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Many theories and commercial software solutions for Advanced Planning and Scheduling, known as APS, have appeared over the years. Ultimately, scheduling systems strive to answer the question of “When should this task be scheduled and what resources should accomplish the work?” This paper examines the available methods for quickly creating production plans and schedules for manufacturers to meet their business objectives.

The Basic Theories

Most APS software uses either:

1. “Rules-based” methods for assigning tasks to resources. These methods are also some1. times called “heuristic” or “deterministic” methods. One advantage of these methods is that the calculated results will be the same for a given input state, making it easier for software users to understand the decision-making process of the rules-based engine. These methods are also well-suited to complex scheduling problems which have many constraints that need to be followed. Rules-based scheduling also allows for “incremental change” of schedules, for example enabling a given task to be manually repositioned by the program user. A downside to rules-based solutions is that they do not guarantee the best possible solution. Also, they often rely on experimentation to determine which rules would deliver the best results for a given set of inputs.
2. “Optimization” based methods seek to minimize or maximize a mathematical objective, with the idea that the “best” results are output for each planning run. Typically, cost or penalty factors must be assigned for use by the optimization function. It can be difficult for users to understand why individual decisions regarding tasks and resources are made, so results can seem counter-intuitive at a detailed level (though in theory the “big-picture” is optimized.) Furthermore, only known variables can be optimized, and the exclusion of an important factor can give unusable results in the real-world. If conditions in the real-world fluctuate, it is common to have to adjust the cost-factors for the optimization engine – resulting in more work for the end user. In practice, optimization-based techniques such as linear programming may be better suited to more static situations where the factors are easily understood. There are other important limitations to using optimization techniques such as linear programming for scheduling problems. It can be very time consuming to build and maintain constraint models and require a high degree of expertise. In addition, there are a wide variety of real-world scenarios that simply cannot be handled by this approach such as sequence-dependent setup times and continuous-time scheduling.

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