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Solving the Quantitative Aspects of the Problem Using Optimization

Because of the supply chain complexities and rich set of quantitative data we have discussed, mathematical optimization technology is the best way to sort through the various options, balance the trade-offs, determine the best locations for facilities, and support better decision making. The mathematical optimization relies on linear and integer programming.

One common misconception we see is that managers sometimes confuse having good data and a good reporting system with having an optimal supply chain. That is, they think that their investment in good data and reporting systems should equip them with the ability to complete network design analysis. (These systems are often called business intelligence systems.) But in reality, if your warehouses or factories are located in the wrong places, these reporting systems will not correct the situation or suggest new locations.

So although these systems do, in fact, generate good reports and allow managers to gain good insights, they do not lead to better designs for the supply chain. That is, they are not built to construct models of your supply chains to which you can apply mathematical optimization. At best, they may allow you to evaluate a small handful of alternatives, but in doing so, you have to define all the details of each of the alternatives. Optimization is a complementary, not competitive, technology that allows you to actually determine the best locations for your facilities. And you can let optimization do the heavy number crunching to determine the details of the alternatives (where to locate, what is made where, how product flows, which customer is served by which warehouse). And, in many cases, if the optimization is set up correctly, it will uncover ideas that you never thought about.

Of course, because these problems are of great strategic value to an organization and touch on many aspects of the business, there will be nonquantitative aspects you must consider. These nonquantifiable aspects are important and are discussed later in this chapter and throughout the book.

With all that said, solving the quantitative aspects of this problem with mathematical optimization is the key to coming up with the best answers. So, let’s start there.

To formulate a logical supply chain network model, you need to think about the following four elements:

  • Objective
  • Constraints
  • Decisions
  • Data

The objective is the goal of the optimization and the criteria we’ll use to compare different solutions. For example, the most common objective in strategic network design is to minimize cost. If our objective is to minimize cost, we can now compare two solutions and judge which one is better based on the cost. When the mathematical optimization engine is running, it searches for the solution with the lowest cost. So with this common example you can see that an optimization problem needs to have a quantifiable objective. It is important to point this out because we have encountered many situations in which supply chain managers say their objective is to “optimize their supply chain.” The appropriate response is to ask what exactly they want to optimize, or what criteria they will use to determine which of two solutions is better. For example, is the key criteria transportation cost, is it service, is it facilities costs, or something else? Later, we’ll discuss optimizing multiple objectives (as long as you can quantify them). And we will show methods for analyzing nonquantifiable factors such as risk and robustness, because these are also very important. But for now, we’ll start with one quantifiable objective. When we understand this one, we’ll be able to understand more detailed analysis later.

The constraints define the rules of a legitimate solution. For example, if you want to just minimize cost, it is probably best to not make any products, not ship anything, or have no facilities. A cost of zero is indeed the minimum; however, that’s clearly not realistic. So there are some logical constraints we must include such as the fact that you want to meet all the demand. There are also constraints that specify which products may be made where, how much production capacity is available, how close your warehouses must be to customers, and a variety of other details. In this step, you also want to be careful not to specify so many constraints that you prohibit the optimization from finding new and creative strategies.

The decisions (sometimes called decision variables) define what you allow the optimization to choose from. So in the optimization of the physical supply chain, the main decisions include how much product moves from one location to another, how many sites are picked, where those sites are, and what product is made in which location. But, certainly, there are other decisions as well. The allowable decisions cannot be separated from the constraints. For example, if you have existing warehouses, you may or may not be able to close some of these sites.

Finally, you must consider the data you have available to you. There may be factors you would like to consider in the optimization, but you do not have the data to support. In this case, you still need to figure out ways to make a good decision. This could include running multiple scenarios, considering approximate data, or adjusting the data you have. We will further discuss a variety of these techniques later in this text.

After you have thought about your problem in terms of the objective, constraints, decisions, and data, there are ways to translate this into a series of equations and then solve the problem using linear and integer programming techniques. This is also sometimes referred to as mixed integer programming (MIP)—the “mix” refers to a mix of linear and integer variables. We will cover what this means in more detail later in the book, and will also provide information on how these problems work. There are whole courses on MIP however, so we will cover the topic only as it relates to supply chain network design problems in this text.

One way to think about a MIP is to think of it as a series of steps that are influenced by the objective, the constraints, and the decision variables. That is, during the steps, the objective steers the solution to more favorable costs and avoids less favorable costs, the constraints set the rules and can prevent it from doing more of what it wants or can force it to do something that is not favorable to the objective, and the decision variables tell it what it is allowed to change. A nice benefit of MIPs is that they solve for all the decisions and consider all the constraints simultaneously. That is, this approach allows you to come up with the overall best solution for a given problem.

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