Originally posted by: PaulAAO

We are using ODME / CPLEX to optimise a set of prices that maximise total margin.

Margin is the product of sales volume and price - cost, and sales volume is a function of log price.

Ideally we would formulate the problem as below, but CPLEX comes up with an error "Function log(dvar float) not available in context CPLEX".

Is there an easy way of formulating this problem so that CPLEX can solve it?  I am sure we aren't the first people to use CPLEX for price optimisation!

DVAR float productPrice[p]

Maximise

sum (p in allProducts) ((productPrice[p] - productCost[p]).(a[p] - b[p].log(productPrice[p])))

subject to:

constraints on price

constraints on sales volume

constraints on unit margin

CPLEX handles problems with linear or quadratic objective functions and linear or quadratic constraints. If your objective function is concave and your feasible region is convex, you could get an approximate solution by doing a piecewise linear approximation to the objective (and to any nonlinear, nonquadratic constraint functions).