Speculative Demand Problem: Solved By Economic Game Theory!

By @AlgoBrain

What is the Speculative Demand Problem?

A Business has 2 Warehouses - 1 local and 1 offshore. The business speculates that there may be higher LOCAL demand than OFFSHORE demand for the same price of the stocked product at that particular time, and in anticipation of higher sales considers shipping stock from its offshore warehouse to its local base.

The penalty for the decision to ship is the payment of freight cost.

Questions Arising

Is the speculation worth it? Will there actually be better sales either way? Will shipping generate higher sales? or lower sales?

The Solution

The solution lies in the adoption of game theory in the form of the speculative demand game. We create a game to model the situation and play for a large number of rounds (say of the order of 10,000 - 100, 000 rounds) to converge at a conclusive result (ship or don't ship).

The Speculative Demand Game

In this 1-player game (the business is the player), the business plays the system. There are only 2 moves for the player (business) - ship or don't ship. In either case the player utilizes fixed resources - demand (local and offshore), stock (local and offshore), price (fixed) and freight cost (fixed penalty for shipping).

Note: Demand is expressed as a weight between 0 and 1


Move 1: Don't Ship

Total Sales = Price*(Local_Demand*Local_Stock + Offshore_Demand*Offshore_Stock)

Move 2: Ship

Total Sales = Price*Local_Demand*(Local_Stock + Offshore_Stock) - Freight


The speculation has value (a win) if for any round of the game one approach yields a greater result than the other. The games must be simulated and played very many times to converge at a definite result.

Demand is modeled as:

demand = lowest _demand + random(1 - lowest_demand)

if demand > 1 then demand = (1+lowest_demand*demand)/(demand - lowest_demand)

Stock is modeled as:

stock = base_stock + random(max_addition)

Of course, price and freight cost are fixed. The games must be played in a binary gaming program such as the  Dimkpa Binary Game Engine.

If we assume the following parameters:

Price = $500
Base Stock  = 10,000 units
Max stock addition = 5,000 units
Lowest demand = 5% of stock = 0.05
Freight cost = $10,000

Then after100,000 rounds of gaming, the Dimkpa Binary Game Engine produced the following results for the speculative demand game:

Game Summary - after 100000 rounds
----------------------------------------
total lost = 50120
lost GOAL = 50120
total WON = 49880
% LOST = 50.12 %
% LOST GOAL = 50.12 %
% WON = 49.88 %
% METHOD 1 PICKED = 50.137 %
% METHOD 2 PICKED = 49.863 %
% METHOD 1 WON = 50.1764234 %
% METHOD 2 WON = 49.8235766 %
% METHOD 1 LOST = 50.0977654 %
% METHOD 2 LOST = 49.9022346 %
% METHOD 1 LOST GOAL = 50.0977654 %
% METHOD 2 LOST GOAL = 49.9022346 %
----------------------------------------

INTERPRETATION:

After 100,000 games, there is a 49.88% chance that the speculation is viable; and a 50.12% chance that it is not viable. If the viability of the speculation is rejected, then either move should yield a similar result. Should the player decide to accept viability of the speculation, then:


MOVE 1: DON'T SHIP

WON: 50.1764234 % of 100,000 games
LOST:  50.0977654 % of 100,000 games

Won MORE times than lost.

MOVE 2: SHIP

WON: 49.8235766 % of 100,000 games
LOST: 49.9022346 %  of 100,000 games

Won LESS times than lost.

VERDICT: DON'T SHIP.

Case Study: Using QuickProfitSim To Do a Feasibility Analysis (1)

Business Investigated: Boutique Restaurant





Business Parameters:

Meals

Types of Meals Served Daily: 12
Average Price Per Meal: $ 80
Average Number of Meals Served Daily (Per type of Meal): 4


Management

How Many Days Open Per Month: 30
Internal Costs Daily - Power/Machinery: $ 200
Operational Costs Per Day: $ 800
Petty Expenses Per Day: $ 300

Staff

How Many Chefs Cook Each Meal: 1
How Much Per Hour Does Each Chef get Paid: $ 25
Average Cooking Time Per Meal: 0.75 hours (45 minutes)







Plugging these values into QuickProfitSim gives us: $ 49,200 profit per month! (see above image)

So a boutique restaurant serving 12 types of meals with an average demand of 4 meals per type of meal a day at $80 a plate on average, working 30 days a month, with a total of $1300 a day in operational and internal expenses, and paying each chef $25 an hour can expect to make:

$ 49,200 in profits every month! And this was estimated in 1 minute by QuickProfitSim. Download the app now and use for your business ideas and planning.

The MDS Dev Team

info@montydimkpa.com
www.montydimkpa.com

QuickProfitSim - the FREE and Easy App for Calculating Business Profits

Free App Estimates Profits for Businesses in Seconds!

Meet QuickProfitSim, the free and easy app that helps businesses estimate profit for new business ideas before making an investment.

Have a new business idea? Why not use QuickProfitSim to quickly and easily figure out how much money your new business idea will generate per month? You don't have to rush blindly into a new business venture, neither do you have to use expensive or complicated software.

QuickProfitSim is a free app - completely free to download, use and share - and its portable so no installation is required. Plus its only 1 Mb - it downloads in seconds!

Simply download the app direct from Rapidshare with 1 click, extract the RAR to any location on your PC and run the program - it's that easy!

--> RapidShare link to download (1 click direct download) --> http://rapidshare.com/files/1450806673/QuickProfitSim.rar

How to Download, Install and Use the QuickProfitSim App:

1. Click this link for 1-click direct download from RapidShare --> http://rapidshare.com/files/1450806673/QuickProfitSim.rar
2. Download the RAR file to your computer and extract the folder to any preferred location
3. Locate the "QuickProfitSim" app and run it
4. The app is interactive - simply type in your values and it estimates your profit!

QuickProfitSim is free to use again and again, so encourage your friends to download by sharing the link or this press release to them. 

QuickProfitSim is made by MDS, a company that provides free business advice and other tools and services aimed at helping small businesses grow. Go download the free app, use it and tell us what you think!

The MDS Dev Team
info@montydimkpa.com
www.montydimkpa.com

Why You Should Simulate Your New Business Idea

Do you have a new business idea? Looking for a risk-free and cost-free way to evaluate BEFORE you invest? Then SIMULATION is the answer.

What is Simulation?

Simulation is when you design a profit model representing your new business idea and subject it to computer analysis to determine how productive it will be in the real world when it is implemented.

Does Simulation Work? Why does it Work?

Simulation works because you use the same variables and parameters (settings) as you would in the real world and you subject your 'model', which represents your actual business idea, to the same kind of scenarios that would apply in real life.

An Example

Say you wanted to open a doughnut business and you have absolutely no idea how it will (or if it will) work. You need to simulate (perform calculations by computer) to determine how productive it will be. Here is the scheme:

A profit simulation works by evaluating CLIENT SIDE, COMPANY SIDE, and JOB SIDE parameters as follows:

CLIENT SIDE

How many types of doughnut ordered per day (types_prod)

Average price of each doughnut (avg_price_prod)

Average number of doughnuts ordered per day (avg_number_ppd)

Commission (total client payment) per day (comm_pd) = (types_prod)*(avg_number_ppd)*(avg_price_prod)

COMPANY SIDE

Working days per month (days_pm)

Internal costs per day - power/machinery (int_costs_pd)

Operational costs per day (op_costs_pd)

Petty expenses per day (oth_exp_pd)

Company daily expenses (com_exp_pd) = (int_costs_pd)+(op_costs_pd)+(oth_exp_pd)

JOB SIDE

Staff to product ratio (staff_prod_ratio)

Average staff wage per hour (wage_ph)

Avg. hours to make product (avg_prod_time)

Total daily Job Cost (daily_job_cost)= (types_prod)*(avg_number_ppd)*(avg_prod_time)*(wage_ph)/(staff_prod_ratio)

PROFIT PER MONTH = (days_pm)*[(comm_pd) - [(com_exp_pd) + (daily_job_cost)]]

Which broken down completely becomes:

Equation for simulating profit (above)

Testing the Model

OK, now we have our profit simulation model all set up – that’s the equation above! Now let’s test it to see if it works.

Let’s say these are typical values for the variables we need:

How many types of doughnut ordered per day (types_prod) = 3

Average price of each doughnut (avg_price_prod) = $12.50

Average number of doughnuts ordered per day (avg_number_ppd) = 50

Working days per month (days_pm) = 30

Internal costs per day - power/machinery (int_costs_pd) = $30

Operational costs per day (op_costs_pd) = $100

Petty expenses per day (oth_exp_pd) = $50

Staff to product ratio (staff_prod_ratio) = 1

Average staff wage per hour (wage_ph) = $10.50

Avg. hours to make product (avg_prod_time) = 0.5

Simply plug these values into the simulation model to get the expected profit per month from this business.

What’s your answer?

$27,225 per month. Now that’s a business I’d LOVE to get into!

Can you see why this is important? Well, that's why you need the free profit simulation service from MDS that takes this data and gives you a free simulation, so you can know how much profit your new business idea will generate per month. Other analytics options are also provided.

Want to get a free simulation for your business? Fill this form HERE or visit http://www.montydimkpa.com/Business+Modeling to get started!

New Shape Discovered!

I discovered a new shape:-

Meet the Dimkpa Automaton:





 Fig: 80-non-repeating Dimkpa Automaton (k=1.06) - smooth



Fig: 80-non-repeating Dimkpa Automaton (k=1.02) (smoothed out)

I know, it looks like a football!

Definition

The Dimkpa Automaton is the locus of a point moving in turns within a square such that it starts from the origin and is always projected at a constant angle.

Equation

The equation governing the Dimkpa Automaton is:



Turns

A turn is a unit of motion of the automaton; where it is initially projected from the origin or somewhere along the base of the square (along the x-axis) to “bounce off” the opposite square edge before bouncing off other edges to return to the base.

For K>1 it is called a non-repeating Dimkpa Automaton and it does not leave the imaginary square onto which it is projected. If K < 1 it becomes a repeating Dimkpa Automaton  and may leave the boundaries of the square.

Relationship to other Known Shapes

If K = 0 it is a square. If K>>1 or K<<1 it is a spiral.

The (beautiful) examples above are non-repeating Dimkpa Automatons. The figure below shows what a 50-turn non-repeating Dimkpa Automaton looks like if it is not smoothed out (Its true shape):








Fig: 50-non-repeating Dimkpa Automaton (plain)











The expression above gives the Area of the Dimkpa Automaton.




 I leave you with a picture of the first Dimkpa Automation ever created! It's a K=1 DA