Supply chain network design in 500 words

I’ve spent more time working on supply chain network (SCN) design problems than any other. This post summarizes the topic.

What is supply chain network design?

SCN design is a strategic problem arising in logistics and supply chain management. Typical SCN design problems involves strategic decisions on the number, location, capacity and missions of the production and distribution facilities a company should use to provide goods to a set of potential markets. It generalizes classical problems such as the facility location problem (and its hundreds of variants) and the multicommodity network design problem, among others. It usually takes the form of a large mixed-integer linear model.

What are the benefits?

The benefits of going through a supply chain design modeling effort are well documented. Over the 1970s to 1990s Arthur Geoffrion and his colleagues did more than 50 of these studies in various companies and governments (their experiences can be found in [1]). They would typically achieve a cost reduction of 5% to 15% while maintaining or improving customer service. Very recent data from the University of Tennessee’s Global Supply Chain Institute estimated the savings of supply chain redesign at the exact same 5-15% range [2]. In some companies, logistics account for up to 50% of the total cost of goods sold; -10% means huge savings.

Why is this problem not “solved” yet?

It may be surprising to some that the savings reported in 2013 are similar to those experienced in the 1990s. While there is now better technology to support supply chain design projects, the stakes are also higher than they have ever been. With global sourcing and offshoring, supply chains have grown bigger, and in many cases, longer. They have also become more complex: more products, more SKUs per product, using different channels for different products, etc. Although we now have more IT than ever (enterprise resource planning systems), gathering, analyzing and formatting data so it will fit the needs of strategic planning is always somewhat of a challenge. In a typical SCN design project, this is where you would spend the bulk of your time.

So, what’s the best model?

There is no “best” model, as the most complex is not always the most appropriate. Strategic problems are always a bit tricky to model. What to include, what not to include really depends on the context of the organization. There are many alternative ways to model some decisions, and selecting a different model may very well lead you to a very different (yet optimal) design! As logistics trade-offs alyways seem to revolve around cost versus speed (aka transporation) these days, your model should at least cover that part quite well. If you live by the number of citations, to the best of my knowledge, the most cited paper was published in 1974 [3] in Management Science and has been cited more than 1080 times. Small or simple SCN design models may be solved to optimality by the best MIP solvers. For the larger and more complex problems, specialized algorithms are required; Benders’ decomposition, Lagrangian relaxation and metaheuristics have been popular in the last 20 years. [1] A.M. Geoffrion and R.F. Powers (1995). Twenty Years of Strategic Distribution System Design: An Evolutionary Perspective, Interfaces 25:5, 105-127. [2] J. Paul Dittmann, Supply Chain Transformation, 2013, FT Press. [3] A.M. Geoffrion and G.W. Graves (1974). Multicommodity distribution system design by Benders decomposition, Management Science 20:5, 822-844.

LP file format: uses and intricacies

LP is one of the most popular formats for explicit description of an optimization model (the other contender being MPS). It uses an algebraic format where you enter the problem’s objective function and constraints line by line. For the last few years I’ve been using that format quite regularly, and I’d say I both hate and like it.  Here is an example taken from the LPSolve documentation:

Maximize
 obj: x1 + 2 x2 + 3 x3 + x4
Subject To
 c1: - x1 + x2 + x3 + 10 x4 <= 20
 c2: x1 - 3 x2 + x3 <= 30
 c3: x2 - 3.5 x4 = 0
Bounds
 0 <= x1 <= 40
 2 <= x4 <= 3
General
 x4
End

Pros

  • LP file format is really easy to read and write.
  • Most mathematical programming solvers are able to read the format (but see con’s below).

Cons

  • The format’s syntax is a bit fuzzy. Each solver has its own implementation. For instance, CPLEX allows you to omit spaces between coefficients and variables (as in 2X_4) whereas in Gurobi you have to put a space (2 X_4). CPLEX and Gurobi allow unnamed constraints, while Sulum requires you to name each constraint.
  • Large models equals very large files, especially when compared to more compact formats such as AMPL.

Uses for LP files

I use LP files for three things, mostly:

  1. Toy models. It’s really easy and quick to write LP files. If a model is small enough to be written by hand, I’ll use LP.
  2. Prototyping. The format is quite easy to write and read, and errors (especially programming errors) are easier to find.
  3. Sharing models. Since I usually code a LP formulation for most models I create as part of the debugging process, I use the same files when sharing my models with other people.

What do you use LP files for?

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