I wish to prgramm a greedy heuristic in maple and would be more than grateful, if someone could help me, since I am no expert in programming.
The problem is a simple stocking problem. There are two parts I wish to stock in my warehouse. I know their demand, delivery time and item cost. From the demand and the delivery time I can calculate the expected backorders given a specified number of units in stock based on a poisson distribution.
In the greedy heuristic step by step I increase the stock of all items by 1 and then calculate the reduction in expected backorders divided by the item cost (some kind of "bang per buck"). I then compare the reduction over all items and increase the stock by one for the item with the highest reduction.
For the output I wish maple to show me the stock level of the two items and the sum of the expected backorders over the two items at each stage of the algorithm.
I only got so far, to programm how two calculate the bang per buck in the first stage, where delta represents the "bang per buck":
Depot Optimization Problem
> L := 0.1; L := 0.08;
Average Base Demand per year
> lambda := 10; lambda := 50;
Item Cost ($ 1000)
> c := 5; c := 1;
Starting Point: Inventory Level
> s := 0; s := 0;
Increase in system effetiveness per dollar(Bang per Buck)
> for i to 2 do
Delta[i] := ((sum((k-s[i])*(L[i]*lambda[i])^k*evalf(exp(-L[i]*lambda[i]))/factorial(k), k = s[i]+1 .. infinity))-(sum((k-s[i]-1)*(L[i]*lambda[i])^k*evalf(exp(-L[i]*lambda[i]))/factorial(k), k = s[i]+2 .. infinity)))/c[i]
> for max(delta, delta) do s[i]= s[i]+1 end do
I would be more than grateful for any help from your side,
Thx so much in advance,