1. Introduction to D.P D.P : Method of finding optimal solution as a sequence of decisions

Ex.1) Routing problem

Ex.2 ) Production planning How many boats should be build in what month to minimize the costs? Orders for delivery at the end of months : Mar.Apr.MayJun.Jul.Aug Construction capacity of boat build up : 4 boats in any month Hold up capacity in stock : 3 boats Overhead cost per month with/without boat build up : 4,000$/ 0$ Construction cost : 10,000$ per boat Stock holding cost : 1,000$ per boat per month In D.P terms, let n : the number of months or stages which remain until the planning horizon, that is, the end of August, is reached. state (n,I ) : the number of boats, i, which are in stock at the start of month corresponding to stage n. For example, (3,2 ) corresponds to two boats in stock at the beginning of June. action k at a given state : build k boats in the current month. r = r(I,k) : the return in any month, that is, the cost incurred in that month.