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Finite Scheduling The process for scheduling that we have described thus far in this chapter, loading work into work centers, leveling the load, sequencing the work, and monitoring its progress, is called infinite scheduling. The term infinite is used because the initial loading process assumes infinite capacity. Leveling and sequencing decisions are made after overloads or underloads have been identified. This iterative process is timeconsuming and not very efficient. An alternative approach to scheduling called finite scheduling assumes a fixed maximum capacity and will not load the resource beyond its capacity. Loading and sequencing decisions are made at the same time, so that the first jobs loaded onto a work center are of highest priority. Any jobs remaining after the capacity of the work center or resource has been reached are of lower priority and are scheduled for later time periods. This approach is easier than the infinite scheduling approach, but it will be successful only if the criteria for choosing the work to be performed, as well as capacity limitations, can be expressed accurately and concisely. Finite scheduling systems use a variety of methods to develop their schedules, including mathematical programming, network analysis, simulation, and expert systems or other forms of artificial intelligence. Because the scheduling system is making the decisions and not the human scheduler, companies may find it difficult to purchase a system off the shelf that can embody their specific manufacturing environment or can be readily updated as changes in the environment occur. Finite schedulers are becoming more popular as software systems become more adaptable and easier to use and as manufacturing environments are simplified and are better understood. There are several finite schedulers available. One of the oldest is IBM's CAPOSS (Capacity Planning and Operations Sequencing System). ISIS, developed at Carnegie-Mellon, was one of the first schedulers to use artificial intelligence. Another prominent finite scheduling system is synchronous manufacturing.
Synchronous Manufacturing In the 1970s, an Israeli physicist named Eliyahu Goldratt responded to a friend's request for help in scheduling his chicken coop business. Lacking a background in manufacturing or production theory, Dr. Goldratt took a commonsense, intuitive approach to the scheduling problem. He developed a software system that used mathematical programming and simulation to create a schedule that realistically considered the constraints of the manufacturing system. The software produced good schedules quickly and was marketed in the early 1980s in the United States. After more than 100 firms had successfully used the scheduling system (called OPT), the creator sold the rights to the software and began marketing the theory behind the software instead. He called his approach to scheduling the theory of constraints. General Motors and other manufacturers call its application synchronous manufacturing. Decision making in manufacturing is often difficult because of the size and complexity of the problems faced. Dr. Goldratt's first insight into the scheduling problem led him to simplify the number of variables considered. He learned early that manufacturing resources typically are not used evenly. Instead of trying to balance the capacity of the manufacturing system, he decided that most systems are inherently unbalanced and that he would try to balance the flow of work through the system instead. He identified resources as bottleneck or nonbottleneck and observed that the flow through the system is controlled by the bottleneck resources. These resources should always have material to work on, should spend as little time as possible on nonproductive activities (e.g., setups, waiting for work), should be fully staffed, and should be the focus of improvement or http://www.prenhall.com/divisions/bp/app/russellcd/PROTECT/CHAPTERS/CHAP14/HEAD05.HTM
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automation efforts. Goldratt pointed out that an hour's worth of production lost at a bottleneck reduces the output of the system by the same amount of time, whereas an hour lost at a nonbottleneck may have no effect on system output.
THE COMPETITIVE EDGE Constraint-Based Scheduling at Flow International Flow International manufactures high-pressure waterjet systems for commercial customers in the paper, food, automotive, and aerospace industries. The systems are used to cut a variety of products from disposable diapers to titanium. Units can cost upward of $500,000, contain hundreds of parts, and require a special alloy with a six-month lead time. Because of their diverse applications, customization is routine and product designs change frequently. Business is good for Flow--in two years, sales have grown from $42 million to $110 million. On-time delivery is important but, with peak demand, is increasingly harder to achieve. Customers demand a turnaround of just one day on spare parts and one week for complete systems. The company employs a highly skilled workforce of 700 individuals organized into 80 work centers, 13 of which utilize CNC equipment. New equipment investment averages $2 million annually. How do you schedule production to ship products on time when dealing with multiple resources, an extensive bill of material, and changing and diverse products? Flow chose the theory of constraints to address these challenges. The production system is too large, interrelated, and dynamic to schedule optimally. It is even too complex to consider all products or all work centers. With the theory of constraints, only the bottleneck operations need to be considered because the most critical resources determine the overall capacity of a plant. Maximizing the throughput of bottlenecks will maximize the throughput of the entire plant. Applying constraint-based scheduling, Flow reduced lot sizes, scheduled bottleneck work centers near to 100% capacity, and underscheduled nonbottleneck work centers to match the output of the bottleneck work centers. Work-in-process inventory decreased by 50% and finished goods inventory by 25%. Orders are completed faster, and new equipment purchases are targeted at relieving bottleneck resources. In addition, costs are down with more rational overtime and outsourcing decisions. Source: Michael Gadbois "Shipments Flow Smoothly at Flow International," IIE Solutions (March 1996): 40-43.
From this realization, Goldratt was able to simplify the scheduling problem significantly. He concentrated initially on scheduling production at bottleneck resources and then scheduled the nonbottleneck resources to support the bottleneck activities. Thus, production is synchronized, or "in sync," with the needs of the bottleneck and the system as a whole. Goldratt's second insight into manufacturing concerned the concept of lot sizes or batch sizes. Goldratt saw no reason for fixed batch sizes. He differentiated between the quantity in which items are produced, called the process batch, and the quantity in which the items are transported, called the transfer batch. Ideally, items http://www.prenhall.com/divisions/bp/app/russellcd/PROTECT/CHAPTERS/CHAP14/HEAD05.HTM
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should be transferred in lot sizes of one. The process batch size for bottlenecks should be large, to eliminate the need for setups. The process batch size for nonbottlenecks can be small because time spent in setups for nonbottlenecks does not affect the rest of the system. The following example illustrates these concepts.
EXAMPLE 14.5
Synchronous Manufacturing
The following diagram contains the product structure, routing, and processing time information for product A. The process flows from the bottom of the diagram upward. Assume one unit of items B, C, and D are needed to make each A. The manufacture of each item requires three operations at machine centers 1, 2, or 3. Each machine center contains only one machine. A machine setup time of 60 minutes occurs whenever a machine is switched from one operation to another (within the same item or between items). Design a schedule of production for each machine center that will produce 100 A's as quickly as possible. Show the schedule on a Gantt chart of each machine center. Use the following synchronous manufacturing concepts:
1. Identify the bottleneck machine. 2. To keep the bottleneck busy, schedule the item first whose lead time to the bottleneck is less than or equal to the bottleneck processing time. 3. Forward schedule the bottleneck machine. 4. Backward schedule the other machines to sustain the bottleneck schedule. 5. Remember that the transfer batch size does not have to match the process batch size. SOLUTION: The bottleneck machine is identified by summing the processing times of all operations to be performed at a machine.
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Machine 2 is identified as the bottleneck, so we schedule machine 2 first. From the product structure diagram, we see three operations that are performed at machine 2-B2, C3, and D2. If we schedule item B first, a B will reach machine 2 every 5 minutes (since B has to be processed through machine 1 first), but each B takes only 3 minutes to process at machine 2, so the bottleneck will be idle for 2 minutes of every 5 minutes. That is not keeping our bottlenecks busy. A similar result occurs if we schedule item D first on machine 2. The bottleneck will be idle for 2 minutes out of every 10 minutes until D has finished processing. The best alternative is to schedule item C first. The first C will not reach machine 2 until time 12, but after that a C will be waiting for the bottleneck machine, because it takes longer for C to be processed through machine 2 than through the first two machines in C's routing sequence combined. We begin our Gantt charts by processing item C through the three machine centers. Before we continue, a few comments about the Gantt charts are needed. The charts will look different from our earlier Gantt charts because we will allow each item to be transferred to the next operation immediately after it is completed at the current operation (i.e., the transfer batch size is 1). We will process the items in batches of 100 to match our demand requirements. The red shaded areas represent idle time between operations due to setup time requirements or because a feeding operation has not yet been completed. Refer to the Gantt charts in Figure 14.2 for the remainder of the discussion. C3 is completed at machine center 2 at time 1512. After setup, it is ready for a new item at time 1572. We have a choice between B2 and D2, since both B1 and D1 can be completed by 1572. Completion time at machine center 2 will be the same regardless of whether B2 or D2 is processed first; however, the completion time at the other machine centers (and thus for product A) will be affected by the bottleneck sequence. From the product structure diagram, we note that B3 can be completed more quickly than D3 because D3 must wait 3 minutes for D2 to be completed, whereas B3 will always have a queue of items from B2 to work on. Thus, we schedule B2 and then D2 on machine center 2. With the bottleneck sequence of C3, B2, D2 established, we can now schedule machine center 1 (C2, B1, B3) and machine center 3 (C1, D1, D3). The completion time for producing 100 A's is 2,737 minutes. The total idle time at the three machine centers is 980 minutes.
14-9. Explain the difference between infinite and finite scheduling. 14-10. How does synchronized manufacturing differ from traditional scheduling? *14-11. Find out more about the Theory of Constraints and its creator, Goldratt. What is unique about this http://www.prenhall.com/divisions/bp/app/russellcd/PROTECT/CHAPTERS/CHAP14/HEAD05.HTM
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approach to scheduling? What do you find most interesting about it? Relate several success stories. *14-12. Examine Pritsker's advanced scheduling systems. What options are available? How is finite scheduling defined? *These exercises require a direct link to a specific Web site. Click Internet Exercises for the list of internet links for these exercises.
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