Warbook and Linear Programming

Operations Research educators can spice up linear programming lessons with Warbook.

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Warbook is a multi-player medieval fantasy game in Facebook, where you try to build a kingdom and an army, and either protect yourself from other players, or attack others in order to expand your land or gain gold.

If you're curious, please read Janette Toral's How To Play Warbook In Facebook.

Anyway, back to the topic: What does Warbook have to do with Linear Programming?

Chances are, if you're teaching linear programming in an Operations Research class, you're probably dealing with college students, some of whom are already playing Warbook. And if they haven't been introduced to WB, you can ask them to solve an LP problem and test it in Warbook.

For example, depending on the kind of Hero you choose in Warbook, you can acquire or upgrade the following types of military personnel:

Soldiers (Defense score of 1)
Knights (DS of 1)
Pikemen (DS of 3)
Elites (DS of 5)

The above defense scores assume you choose the "General" hero-type.

Each military class requires a certain amount of gold each hour. Soldiers require 1 gold unit, Knights and Pikemen each require 2 gold units, while Elites require 3 gold units. Based on the different buildings you have on your land, you will have a certain level of hourly income, say, 20000 gold units.

Acquiring a soldier costs around 100 gold units, while upgrading a soldier to a knight, pikeman, or elite costs 200, 200, and 600 gold units, respectively.

Let's assume that you're a new player with 100,000 gold units on hand, and the other more established and stronger Warbook players are trying to take over your land. An initial strategy for you might be a Defensive one.

The strongest defense of 5 comes from the Elites, but they each cost 3 gold units per hour to maintain. Ordinary soliders only cost 1 gold unit an hour, but each provides only 1 unit of defense. How many of each military type, therefore, should you acquire or upgrade to?

So in Linear Programming (which can be solved using the Solver Add-In tool of MS Excel), you are trying to maximize your Defensive Score.

Maximize Z = 1S + 1K + 3P + 5E,

where S, K, P, E represent the number of soldiers, knights, pikemen or elites you will either acquire or upgrade to.

Subject to the following constraints:

1S + 2K + 2P + 3E <= 20,000 (hourly net income)
100S + 200K + 200P + 600E <= 100,000 (gold on hand)

and the non-negativity constraints:

S >= 0
K >= 0
P >= 0
E >= 0

Using Linear Programming and Excel's Solver, you can compute your ideal military personnel development plan. In the future, I'll post a video tutorial on how to solve LP problems using Excel. And who knows? You might even use it when playing Warbook. :-)

[ First posted on 09/25/2007 by Manuel Viloria ]

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