage such operations. The paper has also briefly presented an approximation model and algorithm for finding analytically the steady-state solutions for any form of arbitrary queuing network. This means that many more alternative options and situations can be analysed in a limited time period than if one uses a simulation approach. Applications of the model have been described for four situations: • the comparative impacts of control at the order acceptance and job release stages on manufacturing lead times, work-in-process and capacity utilisation; • the impact on the performance measures of increased complexity in the production layouts and the product variety; • the relative effects of increasing the buffer capacity at later rather than earlier work stations in the main path flow; • the impact of having high- and low-priority jobs. An obvious extension to the research is to explore the differences found between the more complex job shops and the simple tandem system for larger increases in buffer sizes and increases at more than one interior workstation. Running these further experiments for the simpler job shop (ff) where jobs can only feed forward and for the more complicated job shop, fb(2), with more feedback should provide insight into how far it is the existence of feedback that suggests having larger buffers at the end stations rather than the earlier ones is better. The results presented are only specific for the particular cases studied. However, they provide insight into the general behaviour that could be expected. They demonstrate the value of the model to explore the behaviour of MTO manufacturing issues in general. It is particularly appropriate for exploring WLC issues and for estimating in advance what planning norms to use for any new situation once the desired performance objectives have been set. The results obtained in this research, albeit provisional at this stage, suggest that as the job shop layout becomes more complex, job shops behave very differently to simpler tandem systems. Clearly, the task of WLC in networks of these types is not simple, and would be better if undertaken with the aid of models capable of predicting the non-obvious consequences of management actions.