Moo-rings. Marina Mooring Optimization. Group 8 Route 64 Brian Siefering Amber Mazooji Kevin McKenney Paul Mingardi Vikram Sahney Kaz Maruyama
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1 Moo-rngs Marna Moorng Optmzaton Group 8 Route 64 Bran Seferng Amber Mazooj Kevn McKenney Paul Mngard Vkram Sahney Kaz Maruyama
2 Presentaton Overvew Introducton Problem Descrpton Assumptons Model Formulaton Analyss Conclusons Lessons Learned Questons
3 Introducton What s a moorng? Why an optmzaton problem? Moorng Buoy Moorng Lne Lne Secured to Bedrock
4 Problem Motvaton Moorngs are so scarce that n towns such as Orleans or Truro, the wat to get one can be as long as 20 years. In Sandwch, whch has no moorngs, only slps, the watng lst s closed wth 1,200 watng for a mere 200 spaces. Cape Cod Tmes 8/10/2003
5 Problem Descrpton Objectve: Maxmze Revenue! (also ncrease number of moorngs n marna) Decson Varables: Boat Locatons Dock Channel
6 Problem Descrpton Marna Top Vew Cross Secton 8 Ext Channel Depth, z y x (0,0) (x,y ) Dock 4
7 Assumptons Marna: The bottom of the marna s lnear, slopng down n the +y drecton. Tde change s 2 feet or less. Moorngs: Moorng lnes are weghtless. Moorngs can and wll be moved every y year. At hgh tde, the moorng lne angle s 30. Boats Boats are between 15 and 40 n length. Boats are classfed nto two categores based d on ther hull depth: boats wth hull depths less than 4 and boats wth hull depths between 4 and 8. Placement Moorngs can be precsely placed. The mnmum separaton needed between boat sweeps s fve feet. Bow lne length s neglgble. Boats wll be able to leave moorngs wthout specfed lanes desgnated n a marna.
8 Model Formulaton Harbor Depth Marna Top Vew Cross Secton 8 Ext Channel Depth, z y x (0,0) (x,y ) Dock 4 z ( D max D =D + mn mn y max ) y for 0< y <y max
9 Model Formulaton Boat Sweep Radus Swng Radus, r 2 Tde, T Buoy r 1 Boat Length, L Buffer, B Sea level wth hgh tde Depth, z θ 1 h Sea level wth low tde θ 2 h h = z + T cosθ 1 r 2, z = z tan arccos L + h + B
10 Model Formulaton Moorng Locaton Boundary Constrants Prevent boat locaton and swng crcle from exceedng the marna boundares x r + < X 2, max x r < X 2, mn y r < Y 2, mn y + r < Y 2, max
11 Model Formulaton Moorng Locaton Boundary Constrant Marna Top Vew Cross Secton 8 Entrance Channel r 2, Depth, z (x,y ) y (x k,y k ) r k x (0,0) Dock 4 ( x x ) + ( y k 2 2 y ) k > r 2, + r k, k <
12 Model Formulaton Moorng Depth Boundary Constrant Marna Top Vew Cross Secton 8 Entrance Channel y r 2, (x,y ) Depth, z x (0,0) Dock 4 max D mn D D ( mn + y r 2, ) D >0 Y max
13 Model Formulaton Dock and Harbor Channel Proxmty Prce Combned Proxmty Prcng Entrance Channel (X max,y max ) Iso prce lnes P D = P D, max P D, mn D T Optmal Prce Regon D T y P C = P C, max P C, mn x D T (X mn,y mn ) Dock 2 2 max D T = (X X mn ) + (Y Y mn ) max
14 Model Formulaton Objectve Functon LF = Length Fee P j L, = j DF = Depth Fee = P D + P 1 H1 j H 2 ( D ) DPF = Dock Pr oxmty Fee = P D,max P D 2 ( X x ) + ( Y y ) max mn 2 CPF = Channel Pr oxmty Fee = P C,max P C 2 ( Y y ) + ( X x ) max mn 2 Moorng Fee = LF + DF + DPF + CPF
15 Analyss Run 1 Constant Harbor Depth and No Channel Ext Fee Ext Test 1 - Fxed water depth, no harbor ext fee , , 417 Y Coordnate , , , , , , , , , , , , , , X Coordnate 489, , 36 $ $ Doc $ $ $ $ $
16 Analyss Run 2 Constant Harbor Depth and No Dock Fee $ $ $ Ext $ $ Test 2 - Fxed water depth, no dock fee 41, , , , , , , , , , 357 Y Coordnate , , , , , , , , X Coordnate Doc
17 Analyss Run 3 Fxed Harbor Depth, Equal Proxmty Prcng $ $ $ Ext $ $ Test 3 - Fxed water depth, equal dock and harbor channel ext fee 51, , , , , , 367 Y Coordnate , , , , , , , , , , , X Coordnate 489, 56 $ Doc $ $ $ $
18 Analyss Run 4 Varable water depth Ext 600 Test 4 - Varable water depth, no ext proxmty 307, , , 552 Boats wth deep hulls > Y Coordnate , , , , , , , , , feet deep , , , , , , 41 0, X Coordnate $ Doc $ $ $ $ Boats wth shallow hulls < 8
19 Results Marna Moorng Optmzaton wth 18 Boats Typcal Marna , , , , , , 411 Y Coordnate , , , , , , , , , 188 VS. Y Coordnate , , , , , , , , , , , , , 31 0, , , , , , , , X Coordnate X Coordnate Revenue = $6, Revenue = $5, % IMPROVEMENT!!!
20 Conclusons Optmzaton can sgnfcantly ncrease marna profts. Optmzaton can sgnfcantly ncrease number of moorngs n marna Model s flexble to accommodate constrants of any marna
21 Lessons Learned Need more powerful solver to ncrease number of boats and constrants n optmzaton. Need separate proxmty prcng scheme for each boat length category. Would be convenent to nclude a boat addng algorthm. There are ways to make solver behave better.
22 Questons?
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