Optimization

The heart of APS systems are advanced mathematical algorithms and logic. The mathematics formulate busi­ness problems and solve them to a selected objective function. The challenge is to formulate the problem in discrete terms that characterize the reality of the supply chain's physical attributes and capability then solve it in a reasonable time frame. The answer must satisfy all constraints (capacity, labor, inventory storage, lead times) while using available variables.

Optimization Objectives

Business optimization objective functions can be lowest cost, highest profit, greatest return on assets/investment, or highest customer service. Different objectives are picked for strategic, tactical, and operational planning.

Problem Size

The problem size grows very large because of the mul­tiple effect of combining the number of products, con­straints, variables, work centers, and time buckets. Older technologies were selected because they were able to generate solutions within a reasonable time frame. Ba­sically, they employed simplifying methods to increase solve time. This simplification made the solutions less accurate, less optimal. However, new mathematical methods have greatly improved the solve times. That, in combination with faster computers, has now made accurate representation of the problem possible with­out the earlier simplification sacrifices.

Optimization Technologies

Now and into the future technologies will be combined to accomplish three things: better representation of reality, faster solve times, and an easier way for the user to ab­stractly formulate the business problems in the models.

Finite Capacity Scheduling

The area that will benefit the most from enhancement in these technologies is finite capacity scheduling. These problems are the most complex mathematical problems known to man. Ever-tightening constraints, increasing customer expectation, and shorter lead times will ulti­mately put more pressure on technologies to solve tougher scheduling problems.

Discrete Representation

Bottlenecks in manufacturing float because different rocks pop to the surface at different times. If constrain­ing resources are not represented in the model, then there is no visibility of the bottleneck. Future models will include more constraints that would have overcom­plicated the models in the past, which possibly made them impossible to solve.

Simultaneously Solve

One of the classic techniques used to solve complex models is to treat certain variables as constants and solve for one variable at a time, causing the user to manually iterate the problems to solve for "real" variables. It is not uncommon to have three or more variables that exist in a scheduling problem. Future PCS tools will solve all existing variables simultaneously. Four key ones are lot size, sequence, multilevel coordination, and sourcing. These are all necessarily interdependent.

Alphabet Soup

APS models will take a broader look at the supply chain, as well as automate the solution of many parts at the same time. This will minimize the whipsaw affect illus­trated by the Beer Game.

Continued

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