1. int: nr; % number of reclaimers
2.            % number of rails = nr for stages A,B,C,D,E
3.            % number of rails = (nr + 1) div 2 for stage F
4. set of int: RECLAIMER = 1..nr;
5. bool: stageF; % is this stage F data
6.  
7. int: ns; % number of stockpiles
8. set of int: STOCKPILE = 1..ns;
9. array[STOCKPILE] of int: size; % size in 10000 tonnes
10. array[STOCKPILE] of SHIP: ship; % which ship carries stockpile
11.  
12. int: maxtime; % time considered
13. set of int: TIME = 0..maxtime;
14.  
15. int: nsh; % number of ships
16. set of int: SHIP = 1..nsh;
17. array[SHIP] of TIME: arrival; % when ship arrives in port
18.  
19. int: len; % length of pad
20. set of int: POSITION = 0..len;
21.  
22. int: stack_time;
23. int: reclaim_time;
24. int: reclaim_speed;
25.  
26. array[STOCKPILE] of var POSITION: westend;
27. array[STOCKPILE] of var POSITION: eastend;
28. array[STOCKPILE] of var TIME: stack;
29. array[STOCKPILE] of var TIME: endstack;
30. array[STOCKPILE] of var TIME: reclaim;
31. array[STOCKPILE] of var TIME: finished;
32. array[STOCKPILE] of var RECLAIMER: which;
33.  
34.  
35. % Go crazy here
36.  
37. % Stage A - Packing Problem
38. % Two stockpiles can't overlap in "spacetime"
39.  
40.  
41. % 1) what's the relation between endstack and stack times
42. constraint forall(s in STOCKPILE)(stack[s] + stack_time*size[s] = endstack[s]);
43. % 2) what's the relation between finished and stack times
44. constraint forall(s in STOCKPILE)(stack[s] < finished[s]);
45. % 3) what's the relation between reclaim and endstack times
46. constraint forall(s in STOCKPILE)(endstack[s] <= reclaim[s]);
47. % 4) what's the relation between finished and reclam times
48. constraint forall(s in STOCKPILE)(reclaim[s] + reclaim_time*size[s] = finished[s]);
49. % constraint forall(s in STOCKPILE)(reclaim[s] + reclaim_time*size[s] + reclaim_speed*(size[s]-1) = finished[s]);
50. % 5) what's the relation between eastend and westend offsets
51. constraint forall(s in STOCKPILE)(westend[s] + size[s]= eastend[s]);
52. % 6) packing problem
53. %    a) stockpiles should not overlap in "spacetime", treat them as rectangles
54. %    b) stockpiles can't use more space than there is available
55. %    c) we can't go beyond the time limit
56.  
57. % constraint diffn(westend, stack, size, [stack_time*i|i in size ]);
58. constraint forall(s1, s2 in STOCKPILE where s1<s2)
59. (eastend[s1]<=westend[s2] \/ finished[s1]<= stack[s2] \/ westend[s1] >= eastend[s2] \/ stack[s1]>=finished[s2]);
60.  
61. constraint forall(s in STOCKPILE)(eastend[s]<=len);
62. constraint forall(s in STOCKPILE)(finished[s]<=maxtime);
63.  
64.  
65. % Stage B
66. % Two stockpiles reclaimed by the same reclaimer do not overlap in time
67. %
68. % Tip: write your first custom predicate, i.e.
69.  
70. predicate not_overlap(var STOCKPILE: s1, var STOCKPILE: s2) =
71.      finished[s1] <= reclaim[s2] \/ reclaim[s1] >= finished[s2];
72.  
73.  
74. constraint forall(s1, s2 in STOCKPILE where (s1<s2) /\ which[s1]=which[s2])(not_overlap(s1,s2));
75.  
76. % Stage C
77. % 1) no stockpile can be reclaimed onto a ship before the arrival time of the ship
78. constraint forall(s in STOCKPILE)(arrival[ship[s]] <= reclaim[s]);
79. % 2) also no two stockpiles can be reclaimed onto the same ship at the same time. Make sure these reclaims do not overlap in time.
80. % TIP: reuse your "not_overlap" predicate
81. constraint forall(s1, s2 in STOCKPILE where s1<s2 /\ ship[s1]=ship[s2])(not_overlap(s1,s2));
82.  
83. % Stage D
84. % Add constraints to your model to ensure that if a reclaimer finishes reclaiming a stockpile with westend at x and then has to start reclaiming a stockpile with westend at y there is at least |y − x| ∗ reclaim speed time between these two events.
85. % TIP: just make your "not_overlap" predicate smarter
86. % TIP: you can introduce local variables in the constraints/predicates
87. % let {
88. %  <local variables>
89. % } in <then something>
90.  
91. constraint forall(s1, s2 in STOCKPILE where s1<s2 /\ which[s1]=which[s2])
92. (let{var POSITION: dif = (abs(westend[s1]-westend[s2])* reclaim_speed)} in reclaim[s1]!=reclaim[s2] /\ if (reclaim[s1] < reclaim[s2]) then (reclaim[s2] - finished[s1] >= dif) else (reclaim[s1] - finished[s2] >= dif) endif);
93.  
94.  
95. % Stage E
96. % Add a definition of the objective to your model and change the model to minimize this value.
97. % You may well need to significantly change your search strategy to get good solutions for the objective.
98.  
99. % TIP: definetely change the line below
100. function var int: getSumShipStay() =  sum([ '-'( max([ finished[s] | s in STOCKPILE where ship[s] = sh ]), arrival[sh]) | sh in SHIP]);
101.  
102. var int: obj = getSumShipStay();
103.  
104. % Stage F
105. % Add constraints in your model so that the two reclaimers on rail i numbered 2i − 1 and 2i for i ∈ 1..nr div 2 remain so the western one 2i − 1 is never east of the eastern one 2i. Note they can legitimately be in the same position (this is for simplicity, its not very real). Note that if there are
106. % an odd number of reclaimers the last reclaimer is on its own rail and has no further constraints.
107. % TIP: do some "channeling" and model reclaimers' positions explicitely with a new array of variables.
108.  
109. % set of int: DOUBLE_RAILS = 0..nr div 2-1;
110.  
111. constraint stageF -> (
112.   let { int: rails = nr div 2 } in
113.     forall(rail in 1..rails)(
114.       let {
115.         int: r1 = 2 * rail - 1,
116.         int: r2 = 2 * rail} in forall(s1, s2 in STOCKPILE where which[s1]=r1 /\ which[s2]=r2)(eastend[s1] <= westend[s2])));
117.  
118. % solve minimize obj;
119. solve :: int_search(finished, input_order, indomain_min, complete) minimize obj;
120.  
121. % don't change the output
122. output
123. ["westend  = ", show(westend), ";\n"] ++
124. ["eastend  = ", show(eastend), ";\n"] ++
125. ["stack    = ", show(stack), ";\n"] ++
126. ["endstack = ", show(endstack), ";\n"] ++
127. ["reclaim  = ", show(reclaim), ";\n"] ++
128. ["finish   = ", show(finished) , ";\n"] ++
129. ["which    = ", show(which), ";\n"] ++
130. ["obj = ",show(obj),";\n"]
131. ;
132.