Demand-driven harvest scheduling Sébastien Lacroix FPInnovations Géraldine Gemieux CIRRELT, Université de Montréal Université de Montréal November 4, 2010 3/3/2011 www.fpinnovations.ca 1
Context The forest supply chain is composed of many activities that allows to bring wood fiber to the mills. One way to minimize the cost of those activities is to have a good planning. 2009 FPInnovations. All rights reserved. Copying and redistribution prohibited. 2
Context In the previous planning phases (strategic and tactical), harvest blocks and roads to build have been chosen. In operational planning, this is the time to organize the execution of the forest activities during the year. When? Where? Which harvesting team? What product? 2009 FPInnovations. All rights reserved. Copying and redistribution prohibited. 3
Industry needs FPInnovations tool (FPInterface) allows users to create operational schedules. Complete schedules (i.e. road construction, harvesting, transportation, road side and mill inventory, and mill demands) can be generated and then followed during the execution of such activities. 2009 FPInnovations. All rights reserved. Copying and redistribution prohibited. 4
Industry needs FPInterface Work schedule module works by simulation Add an optimization to FPInterface to help the user to do better planning: Respect all customers demands Consider all activities Consider harvest systems and harvest teams Respect all constraints Consider roadside and forest inventory Minimize forest supply chain costs 2009 FPInnovations. All rights reserved. Copying and redistribution prohibited. 5
Demand-driven harvest scheduling Géraldine GEMIEUX Bernard GENDRON Jacques FERLAND FPInnovations
Outline 1. Problem description 2. Modelling 3. Resolution and analysis of some results 4. Ongoing work
Problem context Supply chain definition iti Supply chain between the forest and mills: Cleaning and road constructions Harvesting Storage in areas Transport Storage at mills
Problem context Forest field and harvesting Partition of the forest field Harvesting area: smallest harvesting unit Sector: set of some harvesting area Harvesting area have different sizes and include volumes of different assortment List of areas available for the harvest planning
Problem context Harvesting 2 types of harvesting teams: Short woods Long woods Some areas can only be harvested by only one type of team. It is important to allocate a proper team to an area. This information depends on areas properties.
Problem context Roads network Roads network is already designed Roads are regarded as harvesting areas which take priority over those served by these roads Cleaningi and roads construction ti are part of harvesting activity in our model.
Problem context Transport About transport: No explicit destination Destination mill is included in the definition of a product A product has only one destination But a mill may need several products
Problem objectif Over a one-year planning horizon(26 periods of 2 weeks) assign teams to areas in order to satisfy the demands at the mills at minimum cost Respect every constraints associated to each supply chain activity
Modelling Supply chain activity set of contstraints Decisions only made for harvesting for harvesting only Storage in areas Transport Storage at mills MIP subproblem Linear problem
Models(1/2) 4 models have been made Model 1 = The most intuitive 26 periods, 184 harvest areas, 25 sectors, 8 teams (6 shortwood, 2 longwood), 11 products Model 2 = Team aggregated model Introduced to eliminate symetry between teams with same properties To make the B&B more efficient 26 periods, 184 harvest areas, 25 sectors, 2 team types, 11 products
Models (2/2) Models 3 and 4 use a new time unit. This unit is defined as each team can harvest only one area by period. Model 3 is equivalent to Model 1 using this time unit Model 4 is equivalent to Model 2 using this time unit For these models decisions about moves between sectors are no more secundary! The new unit is about few hours
Common points between the models Same structure (harvesting MIP), (transport, inventory LP) Sub linear problem associated to transportation and inventory management Binary variables affectation of a working unit to an area during a period
Modelling : Harvesting Access conditions: No harvesting in a area whose access road is not built yet Respect periods of restrictions (hunting, thaw, environmental protection...) Assignement Only one harvesting by area Only 5 harvesting by sector Obviously, an area can only be harvested once
Modelling: Harvesting Production of each harvesting team Each team has a capacity of production Some areas can only be harvested by a specific type of team No interruption during the harvesting of an area Moves between sectors have to be limited
Model 1 : Binary variables z btq = if team q is assigned to area b at period t x btq = 1 if team q starts to work in b in time period t, 0 otherwise y btq = 1 if team q achieves the harvest of b in time period t, 0 otherwise I stq = 1 if team q is in the sector s in time period t, 0 otherwise I ts1s2q = 1 if team q is in sector s1 during the period t but leaves it to go to s2
Model 1 : Continuous Variables α btq = Proportion of the period t when a team q harvesting the area b v IF btk = Volume of product k from the harvesting area b in storage in area in time period t v T btk = Volume of k from harvesting area b carried in time period t v IU kt = Volume of k in storage at mill in time period t e kt = Excess of k in mill storage in time period t R kt = lack of volume de k at mill storage L Kt = Unsatisfied demand of product k at mill in time period t
Model 2: Binary variables z bth = 1 if a team of type h is assigned to area b at period t x bth = 1 if a team of type h starts working in b in time period t, 0 otherwise y bh bth = 1 if a team of type h achieves the harvest of b in time period t, 0 otherwise w btq = 1 if x bth = 1 and q type is h
Model 2 : Continuous variables α bth = Proportion of the period t when a team of type h harvesting the area b v IF btk = Volume of product k from the harvesting area b in storage in area in time period t v T btk = Volume of k from harvesting area b carried in time period t v IU kt = Volume of k in storage at mill in time period t e kt = Excess of k in mill storage in time period t R kt = lack of volume de k at mill storage L Kt = Unsatisfied demand of product k at mill in time period t αw btq = α bth if q is the team of type h that is working on area b at period t
Model 3: Harvesting Less variables needed The subproblem becomes an IP with binary variables. Remain z buq, x buq and variables associated to moves between sectors Less types of constraints But important dimension increase Moves between sectors are more important decisions because the time unit is smaller.
Model 4 : Harvesting The subproblem becomes an IP with binary variables. Remain z buh, x buh
Impossible d'afficher l'image. Votre ordinateur manque peut-être de mémoire pour ouvrir l'image ou l'image est endommagée. Redémarrez l'ordinateur, puis ouvrez à nouveau le fichier. Si le x rouge est toujours affiché, vous devrez peut-être supprimer l'image avant de la réinsérer. Link between the demand and the harvesting Model 1 : Model 2: Model 3: Model 4:
Modelling : Storage in area Storage balances at harvest areas Link between the MIP subproblem and the continuous one.
Modelling: Transportation Capacity for transporting products k from harvesting areas
Modelling : Storage at mills Inventory balance equations at the mills Minimum volume in storage for each period
Objective Model 1 Model 2 Model 3 Model 4
Problems parameters NT = 26 periods (2 weeks each) NK = 11 products NB = 184 harvesting areas NS = 25 sectors NQ= 8 teams (6 short wood, 2 long wood)
Details about constraints,variables nt = 26 Constraints Binary var. Continuous var. Total var. Model 1 3 897 390 103 450 232 172 335 622 Model 2 3 073 692 62 333 172 725 235 058 Model 3 2 481 521 2 291 520 90 101 2 381 621 Model 4 913 441 586 768 90 101 676 869 nss = 5h
Resolution : Rolling horizons approach
Resolution: Rolling horizons approach
Black boxes approach Harvesting black box MIP Different strategies to solve this subproblem: Rolling horizons, decomposition... Transportation Storage black box LP
Resolution : parameters and solver Future demand estimated CPLEX: o Branching priorities o Time limit for B&B running o Use of «Polishing»
Model 1 : Results Analysis Time resolution (1088101 ) < 8 hours Solution gap : 5% Over the year of planification: Demands reached for 10/11 products Sastifying volumes in storage But: Trouble with the 1/11 product (high demand, important initial volumes => teams minimum activities, short-sighted resolution at each horizon) Plan_22_intuitif.xlsx
Model 2 : First results Time resolution (1091005) < 20h Solution Gap : 5% Same trouble for the same product Plan_24_agrégé_gg.xlsx
Future work Compare performances between rolling horizons for complete model and Black boxes strategies Improve moves between sectors and their opening duration for models 1 and 2 Reduce the opening duration of sector over the year Resolution and analysis for models 3 and 4 Tests with different datas Identify the best model Extensions: Introduction of home bases, areas preferences for harvest team.
QUESTIONS??