Min-Maxing your game theory; or: How to Stop Worrying and Suck every Last Bit of Fun out a simulation

Take for example one of those factory assembly games; you know the ones like SimCity BuildIt, Hay Day, Clash of Clans or Boom Beach.  You have raw material and factories - you create and then assemble, trying to fill in the pipeline efficiently to keep the machines thrumming along.  Now, how about we take out the guess work? It takes 3 minutes to build this X widget, but I need X and Y widgets, and Y widget is made out of A and B widgets, and so on.  It's an automation directed graph problem, and one that should lend itself to a program that could be coded to solve the problem. 


1. We have a list of raw materials and each has its own time of creation
2. We have a list of each factory and how many of type widget it can create, how long, and how many parallel queue(s)
3. We can state end goals for our problem solver - I want to make a # batch of X, Y and Z widgets and in the shortest amount of time with instructions to maximize output. Aha! The concept of min-max-ing!


This is a bit involved to be an ACM competition question and a bit complex and convoluted to solve in Excel (but I'm sure it's possible).  Most games don't have that many tiers of products and materials, but when you get past that third layer, my brain starts to melt and I'm not having fun - it's a chore.
Imagine Diner Dash with Cooking Mama where you get an order, then have to go prepare dishes and combine ingredients and other intermediary products to finally produce a meal.  It's bad enough the game gets hectic just doing the greet - sit - order - queue up - pick up - clean up - collect $$ interspersed with crying babies and mop up spills and requests for drinks or napkins or desert as extras (which effect the final collection $$ in how important is this distraction compared to what it will cost me if I don't attend to it).  As an aside, maybe someone will create a Diner Dash / Cooking Mama multi-player online (local net or extranet) co-op game experience so people can simulate working at a restaurant in a group! Sounds like fun -- just as much fun as grinding 80 levels in World of Warcraft and pay 15$ a month for the effort (Yes, you know you play WoW (or SWTOR, EQ, etc.), you know it's a hamster wheel and you tell yourself -- yes, I'm having fun dammit!).


So anyway, back to the topic and shooting down tangent man.
Tier 0 : Factories
Type | Queue Depth


Tier 1 : Ingredients, Intermediate and Final Products
Output Type | Ingredient list | Factory Type Required | Time Manufacturing | Cost


For SCB, all costs are 0. Most games have a money sink and this one uses it for erecting factories and buildings.




To be continued...