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Weekly Updates1. Introduction
Global optimization of enterprises is one of the most crucial and intractable issues in production management. Consequently, current management practice resorts to local optimization, which can lead to poor performance and poor competitiveness. One of the most important global objectives of manufacturing enterprises--reducing mean Work-In-Process (WIP) or mean flowtime subject to due date/throughput constraints--is a function of the enterprise's production control system. In this paper we develop a simulation-based feedback control algorithm, called AWIP (Adaptive WIP), for designing Self-regulating Production Control Systems (SPCSs) such as buffered lines, kanban, base stock and inverse base stock. The proposed feedback control algorithm is analyzed and tested computationally in this paper for a range of applications. Simulation is used to provide the feedback to the controllers, and leads to an iterative numerical computational approach.
The paper is organized as follows. In the rest of this section we review recent literature on SPCSs and their design. In Section 2, the AWIP algorithm is introduced after we present some preliminary concepts. Section 3 presents computational test results obtained from a set of comprehensively designed experiments. In Section 4 we summarize the obtained results.
1.1. SPCSs
We define SPCSs as production control systems that are run by a set of rules that are a function of the system status and do not require human interaction during the operation stage. Widely used SPCSs include buffered lines, kanban, CON WIP (Spearman el al, 1990) and base stock (Gstettner and Kuhn, 1996). A buffered line is a sequence of workstations with finite buffers before each workstation as shown in Fig. 1(a). Production on a workstation starts when there is a part in the buffer before the workstation and there is no part presently loaded on the workstation. After production the part is unloaded from the workstation only when there is enough room in the buffer after the workstation. In a kanban system, containers (cards) are used to control the transfer of items between workstations as shown in Fig. 1(b). Each container remains next to its associated workstation. Production at a workstation starts when the workstation is free and when there is a container with a part from the previous workstation. After processing, the part remains in the container until an empty container is available from the next workstation. When a container becomes available, the part is transferred to the next workstation and the container from which the part was removed returns to the previous workstation and takes a part, or waits for a part, if no part is available. After the last workstation, full containers await demand. CONWIP (CONstant WIP) was first presented by Spearman et al. (1990). With the CONWIP SPCS, parts are associated with a fixed number of containers (cards), which traverse the entire production line as shown in Fig. 1 (c). When a container reaches the end of the line the finished product is removed and the container is sent back to the beginning of the line where it awaits another batch of raw materials. In base stock (BS) SPCS, we set a maximum level for both the physical echelon inventory at each workstation (i.e., the physical inventory at and downstream from the workstation) and a desired level for the net echelon inventory (i.e., the physical echelon inventory minus the awaiting demand). When the net echelon inventory at a workstation falls below its desired level and if there is enough raw material, then the workstation will process parts until the desired net echelon inventory level is reached or the limit on physical echelon inventory at a workstation is reached as shown in Fig. 1(d).
[FIGURE 1 OMITTED]
Important generalizations of these basic systems are tandem CONWIP (Tayur, 1992, 1993; Hopp and Spearman, 1996), segmented systems (Gstettner and Kuhn, 1996), general blocking mechanism (Cheng and Yao, 1993), and production authorization card (Buzacott and Shanthikumar, 1993). Bonvik et al. (1997) suggested some possible combinations of these systems.
A common property of all the above-mentioned systems is that the rules that define the system operation (i.e., that link the input process to the output process) are simple and are a function of the system status through its WIP distribution. This function takes the form of a blocking phenomenon: sometimes idle workstations are not allowed to start production even when all necessary raw materials are available and sometimes even when there is physical room for the finished product. The rules represented by all of the above systems limit the WIP in contiguous portions of the production system. This observation forms the basis of the unified model, called SWIP (Self-regulating WIP), proposed by Masin et al. (1999). SWIP includes all systems mentioned above, and in fact all existing SPCSs.
In a SWIP system the blocking mechanism takes the form of limiting the number of parts in all contiguous portions of the production system, as shown in Fig. 2. We can associate a limit on the number of parts in a contiguous portion of the production system (i, j), [u.sub.ij] with a card loop going from the beginning to the end of the contiguous portion, i.e., between points i and j. We use the term card loop because this limitation can be (and in the kanban and tandem CONWIP systems is) implemented by attaching cards (from a limited supply) to parts when they enter the contiguous portion and detaching the cards (and thus making them available for re-use) when the part leaves the contiguous portion. Of course, this limitation can be implemented electronically using computers, but the physical analogy is still useful.
[FIGURE 2 OMITTED]
Inverse base stock (IBS) is an SPCS derived from SWIP (Masin et al., 1999). The idea behind IBS is to ensure that the raw material is released to the production system as late as possible, but once the material is released, it should be allowed to go as quickly as possible through the production line to the departure point. This is accomplished by not having any card loops between two internal points in the production system. However, one should only allow material to enter the production system if the conditions are right. Having a limit on the number of parts between the starting point and each other point in the system accomplishes this goal, as shown in Fig. 3. Basically, this strategy ensures that the system is not too crowded. Masin et al. (1999) proved for some production environments that for the same throughput, IBS has lower average WIP than BS. Our simulation experience shows that, on average, IBS gets the same throughput with less WIP than kanban, CONWIP and tandem CONWIP lines (Masin and Prabhu, 2001a).
[FIGURE 3 OMITTED]
1.2. SPCS design tools
Queueing theory is a major tool for analyzing and designing SPCSs. Most exact models predict the performance of a single workstation or a Jacksonian network (e.g., Papadopoulos et al. (1993)). However, these models cannot easily analyze systems with multiple workstations and finite buffers; hence a variety of heuristic models have been developed (Dallery and Gershwin, 1992; Buzacott and Shanthikumar, 1993; Gershwin, 1994; Jacobs and Meerkov, 1995; Bitran and Morabito, 1996).
Theoretical methods based on sample path analysis and semi-Markov processes have been developed for identifying important structural properties of SPCSs (Mitra and Mitrani, 1990, 1991; Glasserman and Yao, 1991, 1994; Spearman, 1992; Tayur, 1992, 1993; Buzacott and Shanthikumar, 1993; Cheng and Yao, 1993; Siha, 1994; Ramesh et al., 1997; Masin et al., 1999). The main structural properties include stochastic ordering, variability ordering and stochastic convexity properties with respect to the control parameters as well as arrival and service processes.
Other interesting approaches have been taken by Hopp and Spearman (1991), Duenyas and Hopp (1992), Spearman and Zazanis (1992), Duenyas et al. (1993), Duenyas (1994), Gershwin and Goldis (1995), Jacobs and Meerkov (1995), Gstettner and Kuhn (1996), Hopp and Spearman (1996), Kuo et al. (1996), Powell and Pyke (1996), So (1997) and Dar-El et al. (1999). Hopp and Roof (1998) used statistical control for periodically updating the number of cards in a CONWIP production system.
Schor (1995) and Gershwin and Schor (2000) use gradient optimization for designing buffered lines, which is the best algorithm to date for optimization of throughput for a given buffer size (maximum WIP) or vice versa. Schor (1995) has also applied this algorithm for profit maximization where the average WIP is taken into account, and this was found to be better than the algorithm proposed by Seong et al. (1995).
The design tools described above are quite limited because they have been developed only for specific producation environments (mostly kanban and buffered lines) and specific performance measures (mostly throughput and maximum WIP). Masin et al. (2005) suggested a new heuristic optimization method called TradeOffs Programming (TOP) for SPCS design. TOP is a technique closely related to multi-objective dynamic programming that attempts to optimize inseparable problems. TOP is based on the idea that given correctly defined performance measures, many systems are nearly separable, and we can decompose the overall system using efficiency frontiers of simulated performance measures of the subsystems. TOP was found to be near-optimal, robust and applicable for designing all SPCSs in either transient or steady state for all system performance measures. However, TOP is relatively time-consuming for large-scale systems, especially in some production environments (such as assembly/disassembly systems, job shop) and production controls (such as SWIP).
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