# Scheduling (production processes)

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Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. Scheduling is used to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials.

## Contents

It is an important tool for manufacturing and engineering, where it can have a major impact on the productivity of a process. In manufacturing, the purpose of scheduling is to minimize the production time and costs, by telling a production facility when to make, with which staff, and on which equipment. But it's an academic purpose[ disputed ]. From a business point of view, the first priority purpose is to keep the customer's due date[ citation needed ]. Most major factories ask for scheduling to smooth flow production, level the production, keep safety stock, keep cycle time, or keep assigning jobs to auto-machines or lines as the next priority.

In some situations, scheduling can involve random attributes, such as random processing times, random due dates, random weights, and stochastic machine breakdowns. In this case, the scheduling problems are referred to as Stochastic scheduling.

## Overview

Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process. Companies use backward and forward scheduling to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials.

• Forward scheduling is planning the tasks from the date resources become available to determine the shipping date or the due date.
• Backward scheduling is planning the tasks from the due date or required-by date to determine the start date and/or any changes in capacity required.

The benefits of production scheduling include:

• Process change-over reduction
• Inventory reduction, leveling
• Reduced scheduling effort
• Increased production efficiency
• Labor load leveling
• Accurate delivery date quotes
• Real time information

Production scheduling tools greatly outperform older manual scheduling methods. These provide the production scheduler with powerful graphical interfaces which can be used to visually optimize real-time work loads in various stages of production, and pattern recognition allows the software to automatically create scheduling opportunities which might not be apparent without this view into the data. For example, an airline might wish to minimize the number of airport gates required for its aircraft, in order to reduce costs, and scheduling software can allow the planners to see how this can be done, by analyzing time tables, aircraft usage, or the flow of passengers.

## Key concepts in scheduling

A key character of scheduling is the productivity, the relation between quantity of inputs and quantity of output. Key concepts here are:

• Inputs : Inputs are plant, labor, materials, tooling, energy and a clean environment.
• Outputs : Outputs are the products produced in factories either for other factories or for the end buyer. The extent to which any one product is produced within any one factory is governed by transaction cost.
• Output within the factory : The output of any one work area within the factory is an input to the next work area in that factory according to the manufacturing process. For example, the output of cutting is an input to the bending room.
• Output for the next factory : By way of example, the output of a paper mill is an input to a print factory. The output of a petrochemicals plant is an input to an asphalt plant, a cosmetics factory and a plastics factory.
• Output for the end buyer : Factory output goes to the consumer via a service business such as a retailer or an asphalt paving company.
• Resource allocation : Resource allocation is assigning inputs to produce output. The aim is to maximize output with given inputs or to minimize quantity of inputs to produce required output.

## Scheduling algorithms

Production scheduling can take a significant amount of computing power if there are a large number of tasks. Therefore, a range of short-cut algorithms (heuristics) (a.k.a. dispatching rules) are used:

## Batch production scheduling

### Background

Batch production scheduling is the practice of planning and scheduling of batch manufacturing processes. See Batch production. Although scheduling may apply to traditionally continuous processes such as refining, [1] [2] it is especially important for batch processes such as those for pharmaceutical active ingredients, biotechnology processes and many specialty chemical processes. [3] [4] Batch production scheduling shares some concepts and techniques with finite capacity scheduling which has been applied to many manufacturing problems. [5] The specific issues of scheduling batch manufacturing processes have generated considerable industrial and academic interest.

### Scheduling in the batch processing environment

A batch process can be described in terms of a recipe which comprises a bill of materials and operating instructions which describe how to make the product. [6] The ISA S88 batch process control standard [7] provides a framework for describing a batch process recipe. The standard provides a procedural hierarchy for a recipe. A recipe may be organized into a series of unit-procedures or major steps. Unit-procedures are organized into operations, and operations may be further organized into phases.

The following text-book recipe [8] illustrates the organization.

• Charge and Mix materials A and B in a heated reactor, heat to 80C and react 4 hours to form C.
• Transfer to blending tank, add solvent D, Blend 1hour. Solid C precipitates.
• Centrifuge for 2 hours to separate C.
• Dry in a tray dryer for 1 hour.

A simplified S88-style procedural organization of the recipe might appear as follows:

• Unit Procedure 1: Reaction
• Operation 1: Charge A & B (0.5 hours)
• Operation 2: Blend / Heat (1 hour)
• Operation 3: Hold at 80C for 4 hours
• Operation 4: Pump solution through cooler to blend tank (0.5 hours)
• Operation 5: Clean (1 hour)
• Unit Procedure 2: Blending Precipitation
• Operation 1: Receive solution from reactor
• Operation 2: Add solvent, D (0.5 hours)
• Operation 3: Blend for 2 hours
• Operation 4: Pump to centrifuge for 2 hours
• Operation 5: Clean up (1 hour)
• Unit Procedure 3: Centrifugation
• Operation 1: Centrifuge solution for 2 hours
• Operation 2: Clean
• Unit Procedure 4: Tote
• Operation 1: Receive material from centrifuge
• Operation 2: Load dryer (15 min)
• Unit Procedure 5: Dry
• Operation 1: Load
• Operation 2: Dry (1 hour)

Note that the organization here is intended to capture the entire process for scheduling. A recipe for process-control purposes may have a more narrow scope.

Most of the constraints and restrictions described by Pinedo [9] are applicable in batch processing. The various operations in a recipe are subject to timing or precedence constraints that describe when they start and or end with respect to each other. Furthermore, because materials may be perishable or unstable, waiting between successive operations may be limited or impossible. Operation durations may be fixed or they may depend on the durations of other operations.

In addition to process equipment, batch process activities may require labor, materials, utilities and extra equipment.

### Cycle-time analysis

In some simple cases, an analysis of the recipe can reveal the maximum production rate and the rate limiting unit. In the process example above if a number of batches or lots of Product C are to be produced, it is useful to calculate the minimum time between consecutive batch starts (cycle-time). If a batch is allowed to start before the end of the prior batch the minimum cycle-time is given by the following relationship: [10]

${\displaystyle CT_{min}={\begin{matrix}max\\j=1,M\end{matrix}}\lbrace \tau _{j}\rbrace }$

Where CTmin is the shortest possible cycle time for a process with M unit-procedures and τj is the total duration for the jth unit-procedure. The unit-procedure with the maximum duration is sometimes referred to as the bottleneck. This relationship applies when each unit-procedure has a single dedicated equipment unit.

If redundant equipment units are available for at least one unit-procedure, the minimum cycle-time becomes:

${\displaystyle CT_{min}={\begin{matrix}max\\j=1,M\end{matrix}}\lbrace \tau _{j}/N_{j}\rbrace }$

Where Nj is the number of redundant equipment for unit procedure j.

If equipment is reused within a process, the minimum cycle-time becomes more dependent on particular process details. For example, if the drying procedure in the current example is replaced with another reaction in the reactor, the minimum cycle time depends on the operating policy and on the relative durations of other procedures. In the cases below, an increase in the hold time in the tote can decrease the average minimum cycle time.

### Visualization

Various charts are used to help schedulers visually manage schedules and constraints. The Gantt chart is a display that shows activities on a horizontal bar graph in which the bars represent the time of the activity. Below is an example of a Gantt chart for the process in the example described above.

Another time chart which is also sometimes called a Gantt chart [11] shows the time during which key resources, e.g. equipment, are occupied. The previous figures show this occupancy-style Gantt chart.

Resources that are consumed on a rate basis, e.g. electrical power, steam or labor, are generally displayed as consumption rate vs time plots.

### Algorithmic methods

When scheduling situations become more complicated, for example when two or more processes share resources, it may be difficult to find the best schedule. A number of common scheduling problems, including variations on the example described above, fall into a class of problems that become very difficult to solve as their size (number of procedures and operations) grows. [12]

A wide variety of algorithms and approaches have been applied to batch process scheduling. Early methods, which were implemented in some MRP systems assumed infinite capacity and depended only on the batch time. Such methods did not account for any resources, and would produce infeasible schedules. [13]

Mathematical programming methods involve formulating the scheduling problem as an optimization problem where some objective, e.g. total duration, must be minimized (or maximized) subject to a series of constraints which are generally stated as a set of inequalities and equalities. The objective and constraints may involve zero-or-one (integer) variables as well as nonlinear relationships. An appropriate solver is applied for the resulting mixed-integer linear or nonlinear programming (MILP/MINLP) problem. The approach is theoretically guaranteed to find an optimal solution if one exists. The disadvantage is that the solver algorithm may take an unreasonable amount of time. Practitioners may use problem-specific simplifications in the formulation to get faster solutions without eliminating critical components of the scheduling model. [14]

Constraint programming is a similar approach except that the problem is formulated only as a set of constraints and the goal is to arrive at a feasible solution rapidly. Multiple solutions are possible with this method. [15] [16]

Agent-based modeling describes the batch process and constructs a feasible schedule under various constraints. [17] By combining with mixed-integer programming or simulated-based optimization methods, this approach could achieve a good balance between the solution efficiency and the schedule performance. [18]

## Related Research Articles

Computerized batch processing is the running of "jobs that can run without end user interaction, or can be scheduled to run as resources permit."

A workflow consists of an orchestrated and repeatable pattern of activity, enabled by the systematic organization of resources into processes that transform materials, provide services, or process information. It can be depicted as a sequence of operations, the work of a person or group, the work of an organization of staff, or one or more simple or complex mechanisms.

Managerial economics is a branch of economics which deals with the application of the economic concepts, theories, tools, and methodologies to solve practical problems in a business these business decisions not only affect daily decisions, also affects the economic power of long-term planning decisions, its theory is mainly around the demand, production, cost, market and so on several factors. In other words, managerial economics is a combination of economics theory and managerial theory. It helps the manager in decision-making and acts as a link between practice and theory. It is sometimes referred to as business economics and is a branch of economics that applies microeconomic analysis to decision methods of businesses or other management units.

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers. It is used to empirically measure productive efficiency of decision making units (DMUs). Although DEA has a strong link to production theory in economics, the tool is also used for benchmarking in operations management, where a set of measures is selected to benchmark the performance of manufacturing and service operations. In benchmarking, the efficient DMUs, as defined by DEA, may not necessarily form a “production frontier”, but rather lead to a “best-practice frontier”.

A chemical plant is an industrial process plant that manufactures chemicals, usually on a large scale. The general objective of a chemical plant is to create new material wealth via the chemical or biological transformation and or separation of materials. Chemical plants use specialized equipment, units, and technology in the manufacturing process. Other kinds of plants, such as polymer, pharmaceutical, food, and some beverage production facilities, power plants, oil refineries or other refineries, natural gas processing and biochemical plants, water and wastewater treatment, and pollution control equipment use many technologies that have similarities to chemical plant technology such as fluid systems and chemical reactor systems. Some would consider an oil refinery or a pharmaceutical or polymer manufacturer to be effectively a chemical plant.

Operations management is an area of management concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services. It involves the responsibility of ensuring that business operations are efficient in terms of using as few resources as needed and effective in terms of meeting customer requirements. Operations management is primarily concerned with planning, organizing and supervising in the contexts of production, manufacturing or the provision of services.

A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling, and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity.

The genetic algorithm is an operational research method that may be used to solve scheduling problems in production planning.

A master production schedule (MPS) is a plan for individual commodities to be produced in each time period such as production, staffing, inventory, etc. It is usually linked to manufacturing where the plan indicates when and how much of each product will be demanded. This plan quantifies significant processes, parts, and other resources in order to optimize production, to identify bottlenecks, and to anticipate needs and completed goods. Since a MPS drives much factory activity, its accuracy and viability dramatically affect profitability. Typical MPSs are created by software with user tweaking.

Job shop scheduling or the job-shop problem (JSP) is an optimization problem in computer science and operations research in which jobs are assigned to resources at particular times. The most basic version is as follows: We are given n jobs J1J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan. The makespan is the total length of the schedule.

Manufacturing execution systems (MES) are computerized systems used in manufacturing to track and document the transformation of raw materials to finished goods. MES provides information that helps manufacturing decision makers understand how current conditions on the plant floor can be optimized to improve production output. MES works in real time to enable the control of multiple elements of the production process.

A glossary of terms relating to project management and consulting.

Industrial engineering is an engineering profession that is concerned with the optimization of complex processes, systems, or organizations by developing, improving and implementing integrated systems of people, money, knowledge, information, equipment, energy and materials.

OptiY is a design environment providing modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling.

AIMMS is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore.

Kimeme is an open platform for multi-objective optimization and multidisciplinary design optimization. It is intended to be coupled with external numerical software such as computer-aided design (CAD), finite element analysis (FEM), structural analysis and computational fluid dynamics tools. It was developed by Cyber Dyne Srl and provides both a design environment for problem definition and analysis and a software network infrastructure to distribute the computational load.

Industrial and production engineering (IPE) is an interdisciplinary engineering discipline that includes manufacturing technology, engineering sciences, management science, and optimization of complex processes, systems, or organizations. It is concerned with the understanding and application of engineering procedures in manufacturing processes and production methods. Industrial engineering dates back all the way to the industrial revolution, initiated in 1700s by Sir Adam Smith, Henry Ford, Eli Whitney, Frank Gilbreth and Lilian Gilbreth, Henry Gantt, F.W. Taylor, etc. After the 1970s, industrial and production engineering developed worldwide and started to widely use automation and robotics. Industrial and production engineering includes three areas: Mechanical engineering, industrial engineering, and management science.

In production and project management, a bottleneck is one process in a chain of processes, such that its limited capacity reduces the capacity of the whole chain. The result of having a bottleneck are stalls in production, supply overstock, pressure from customers, and low employee morale. There are both short and long-term bottlenecks. Short-term bottlenecks are temporary and are not normally a significant problem. An example of a short-term bottleneck would be a skilled employee taking a few days off. Long-term bottlenecks occur all the time and can cumulatively significantly slow down production. An example of a long-term bottleneck is when a machine is not efficient enough and as a result has a long queue.

Production planning is the planning of production and manufacturing modules in a company or industry. It utilizes the resource allocation of activities of employees, materials and production capacity, in order to serve different customers.

Theory of constraints (TOC) is an engineering management technique used to evaluate a manageable procedure, identifying the largest constraint (bottleneck) and strategizing to reduce task time and maximise profit. It assists in determining what to change, when to change it, and how to cause the change. The theory was established by Dr. Eliyahu Goldratt through his 1984 bestselling novel The Goal. Since this time, TOC has continued to develop and evolve and is a primary management tool in the engineering industry. When Applying TOC, powerful tools are used to determine the constraint and reduce its effect on the procedure, including:

## References

1. Marcus V. Magalhaes and Nilay Shah, “Crude Oil Scheduling,” Foundations of Computer-Aided Operations (FOCAPO) 2003,pp 323-325.
2. Zhenya Jia and Marianthi Ierapetritou, “Efficient Short-Term Scheduling of Refinery Operation Based on a Continuous Time Formulation,” Foundations of Computer-Aided Operations (FOCAPO) 2003, pp 327-330
3. Toumi, A., Jurgens, C., Jungo, C., MAier, B.A., Papavasileiou, V., and Petrides, D., “Design and Optimization of a Large Scale Biopharmaceutical Facility using Process Simulation and Scheduling Tools,” Pharmaceutical Engineering (the ISPE magazine) 2010, vol 30, no 2, pp 1-9.
4. Papavasileiou, V., Koulouris, A., Siletti, C., and Petrides, D., “Optimize Manufacturing of Pharmaceutical Products with Process Simulation and Production Scheduling Tools,” Chemical Engineering Research and Design (IChemE publication) 2007, vol 87, pp 1086-1097
5. Michael Pinedo, Scheduling Theory, Algorithms, and Systems,Prentice Hall, 2002,pp 1-6.
6. T. F. Edgar, C.L. Smith, F. G. Shinskey, G. W. Gassman, P. J. Schafbuch, T. J. McAvoy, D. E. Seborg, Process control, Perry’s Chemical Engineer’s Handbook, R. Perry and D. W. Green eds.,McGraw Hill, 1997,p 8-41.
7. Charlotta Johnsson, S88 for Beginners, World Batch Forum, 2004.
8. L.T. Biegler, I. E. Grossman and A. W. Westerberg, Systematic Methods of Chemical Process Design, Prentice Hall, 1999 p181.
9. M. Pinedo, 2002, pp 14-22.
10. Biegler et al. 1999, p187
11. M. Pinedo, 2002, p430
12. M. Pinedo, 2002, p28
13. G. Plenert and G/ Kirchmier, 2000, pp38-41
14. C. Mendez, J. Cerda, I. Grossman, I. Harjunkoski, M. Fahl, State of the art Review of Optimization Methods for Short Term Scheduling of Batch Processes, Computers and Chemical Engineering, 30 (2006), pp 913-946
15. I. Lustig, Progress in Linear and Integer Programming and Emergence of Constraint Programming, Foundations of Computer-Aided Operations (FOCAPO) 2003, 133-151
16. L. Zeballos and G.P. Henning, A Constraint Programming Approach to the Multi-Stage Batch Scheduling Problem, Foundations of Computer-Aided Operations (FOCAPO), 2003, 343-346
17. Chu, Yunfei; You, Fengqi; Wassick, John M. (2014). "Hybrid method integrating agent-based modeling and heuristic tree search for scheduling of complex batch processes". Computers & Chemical Engineering. 60: 277–296. doi:10.1016/j.compchemeng.2013.09.004.
18. Chu, Yunfei; Wassick, John M.; You, Fengqi (2013). "Efficient scheduling method of complex batch processes with general network structure via agent-based modeling". Aiche Journal. 59 (8): 2884–2906. doi:10.1002/aic.14101.
• Blazewicz, J., Ecker, K.H., Pesch, E., Schmidt, G. und J. Weglarz, Scheduling Computer and Manufacturing Processes, Berlin (Springer) 2001, ISBN   3-540-41931-4
• Herrmann, Jeffrey W., editor, 2006, Handbook of Production Scheduling, Springer, New York.
• McKay, K.N., and Wiers, V.C.S., 2004, Practical Production Control: a Survival Guide for Planners and Schedulers, J. Ross Publishing, Boca Raton, Florida. Co-published with APICS.
• Pinedo, Michael L. 2005. Planning and Scheduling in Manufacturing and Services, Springer, New York.
• Conway, Richard W., Maxwell, William L., Miller, Louis W., Theory of Scheduling, Dover Publications June 2003, ISBN   978-0486428178