Real Estate and the Knapsack Problem

As an industrial engineer, part of my background is how to take normal everyday problems and solve them efficiently and quickly.  I solve the same problems as others but have a set of tools at my disposal that your normal practitioners who have been doing it for years may have figured out but never formalized.

This is significant in real estate because there are two classes of industrial engineering problems that are worked through everyday but generally using inefficient methods:  knapsack problems and cutting stock problems.

The two problems that are dealt with everyday are:  1) how much space does a tenant need given a set of employees and an existing real estate portfolio and 2) how should that space be laid out to give the most efficient use of space.  Solving these two problems minimizes the total amount of space required for the client and best aligns it with their operational needs (two common topics around here).  Traditionally problem 1 is solved by brokers or real estate professionals that use the A times B equals C method.  Problem 2 is solved by designers and architects who often end up at the right result – but also miss the mark often – because they follow non-classical approaches to the problem or just create several designs and go with the best.

In school, real estate isn’t a well known career path for industrial engineers.  Similarly, once in the industry there is a surprising lack of structured, engineering thinking.  There is a significant gap that can be filled by thinking through these classic problems differently.

My Favorite Metric

I’m an industrial engineer (as I may have mentioned a few times).  My favorite concept from the Georgia Tech program was knapsack problems.  Given a limited amount of space (like a building) how do you best fill it for maximum value.  The simplest solution to most Knapsack problems is called the Greedy Algorithm.  For each possibly item you could add to your knapsack you calculate the value per cost.  Then you simply fill in the bag with your highest value per cost items until the bag is full.  Pretty straightforward.

The concept of value per cost is a difficult one for many people.  In real estate an example would be revenue per square foot.  Law firms do his extremely well – they track the top line performance of each of their attorneys at each facility.  Value doesn’t have to mean revenue though.  For manufacturing real estate portfolios an example would be units produced per square foot.

Standard real estate portfolios measure things that typically don’t tie to a value driver.  Square feet per seat, cost per square foot, people per seat, vacancy rate – none of these are tied to business value.  For understanding the value proposition there are a couple of options:  revenue (obviously), units produced or processed, employee productivity, or future revenue/innovation.  There are many more, but these should give you a sense of what to look for.

If real estate wants to be at the strategic business table, this is the way that we need to think.  A focus on business value is step 1.  Measuring impact against that value is step 2.

What is Knapsack and Why We Use It

Knapsack problems are a type of problem that involves deciding which of a number of items should be placed into a limited amount of space. The problem type gets its name from trying to fill a backpack (knapsack) with items needed to go camping. In the classic scenario the items are a compass, matches, map, portable grill, food, clothes, tent, books, hunting equipment, etc. Each of these items has an assigned weight and value to the packer. If only 30 pounds can be held in the backpack which items should be chosen?

The problem boils down to a cost/value association in it’s simplest form. Matches have a value of 10 and a weight of almost nothing, while a book has a relative value of 2 and a weight of maybe 2 pounds. It’s a fairly simple decision to pack the matches before you pack the book. More decisions fall under this philosophy than realized. Anytime there is a choice between two items there is a potential knapsack problem.

Why am I explaining this? Well, not all problems are that cut and dry. Think about a distribution center and deciding the storage medium that should be used. It’s a form of knapsack problem with several expandable size bags. Each rack type is a knapsack (Pallet Rack, Carton Storage, Floor Storage, Bin Shelving, etc.) and each item needs to be placed into one. Imagine the costs involved: real estate, labor, material handling equipment, cost of the storage medium. They all vary by rack type. The Value of each item is how quickly it moves through the warehouse (lines per day and seasonality). Now run this evaluation over 5,000+ SKU types. Not a simple problem anymore but it can make a big difference in the effectiveness of your distribution center or distribution network.

Thinking in terms of Knapsack provides definition to problems that previously would not have had much form. It allows an evaluation method for each of the options that must be considered as long as there is an ability to assign a Cost and Value. Cost could be anything from money to size to weight to business flexibility. Likewise, Value could be money, growth potential, profit potential or speed. Assuming that a very reliable and understandable Cost and Value are assigned to each decision variable, a solution can be reached.

Obviously not all problems can fall be solved using Knapsack and not all solutions reached by using this method will be optimal. There are some grey areas around the theory. For certain Cost/Value ratios it is better to not fill up the bag than to continue filling it. Some decisions allow you to pick an option multiple times with decreasing value each time (if you want to pack three books and two boxes of matches). However, it provides the framework to begin thinking through some of the decisions facing you today. Making decisions is one of the most difficult jobs in business and sometimes it is near impossible to make them without outside help. The cost of making a bad decision usually outweighs the cost of bringing in help to make the right one.

Technorati Tags: knapsack, consulting, decision making