! MODELLING TO ACHIEVE A SUSTAINABALE FOREST STRUCTURE ! WITHIN THE HISTORIC RANGE OF VARIABLILITY ! This model is testing a range of variability formulation of the goal program ! Mean targets for a target structure are selected based on an assessment of historic ! ranges of variability. Then a magement decision is made as to the range r acceptable !acceptable variation to allow in a planning model. To formulate the mean targets are !formulated as before as a target structure in a given period. The ranges are defined !and used to set up a weighting scheme that sets a very high weights on deviations of planned !structure outside of the specified range. ! !THIS FILE IS A POLICY MODEL THAT IS TO BE CONCATONATED !WITH THE DESIRED FUTURE CONTITION RESOURCE CAPABILITY !MODEL (DPEMDFC.RCM) AND SOLVED WITH LINDO OR CWHIZ. ! !Objective is to minimize the variable (RWDVSUM) which is !the sum of weighted deviations within and outside ! of the historic range of forest structure variability ! ! MIN RWDVSUM SUBJECT TO !land area constraints IAREAA) AREAA = 1000 IAREAB) AREAB = 500 IAREAC) AREAC = 1000 !for this example the target forest structure is to be !achieved by period 8. This means deviation variables and !related constraints will have to be defined for periods !8 through 12 ! !PERIOD 8 DEVIATIONS GOAL608) M6D8 +M6M8 - DP6A8 -DP6B8 + DM6A8 +DM6B8 = 600 GOAL508) M5D8 +M5M8 - DP5A8 -DP5B8 + DM5A8 +DM5B8 = 400 GOAL408) M4D8 +M4M8 - DP4A8 -DP4B8 + DM4A8 +DM4B8 = 600 GOAL308) M3D8 +M3M8 - DP3A8 -DP3B8 + DM3A8 +DM3B8 = 400 GOAL208) M2D8 +M3M8 - DP2A8 -DP2B8 + DM2A8 +DM2B8 = 300 GOAL108) M1M8 - DP1A8 -DP1B8+ DM1A8 + DM1B8 = 200 !PERIOD 9 DEVIAIONS GOAL609) M6D9 +M6M9 - DP6A9 -DP6B9 + DM6A9 +DM6B9 = 600 GOAL509) M5D9 +M5M9 - DP5A9 -DP5B9 + DM5A9 +DM5B9 = 400 GOAL409) M4D9 +M4M9 - DP4A9 -DP4B9 + DM4A9 +DM4B9 = 600 GOAL309) M3D9 +M3M9 - DP3A9 -DP3B9 + DM3A9 +DM3B9 = 400 GOAL209) M2D9 +M3M9 - DP2A9 -DP2B9 + DM2A9 +DM2B9 = 300 GOAL109) M1M9 - DP1A9 -DP1B9+ DM1A9 + DM1B9 = 200 !PERIOD 10 DEVIATIONS GOAL610) M6D10 +M6M10 - DP6A10 -DP6B10 + DM6A10 +DM6B10 = 600 GOAL510) M5D10 +M5M10 - DP5A10 -DP5B10 + DM5A10 +DM5B10 = 400 GOAL410) M4D10 +M4M10 - DP4A10 -DP4B10 + DM4A10 +DM4B10 = 600 GOAL310) M3D10 +M3M10 - DP3A10 -DP3B10 + DM3A10 +DM3B10 = 400 GOAL210) M2D10 +M3M10 - DP2A10 -DP2B10 +DM2A10 +DM2B10 = 300 GOAL110) M1M10 - DP1A10 -DP1B10 + DM1A10 +DM1B10 = 200 !period 11 deviations GOAL611) M6D11 +M6M11 - DP6A11 -DP6B11 + DM6A11 +DM6B11 = 600 GOAL511) M5D11 +M5M11 - DP5A11 -DP5B11 + DM5A11 +DM5B11 = 400 GOAL411) M4D11 +M4M11 - DP4A11 -DP4B11 + DM4A11 +DM4B11 = 600 GOAL311) M3D11 +M3M11 - DP3A11 -DP3B11 + DM3A11 +DM3B11 = 400 GOAL211) M2D11 +M3M11 - DP2A11 -DP2B11 +DM2A11 +DM2B11 = 300 GOAL111) M1M11 - DP1A11 -DP1B11 + DM1A11 +DM1B11 = 200 !period 12 deviations GOAL612) M6D12 +M6M12 - DP6A12 -DP6B12 + DM6A12 +DM6B12 = 600 GOAL512) M5D12 +M5M12 - DP5A12 -DP5B12 + DM5A12 +DM5B12 = 400 GOAL412) M4D12 +M4M12 - DP4A12 -DP4B12 + DM4A12 +DM4B12 = 600 GOAL312) M3D12 +M3M12 - DP3A12 -DP3B12 + DM3A12 +DM3B12 = 400 GOAL212) M2D12 +M3M12 - DP2A12 -DP2B12 + DM2A12 +DM2B12 = 300 GOAL112) M1M12 - DP1A12 -DP1B12 +DM1A12 + DM1B12 = 200 ! defining the ranges of the deviation variables. The variables within the range !are constrained to be less than the difference between the mean value of the !range and the upper (or lower) managed limit to the range. ! Assume the upper and lower ranges respectively for goals 6 through 1 are ! Goal 6; +400, -200, Goal 5; +200, -100, Goal 4; +200, -200 , !Goal 3; +150, -100, Goal 2; +200, -200, Goal 1; +100, -100. !These ranges hold for periods 8,9,10,11 and 12. !PERIOD 8 RANGES DP6A8 < 400 DM6A8 < 200 DP5A8 < 200 DM5A8 < 100 DP4A8 < 200 DM4A8 < 200 DP3A8 < 150 DM3A8 < 100 DP2A8 < 200 DM2A8 < 200 DP1A8 < 100 DM1a8 < 100 ! PERIOD 9 RANGES DP6A9 < 400 DM6A9 < 200 DP5A9 < 200 DM5A9 < 100 DP4A9 < 200 DM4A9 < 200 DP3A9 < 150 DM3A9 < 100 DP2A9 < 200 DM2A9 < 200 DP1A9 < 100 DM1a9 < 100 !PERIOD 10 RANGES DP6A10< 400 DM6A10< 200 DP5A10< 200 DM5A10< 100 DP4A10< 200 DM4A10< 200 DP3A10< 150 DM3A10< 100 DP2A10< 200 DM2A10< 200 DP1A10< 100 DM1a10< 100 ! PERIOD 11 RANGES DP6A11< 400 DM6A11< 200 DP5A11< 200 DM5A11< 100 DP4A11< 200 DM4A11< 200 DP3A11< 150 DM3A11< 100 DP2A11< 200 DM2A11< 200 DP1A11< 100 DM1a11< 100 !PERIOD 12 RANGES DP6A12< 400 DM6A12< 200 DP5A12< 200 DM5A12< 100 DP4A12< 200 DM4A12< 200 DP3A12< 150 DM3A12< 100 DP2A12< 200 DM2A12< 200 DP1A12< 100 DM1a12< 100 ! CREATING THE RANGE WEIGHTED OBJECTIVE VARIABLE WDVSUM WHERE THE "B" DEVIATIONS !OUTSIDE THE RANGE CARRY A WEIGHT OF 10 RELATIVE TO DEVIATIONS WITHIN THE RANGE. RWDVSUM) +DP6A8 + 10DP6B8 + DM6A8 + 10DM6B8 +DP5A8 + 10DP5B8 + DM5A8 + 10DM5B8 +DP4A8 + 10DP4B8 + DM4A8 + 10DM4B8 +DP3A8 + 10DP3B8 + DM3A8 + 10DM3B8 +DP2A8 + 10DP2B8 + DM2A8 + 10DM2B8 +DP1A8 + 10DP1B8 + DM1A8 + 10DM1B8 !PERIOD 9 +DP6A9 + 10DP6B9 + DM6A9 + 10DM6B9 +DP5A9 + 10DP5B9 + DM5A9 + 10DM5B9 +DP4A9 + 10DP4B9 + DM4A9 + 10DM4B9 +DP3A9 + 10DP3B9 + DM3A9 + 10DM3B9 +DP2A9 + 10DP2B9 + DM2A9 + 10DM2B9 +DP1A9 + 10DP1B9 + DM1A9 + 10DM1B9 !PERIOD 10 +DP6A10+ 10DP6B10+ DM6A10+ 10DM6B10 +DP5A10+ 10DP5B10+ DM5A10+ 10DM5B10 +DP4A10+ 10DP4B10+ DM4A10+ 10DM4B10 +DP3A10+ 10DP3B10+ DM3A10+ 10DM3B10 +DP2A10+ 10DP2B10+ DM2A10+ 10DM2B10 +DP1A10+ 10DP1B10+ DM1A10+ 10DM1B10 !PERIOD 11 +DP6A11+ 10DP6B11+ DM6A11+ 10DM6B11 +DP5A11+ 10DP5B11+ DM5A11+ 10DM5B11 +DP4A11+ 10DP4B11+ DM4A11+ 10DM4B11 +DP3A11+ 10DP3B11+ DM3A11+ 10DM3B11 +DP2A11+ 10DP2B11+ DM2A11+ 10DM2B11 +DP1A11+ 10DP1B11+ DM1A11+ 10DM1B11 !PERIOD 12 +DP6A12+ 10DP6B12+ DM6A12+ 10DM6B12 +DP5A12+ 10DP5B12+ DM5A12+ 10DM5B12 +DP4A12+ 10DP4B12+ DM4A12+ 10DM4B12 +DP3A12+ 10DP3B12+ DM3A12+ 10DM3B12 +DP2A12+ 10DP2B12+ DM2A12+ 10DM2B12 +DP1A10+ 10DP1B12+ DM1A12+ 10DM1B12 - RWDVSUM = 0 HTL2) H2 - 0.8 H1 >= 0 HTU2) H2 - 1.2 H1 <= 0 HTL3) - 0.8 H2 + H3 >= 0 HTU3) - 1.2 H2 + H3 <= 0 HTL4) - 0.8 H3 + H4 >= 0 HTU4) - 1.2 H3 + H4 <= 0 HTL5) - 0.8 H4 + H5 >= 0 HTU5) - 1.2 H4 + H5 <= 0 HTL6) - 0.8 H5 + H6 >= 0 HTU6) - 1.2 H5 + H6 <= 0 HTL7) - 0.8 H6 + H7 >= 0 HTU7) - 1.2 H6 + H7 <= 0 HTL8) - 0.8 H7 + H8 >= 0 HTU8) - 1.2 H7 + H8 <= 0 HTL9) - 0.8 H8 + H9 >= 0 HTU9) - 1.2 H8 + H9 <= 0 HTL10) - 0.8 H9 + H10 >= 0 HTU10) - 1.2 H9 + H10 <= 0 HTL11) - 0.8 H10 + H11 >= 0 HTU11) - 1.2 H10 + H11 <= 0 HTL12) - 0.8 H11 + H12 >= 0 HTU12) - 1.2 H11 + H12 <= 0 !THE FOLLOWING CONSTRAINT SET IS NEEDED WITH ALL GOAL !PROGRAMMING MODELS TO ENSURES THAT THE DEVIATION !VARIABLES DO NOT RELAX THE LAND CONSTRAINTS AND ALLOW !THE DECISION VARIAABLES TO BECOME UNBOUNDED MD1AREA) M1D1 + M2D1 + M3D1 + M4D1 + M5D1 + M6D1 +M1M1 + M2M1 + M3M1 + M4M1 + M5M1 + M6M1 = 2500 MD2AREA) M1D2 + M2D2 + M3D2 + M4D2 + M5D2 + M6D2 +M1M2 + M2M2 + M3M2 + M4M2 + M5M2 + M6M2 = 2500 MD3AREA) M1D3 + M2D3 + M3D3 + M4D3 + M5D3 + M6D3 +M1M3 + M2M3 + M3M3 + M4M3 + M5M3 + M6M3 = 2500 MD4AREA) M1D4 + M2D4 + M3D4 + M4D4 + M5D4 + M6D4 +M1M4 + M2M4 + M3M4 + M4M4 + M5M4 + M6M4 = 2500 MD5AREA) M1D5 + M2D5 + M3D5 + M4D5 + M5D5 + M6D5 +M1M5 + M2M5 + M3M5 + M4M5 + M5M5 + M6M5 = 2500 MD6AREA) M1D6 + M2D6 + M3D6 + M4D6 + M5D6 + M6D6 +M1M6 + M2M6 + M3M6 + M4M6 + M5M6 + M6M6 = 2500 MD7AREA) M1D7 + M2D7 + M3D7 + M4D7 + M5D7 + M6D7 +M1M7 + M2M7 + M3M7 + M4M7 + M5M7 + M6D7 = 2500 MD8AREA) M1D8 + M2D8 + M3D8 + M4D8 + M5D8 + M6D8 +M1M8 + M2M8 + M3M8 + M4M8 + M5M8 + M6M8 = 2500 MD9AREA) M1D9 + M2D9 + M3D9 + M4D9 + M5D9 + M6D9 +M1M9 + M2M9 + M3M9 + M4M9 + M5M9 + M6M9 = 2500 MD10AREA) M1D10 + M2D10 + M3D10 + M4D10 + M5D10 + M6D10 +M1M10 + M2M10 + M3M10 + M4M10 + M5M10 + M6M10 = 2500 MD11AREA) M1D11 + M2D11 + M3D11 + M4D11 + M5D11 + M6D11 +M1M11 + M2M11 + M3M11 + M4M11 + M5M11 + M6M11 = 2500 MD12AREA) M1D12 + M2D12 + M3D12 + M4D12 + M5D12 + M6D12 +M1M12 + M2M12 + M3M12 + M4M12 + M5M12 + M6M12 = 2500