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abeham/mathpuzzle_banana.mzn

Last active December 9, 2018 20:37
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MiniZinc model that solves a math puzzle involving bananas and a camel
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mathpuzzle_banana.mzn
% A farmer has 300 bananas which she wants to sell at a market 100km away.
% Her camel can carry 100 bananas at once, and eats one banana per km.
% What is the most bananas she can bring to the market?
int: capacity = 100;
int: distance = 100;
int: init_stock = 300;
int: maxtrips = ceil(init_stock / capacity);
int: maxlegs = 4; % maximum amount of legs the journey is partitioned into, a leg consists of hauling a certain load over a certain distance
set of int: legs = 1..maxlegs;
array[legs] of var 0..distance: travel; % the distance of each leg
array[legs] of var 0..init_stock: consumed; % how much banana the camel consumes in this leg
array[legs] of var 0..init_stock: load; % how much banana is carried in this leg
array[legs] of var 0..maxtrips: trips; % how many trips in direction of the market are required to haul the load
array[0..maxlegs] of var 0..init_stock: stock; % the remaining banana at the end of the leg
constraint sum(l in legs)(travel[l]) = distance; % the sum of the travelled distance must equal the distance to the market
constraint stock[0] = init_stock;
constraint forall(l in legs)(stock[l] = load[l] - consumed[l]); % the remaining bananas at the end of the leg
constraint forall(l in legs)(load[l] <= stock[l-1]); % we must not carry more banana than we had at the end of the last leg
constraint forall(l in legs)(consumed[l] = 2 * (trips[l] - 1) * travel[l] + travel[l]); % we have one less back trips than forth trips
constraint forall(l in legs)(trips[l] >= load[l] / capacity); % the number of trips required to carry the load
solve maximize stock[maxlegs]; % we want to have as much bananas hauled to the market as possible
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