In optimization, settle for the near optimum

As an MSc in operations management, I started my career analysing inventory parameters in a 35 main distribution centre, up to 350 locations, four level multi-echelon inventory network. The odd 100.000 spare parts my department was planning ranged from 0.01 US$ to 200k US$ in cost price and demand ranged from less then 1 spare part a year to over a 1000. The whole goal of the department I worked in was to optimize customer service whilst minimizing 0.5 billion US$ inventory. A rocket scientist was wondering how to improve allocation algorithms and personally I worked on algorithms to introduce and service new products in to this distribution network.

Later in my career I worked for several multi national FMCG companies that had more then US$100m of inventory on the balance sheet and wondered why the only inventory optimization they did was done on the back of an envelope. Focus on optimizing this inventory and you save 20%-30% working capital against a ROCE (Return on capital employed) of 10%-15%, that means putting between 2 and 4.5 million US$ in your pocket. Why not optimize this? Maybe there were just bigger fish to fry.

This story shows that the first hurdle to inventory optimization is to ‘get it on the agenda’! Fortunately, the IE group inventory optimization summit will focus with case studies on engaging senior leaders amongst many other things. See for an overview: http://www.theiegroup.com/Inventory_Optimization/Overview.html

But once you have inventory optimization on the agenda be aware of some other limitations in finding an optimal solution.

Optimization model: a mathematical model used to calculate an optimal solution in a supply chain network describes and optimizes only a sub part of the real world. Optimizing that part doesn’t mean necessarily optimizing your real world, although you might come close.

Complexity: Operations research tells us there is such a thing as the hardest category of problems: the NP-complete problems. These are problems that cannot be optimally solved within a linear time algorithm. A multi-echelon inventory problem, where replenishment can happen from neighbouring DC’s in the network will probably be NP-complete. Hence you have no guarantee to find an optimum solution in an acceptable timeframe.

Chaos: Chaos exists everywhere, also in our supply chain. Some of the research from Professor Richard Wilding applies chaos theory on inventory models and shows that chaos exists in inventory models indeed. This can mean that if the starting position in your optimization model is slightly different (a reorder point of 2.0000001 versus 2), after many iterations and feedback loops, the optimization algorithm can go wild and… whoops there goes the optimum.

Human decision making: after all the rational and mathematical logic used in the optimization algorithms, some people have to make decisions to implement to optimum solution. Behaviour and decisions, especially under pressure of time and politics, are often not rational. Perception of quality, prices and performance differ from person to person within a company, and even more so between the company and its suppliers and customers in different countries with different cultures, values and motivations. At the Erasmus University in the Netherlands Operations Management is turning a whole new chapter to Behavioral Operations Management; see

http://j.mp/p7LKt3. Behavioral Operations Management examines the behavior of actual human agents in complex decision problems. It introduces the understanding of human behavior to the practice of operations management.

With all the above uncertainties in mind, good heuristics or approximation algorithms can give you good quality outcome, although not optimal. It’s often not worth the time and resources to further chase the optimum, when a near optimum solution has already been reached. Use your resources to reduce risk or increase flexibility in your network, not to chase the optimum.

Therefor once optimization is on the agenda, settle for the near optimum.

One thought on “In optimization, settle for the near optimum

  1. Chaos exists everywhere, also in our supply chain. Some of the research from Professor Richard Wilding applies chaos theory on inventory models and shows that chaos exists in inventory models indeed. This can mean that if the starting position in your optimization model is slightly different (a reorder point of 2.0000001 versus 2), after many iterations and feedback loops, the optimization algorithm can go wild and… whoops there goes the optimum.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s