Neighbourhood Structures for the Hierarchical Planning Problem on the Glass Container Industry

Transcription

1 Neighbourhood Structures for the Hierarchical Planning Problem on the Glass Container Industry B Almada-Lobo 1 ; JF Oliveira 1,2 ; MA Caravilla 1,2 1 FEUP Faculdade de Engenharia da Universidade do Porto 2 INESC Porto Instituto de Engenharia e Sistemas de Computadores almada.lobo@fe.up.pt 2005, 5th April Agenda 1. Glass Container Manufacturing Process 2. Glass Container Industry 3. Hierarchical Production Planning System 3.1. Long-Term Level 3.2. Short-Term Level 4. Neighbourhood Structures for the Long-Term Level 5. Ongoing and Future Wor Bernardo Almada-Lobo 2 1

2 1. Glass Container Manufacturing Process Three main sub-processes - Glass GassProduction o - Containers Manufacturing One supporting sub-process - Decoration - Palletising Raw materials silos Hot-end Cold-end Quality Control Final Product Bernardo Almada-Lobo 3 1. Glass Container Manufacturing Process (cont.) Reception and Control of Raw Materials Raw Materials Storage Filling, Weighting and Mixing Bernardo Almada-Lobo 4 2

3 1. Glass Container Manufacturing Process (cont.) Furnaces operate continuously Glass paste colour (amber, flint, green) Furnace Melting Capacity (tonnes/day) f (Colour) high sequence dependent setup times involved in a colour change furnace colour specialization Furnace output can vary to a limited extent Unrelated Parallel Moulding Moulding machine has four main characteristics: - Number of individual sections - Number of mould cavities per section (single, double or triple-gob machine) - Distance between the moulds - Manufacturing process Blow-blow Press-and-blow Not negligible sequence dependent setup times in product changeovers Machine balancing Job-splitting not allowed Bernardo Almada-Lobo 5 1. Glass Container Manufacturing Process (cont.) Reheating Kiln Inspection Shipping Surface treatment Palletising Bernardo Almada-Lobo 6 3

4 1. Glass Container Manufacturing Process (cont.) Raw-materials Melting rate (tonnes/day) Furnace Feeders M1 M2 Mn Molding (with different settings) Hot zone Semi-Continuous process Single-Operation type Lehrs Inspection Cold zone Pacing Bernardo Almada-Lobo 7 2. Glass Container Industry Sales of glass containers: - High seasonality (beer in Summer ) - High variability (intermediary product) Production capacity almost constant Mae-to-Stoc Industry Changeover costs Container glass is typically y manufactured closer to the end user Strong focus on improving efficiencies and reducing costs to remain competitive Capital intensive industry Bernardo Almada-Lobo 8 4

5 3. Hierarchical Production Planning System Complexity of glass container production process Dynamic and stochastic nature of this production environment Interdependencies between decisions that are made at and affect different organisational echelons Hierarchical Production Planning with 2 broad levels: Long-term planning Short-term planning Bernardo Almada-Lobo Long-Term Level Objectives meeting customer demands (raning in A, B or C importance) - Stocouts and delivery commitments maximizing the utilization of production facilities (throughput) - minimizing lost production capacity due to changeovers - products sharing the same colour and manufacturing process have negligible setup times minimising inventory investment (above safety stocs) minimising transportation costs - customers aggregation in pre-defined geographic areas Bernardo Almada-Lobo 10 5

6 3.1 Long-Term Level (cont.) Output - Monthly production plan to a rolling 12 months horizon - Colour campaigns and manufacturing process sub-campaigns scheduling - Number and dimension of product lots (lot-sizing) - Assignment of products into machines of Furnace A Frozen period A3 P1 P2 P4 P3 P1 P11 P12 P5 P4 P6 P8 P9 P5 P8 P3 P5 P10 P2 P6 P month Legend Sub-Campaign of Sub-Campaign of UV-NNPB Sub-Campaign of EG-SS Sub-Campaign of EG-NNPB UV - Ultraviolet Colour EG - Emerald Green Colour BB - Blow-Blow Manufacturing Process NNPB - Narrow Nec Press-and-Blow Manufacturing Process Bernardo Almada-Lobo Long-Term Level (cont.) Granularity of information - Time Aggregation (Macro-periods vs. Micro-periods) - Resource Aggregation ( into Furnaces) machine-balancing constraints - Product Aggregation (Colour and Manufacturing Process Families)? Finished product (container) vs. Final product (pallets) Bernardo Almada-Lobo 12 6

7 3.2 Short-Term Level Objectives Satisfaction of customers due dates (on a weely basis) Maximization of the resources utilization - maximizing the furnaces glass melted tonnage - minimizing lost production capacity due to product changeovers Additional Constraints Operational - Changing the lot on a machine only possible on wee days - Number of changes per wee limited per facility - Daily furnace capacity stopping some machine sections Commercial - Safety stoc demanded by large costumers Bernardo Almada-Lobo Short-Term Level (cont.) Output - Daily production plan to a rolling 2 months horizon - Sequences of the products in the processors Frozen period Furnace A Month Wee Day A P8 P10 May April P Bernardo Almada-Lobo 14 7

8 4. Neighbourhood Structures for the Long-Term Level MILP Formulation Minimize: it I it - Based on the GLSP it ijs - Additional constraints - Parallel machine environment + sequence dependent setup times NP-hard - Finding a feasible solution is NP-complete) Heuristic Procedures to solve this problem Subject to: h st Q (1) i, K y Y cad, is ss t i ij Cap yt ijs St i, j, K y st ij Qijs, ss t, y,t (2) I it I it1 Yis cadi procit, i, t (3), ss t Y is 1,, s (4) i K y is Y 1, y,i, s (5) is Yis Qijs, i,,j, s j i (6) Y Y,,i,j, s j i (7) K s s Qijs 1 1 i Y is Yjs 1, y, s, l, i l, j l (8) y K y Y 0, i, D (9) is I 0 ; Y, Q 0,1 (10) it is ijs Bernardo Almada-Lobo 15 Moves applied to a given solution x to generate neighbours - Insertions - Swaps - Hybrid (partial) swaps These modifications involve shifting: - Colour campaigns Manufacturing process sub-campaigns Item lots Bernardo Almada-Lobo 16 8

9 Shifts applied to Colour Campaigns [1] Hybrid swap-insertion colour campaign Selection of a colour campaign (from a source furnace) Selection of a target furnace ( from the source one) Insertion into target furnace, preserving the starting date Shifting of the overlapped lots to the gap on the source furnace No reparation mechanism CB-BB EG-BB EG-NNPB Effects Breas one or more colour campaigns on the target furnace Change the number and length of colour campaigns Interaction between furnaces colour campaign/furnace assignments EG-BB UV-NNPBCB-BB EG-BB UV-NNPB EG-BB B3 CB-BB CB-BB UV-NNPB UV-NNPB CB-BB CB-BB UV-NNPB CB-BB CB-BB UV-NNPB UV-NNPB Legend Colour changeover setup time Manufacturing process changeover setup time Bernardo Almada-Lobo 17 Shifts applied to Colour Campaigns [2] NS2-Colour Campaigns Swap - Selection of Colour campaign 1 (C) from a source furnace - Selection of Colour campaign 2 (C) from a target furnace - Swap Cwith C - Reparation Mechanism: the exceeding production of a furnace is shifted to the end of the horizon of the furnace with surplus capacity Effects - Different Colour Campaign / furnaces assignment on both furnaces (if source furnace target furnace) - Change the number and length of colour campaigns - Interaction between furnaces - Breas the last colour campaign of the furnace with lac of capacity (with the reparation mechanism) - Reparation mechanism may create new colour campaigns on the surplus capacity furnace Initial Solution Neighbour B3 Bernardo Almada-Lobo 18 9

10 Shifts applied to Colour Campaigns [3] NS3-Partial Colour Campaigns Swap - Selection of Colour campaign 1 (C) from a source furnace - Selection of Colour campaign 2 (C) from a target furnace - Swap minor Colour campaign with part of the major colour campaign - No reparation mechanism Effects - Different Colour Campaign / furnaces assignment on both furnaces - Change the number and length of colour campaigns - Breas the major colour campaign - Interaction between furnaces B3 B3 Bernardo Almada-Lobo 19 Shifts applied to Colour Campaigns [4] NS1 - Colour Campaigns Insertion - Selection of a Colour campaign (from a source furnace) - Selection of a target Furnace (from the source one) - Insertion of the colour campaign, preserving the starting date B3 - Postpone the overlapped lots on target furnace - Reparation mechanism: Effects - Breas a colour campaign on the target furnace without the reparation mechanism (and eventually another one with the reparation mechanism) - Change the number and length of colour campaigns B3 - Interaction between furnaces (due to reparation mechanism) - Different Colour Campaign / furnaces assignment on the target furnace - Reparation mechanism may create new colour campaigns Bernardo Almada-Lobo 20 10

11 Shifts applied to Manufacturing Process Sub-Campaigns [1] NS6-Sub-Campaigns Swap Effects - Selection of sub-campaign 1 (from a source machine) - - CCP1 Change the number and length of sub- campaigns - Selection of sub-campaign 2 (from a target machine) - Interaction between machines - CCP2 - Breas the sub-campaign on the machine with - Swap CCP1 with CCP2 lac of capacity (with the reparation mechanism) - Reparation mechanism - Different sub-campaigns assignment on both machines Reparation mechanism may create new sub-campaigns Bernardo Almada-Lobo 21 Shifts applied to Manufacturing Process Sub-Campaigns [2] NS7-Partial swap sub-campaigns - Selection of sub-campaign 1 (from a source machine) - CCP1 - Selection of sub-campaign 2 (from a target machine) - CCP2 - Swap CPP1 with the overlapped lots with the same colour (that may belong to CPP2 or others sub-campaigns) - No reparation mechanism Effects B3 Breas the sub-campaign on the target machine Change the number and length of subcampaigns Interaction between machines Different sub-campaigns assignment on target machine B3 Bernardo Almada-Lobo 22 11

12 Shifts applied to Item Lots [1] NS8-Item Lots Insertion - Selection of an item lot of a sub-campaign on the source machine (LOT1) - Selection of a lot of the same item (LOT2) on a target machine, if its starting date is after the LOT1 starting date of a sub-campaign on the source machine (F1P1) - Insertion LOT2 after LOT1 on the source machine - Postpone the overlapped lots on source machine and on the other machines in order to satisfy the strong colour constraint. P1 P2 P5 P4 P3 P3 P5 P1 P6 P9 P3 P4 P4 P9 P2 P8 P2 P6 Effects P1 P2 P2 - Change the number and length of item lots - Interaction between machines - Different Lot / machine assignment - No reparation mechanism P5 P1 P3 P5 P4 P6 P4 P3 P6 P9 P3 P4 P9 P2 P8 Bernardo Almada-Lobo 23 Shifts applied to Item Lots [2] NS9-Partial Item Lots Insertion - Selection of a Colour Campaign 1 C (from a source furnace) - Selection of a Colour Campaign 2 C = colour of C (from a target furnace) - Insert the lots of first x days of C to the end of C horizon - Postpone the overlapped lots on source furnace and anticipate the lots following the lots removed on target furnace - Reparation mechanism Machine P1 P2 P5 P4 P3 P5 P1 P6 P9 P3 P4 P9 P2 P8 x P2 P3 P6 P4 Effects Machine P1 P2 P5 - Change the dimension of campaigns and sub-campaigns - Different Lot / machine assignment P5 P1 P3 P4 P4 P3 P6 P2 P9 P3 P4 P6 P9 P2 P8 Bernardo Almada-Lobo 24 12

13 MAIN EFFECTS SHIFTS OF Colour/Process Colour Campaigns Sub-Campaigns Items NS1 NS2 NS3 NS4 NS5 NS6 NS7 NS8 NS9 Breas the colour campaign of one of the furnaces Breas the colour/process sub-campaign of one of the furnaces (without reparation mechanism) Changes the number and the length of the colour campaigns Changes the number and the length of the colour/process sub-campaigns Demands a reparation mechanism Furnaces' interaction ' interaction Number of furnaces in which the assignment colour campaign/furnace change Changes the number and the item lots dimension Changes the assignment item/machine Bernardo Almada-Lobo Ongoing and Future Wor IMPLEMENTATION - Constructive Heuristics for generation of initial solutions Composite dispatching rules - Local Neighbourhood Search Heuristics - Meta-Heuristics: GRASP BAVidro instances (4 plants, 8 furnaces, 26 machines, 600 product types, ) Bernardo Almada-Lobo 26 13

14 Neighbourhood Structures for the Hierarchical Planning Problem on the Glass Container Industry B Almada-Lobo 1 ; JF Oliveira 1,2 ; MA Caravilla 1,2 1 FEUP Faculdade de Engenharia da Universidade do Porto 2 INESC Porto Instituto de Engenharia e Sistemas de Computadores almada.lobo@fe.up.pt 2005, 5th April 14