Modelling Mathematical Models Put into Excel Spreadsheets

Modelling ideas Input Variables Decision Variables Targets

First Maths Profit = Revenue - Cost Linear Cost: Linear Revenue Cost = Fixed Cost + N* Variable Cost Linear Revenue Revenue = N* Price Piecewise Linear Revenue Revenue = N1*Price1 + N2*Price2 + … (e.g. when you can sell some t-shirts at a premium)

Dealing with uncertainty Projections using falling value of money Projected Costs Dealing with uncertainty (actually still to come in lecture) Projections using falling value of money 100 pounds now is worth more than the promise of 100 pounds next year Break-even analyses

Spreadsheets Absolute and relative addresses If statements Range names Making one-way tables Two-way tables Goal Seek

Uncertainty Sam’s Bookshop Sam does not know how many books to order. They are cheaper the more he orders He has to sell them cheaply if he does not sell them quickly He does not know how many he can sell

They are cheaper the more he orders First 1000 books are 24 dollars each; next 1000 23 etc. Use a Vertical Lookup Table

Uncertain Sales

Expected Value Suppose somebody throws a dice and gives you a pound for each dot on the side that comes up E.g. if a 4 is thrown you get 4 pounds How much money can you expect to get on average?

Well there is a 1 in 6 chance of getting one pound + a 1 in 6 chance of getting 2 pounds etc. 1/6 (1) + 1/6 (2) + … + 1/6 (6) = 3.5 pounds

Back to Sam Want to maximise Profit Profit =Revenue-Cost Revenue =Units_sold_at_regular_price*Regular_price+ Units_sold_at_leftover_price*Leftover_price

Units_sold_at_leftover_price = Order - Units_sold_at_regular_price Units_sold_at_regular_price = MIN(Order_quantity,Demand) = IF(Order_quantity < Demand, Order_quantity,Demand)

Cost =VLOOKUP (Order_quantity,CostLookup,2)

Make a Table

For each line of the table we can compute an expected value of profit by multiplying the profits by the demand probailities and adding

Expected profit for order of 2000 is: .025*30000 + .05*40,000 + ….