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Quantitative Elements of Building Network Optimization Models

Supply chains are extremely complex and the amount of associated data captured to describe them is exceptionally large.  How do we take all of this data and use it to develop a supply chain strategy?  After the data is validated and cleansed, it is loaded into a sophisticated network optimization software.  This software is utilized to sort through many possibilities to determine the recommended solution and strategy (for example – where are the optimal number and location of facilities, their mission and size).  There are certainly many qualitative aspects that need to be considered, but first, the network optimization software must analyze the mathematical problem at hand.  Today, I would like to review the 3 types of quantitative elements utilized to help inform the network optimization software and ultimately determine a go forward supply chain strategy.


The objective is simply the quantitative goal of the network optimization. Remember, we are using a highly sophisticated optimization engine.  An objective function is required to set up the solver. We cannot simply “optimize” the supply chain or “fix” a supply chain.  We also use this objective function to compare various alternatives.  For example, the most common objective in strategic network design is minimizing cost.  With this objective, it is easy to compare different networks.  For example, how does a 3 warehouse network compare to a 4 warehouse network?  Another objective we often use is service.  Specifically, we would set an objective such as “95% of the demand must be within 400 miles of a DC”.   In this case, we can determine the number of distribution centers needed to meet that objective.  Sometimes we optimize on multiple objectives (but we must be able to quantify them).  For example, we may ask the model to solve for the lowest cost answer within 0.5% (objective 1) while minimizing the average distance to customer (objective 2).

Decision Variables

Decisions or decision variables are those variables from which the optimization decides to pick. The model makes decisions such as how much volume should be serviced from each facility to each customer, where the facilities should be located, how many facilities you should have, etc. These decisions are often very closely tied to the constraints.


Constrains are the business rules that must be obeyed in order for a realistic solution.  For example, you could choose to not service any customer demand and get a very low cost.  However, this would not be practical.  So a key constraint would be to satisfy all demand (or have a financial penalty for not servicing demand). Other constraints could be the maximum capacity of a facility (space, throughput or production quantity), product eligibility (which facilities can produce which products), or the amount of product required to open up a facility. However, it is important to not “over-constrain” the model as to prevent the optimization from finding a unique solution or no solution at all (i.e. an infeasible solution).

After the objective, decision variables and constraints are determined, the model writes a series of equations to solve the problem at hand.  The optimization solver will then consider all the constraints and decisions simultaneously to output the best solution based on the objective set.  Finally, the various solutions are compared and contrasted quantitatively and qualitatively to determine a recommended solution for a businesses’ supply chain.
—Brad Barry, St. Onge Company

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