(!********************************************************************* Mosel NL examples ================= file bookdisc.mos ````````````````` A bookstore has the following discount policy: For each USD 1 you spend you get 0,1 % discount on your next purchase. Example: If you have to buy three books that cost USD 10 USD 20 and USD 30 you could buy the USD 30 book today, the USD 10 book tomorrow (on which you'll get a 3 % discount), and the USD 20 book the following day (on which you'll get a 1 % discount). Or you could buy the USD 30 book and the USD 20 book today, and the USD 10 book tomorrow (with a 5 % discount). What is the cheapest way to buy N books (for given prices) ? Based on AMPL model bookdisc.mos by M.J.Chlond Reference: J. & L. Poniachik, Hard-to-Solve Brainteasers (p16), Sterling (c) 2008 Fair Issac Corporation author: S. Heipcke, Jul. 2003, rev. Mar 2013 *********************************************************************!) model "bookdisc" uses "mmxnlp" parameters N = 8 ! Number of books D = 4 ! Number of days DISC = 0,001 ! Discount factor end-parameters declarations BOOKS = 1..N ! Set of books DAYS = 1..D ! Set of days COST: array(BOOKS) of real ! Cost of books ifbuy: array(BOOKS,DAYS) of mpvar ! ifbuy[i,j]=1 if book i bought on day j, 0 otherwise total: array(DAYS) of mpvar ! Total cost of books on day j totcost: mpvar ! Total cost of all books end-declarations forall(i in BOOKS,j in DAYS) ifbuy(i,j) is_binary ! forall(j in DAYS) total(j) is_integer ! Generate random book prices setrandseed(3) forall(i in BOOKS) COST(i):= 10+round(50*random) ! Objective: total cost totcost = sum(i in BOOKS) COST(i) - sum(k in DAYS | k>1) DISC*total(k-1)*total(k) ! Total cost per day forall(j in DAYS) total(j) = sum(i in BOOKS) COST(i)*ifbuy(i,j) ! Every book is bought on one day forall(i in BOOKS) sum(j in DAYS) ifbuy(i,j) = 1 ! Solve the problem setparam("xnlp_verbose",true) setparam("xnlp_solver",0) minimize(totcost) ! Solution printing TOTCOST:= sum(i in BOOKS) COST(i) writeln("Total cost: ", strfmt(getsol(totcost),5,2), " (orig: ", TOTCOST, ") discount:", strfmt((TOTCOST-totcost.sol)/TOTCOST * 100,5,2), "%" ) forall(i in BOOKS) BDay(i):=round(getsol(sum(j in DAYS) j*ifbuy(i,j))) forall(i in BOOKS) writeln("Book ", i, " bought on day ", BDay(i), " at ", strfmt(COST(i)*(1-if(BDay(i)>1, DISC*total(BDay(i)-1).sol,0)),5,2), " (orig: ", strfmt(COST(i),5,2), ")" ) end-model