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Optimization approaches – Integer and Mixed Integer Programming

Two optimization approaches, developed by operations research and the management sciences, have been incorporated into the technology toolbox of SCM. They fall into the categories of optimal solutions and heuristic solutions, and both are proving to be beneficial to the planning and execution activities of SCM.

 Optimal Techniques

Optimal techniques are based on mathematical algorithms that use a series of formulae to represent the variables and constraints of the problem and generate a result based on the goal of maximizing or minimizing some objective function.

Linear Programming

Linear programming models are used for problems in which linear equations can be used to define the objectives and constraints of the SCM planning problem. This problem-solving method results in an optimal solution. A simple example of the type of problem this approach is used follows.

Heuristic Solutions

Heuristic solutions for addressing SCM planning are based on various models, rules of thumb, and the concept of intelligent trial and error to improve the solution results. Beginning with a known feasible solution to the problem, the heuristic approach follows rules to incrementally modify the variables in the problem and then analyze the results (feedback). If the objective improves, the process is repeated. This continues until the objective no longer gets better. This approach will produce an optimized solution, but not necessarily the optimal solution

Genetic Algorithms

Genetic algorithms work well on mixed (continuous and discrete) problems. The process looks for optimized solutions from a large set of possible solutions. These are crossbred or mutated to form new sets of solutions. This continues from one generation to the next until a reasonably optimized solution is developed. Processing genetic algorithms can be computation-intensive, but they generally work better than other approaches for certain types of optimization problems.

Simulated Annealing

This technique for optimizing solutions is based on a theory from statistical mechanics. It works by stimulating the process nature performs in optimizing the energy of a crystalline solid, when it is annealed to remove defects in its atomic arrangement. It is used to approximate the solution of very large optimization problems and works well with nonlinear objectives and arbitrary constraints. One criticism, however, is that it can be slow in determining an optimal solution.

Exhaustive Enumeration

This process involves looking at all possible alternatives to find the best solution and is therefore only used when there are few variable alternatives to evaluate. It takes an enormous amount of computing power to evaluate all possible combinations of a complex problem. Most SCM problems are too large for this approach. Even with today’s supercomputers, they cannot be completely enumerated in polynomial time.

It infrastructure

IT infrastructure is made up of the underlying technology products on which the SCM technologies run. It consists of networks, databases, and application interfaces that support supply chain information flows and that allow supply chain applications to communicate with other applications. These building blocks provide the key to being able to take advantage of the many supply chain products and services available in the marketplace.

Last word

Companies need to be alert to the technologies that will make them either winners or losers in this new supply chain environment. Supply chain management has emerged as one.

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