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Dry and Buy decision for kiln scheduling
- 1. Dry-or-buy decision support for dry kiln scheduling in furniture production ARMAN R. YAGHUBIAN, THOM J. HODGSON & JEFFREY A. JOINES Himanshu Bhokarikar | Ankit Ranjan Biswa Ranjan Barik | Vardhan Reddy Project 15 OHM Term Project
- 2. Introduction
- 3. FURNITURE MAKING PROCESS Shaping, Finishing, Polishing etc. GREEN LUMBER X DRIED LUMBER Cost Dried Lumber procuring methods Buying Dried Lumber from open market Buying Green Lumber and drying using inhouse kilns Background Understanding furniture production: Green lumber Vs dry lumber - root cause for dry-buy decision Raw Wood Green Lumber Dried Lumber Dimensional stability Biological degradation Strength Nail holding ability Low High V. Low Low Low V. High Low High High High Significantly more expensive Comparatively cheaper Assumed unlimited supply Supply is limited by the capacity of in-house kilns Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 4. Possible Solutions 1 2 3 Iterative "What-If" Cost Analysis X Trial-and-error, suboptimal for large problem Mathematical programming, cost minimization (IP) NP-completeness, computational complexity Three-phase heuristic local search Faster computation, not always optimal Background Solution Approaches and Constraints: Iterative, LP, Heuristics Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 5. Formulation
- 6. OBJECTIVE FUNCTION X Decision Variables Amount of demand j outsourced No. of jobs assigned to kiln k of demand j Parameters Per Sq. Foot cost of dried lumber Cost of drying demand j in kiln k Demand j (in board feet) Per Sq. Foot cost of green lumber Risk Assessment Introduction Methodology Analysis Mitigation Formulation Understanding furniture production: Formulating trade-off between buying Vs drying lumber Cost of Buying Dried Lumber Total cost of Drying Green Lumber Cost of Buying Green Lumber Introduction Conclusion Modelling Formulation
- 7. 1 2 3 The processing time + starting time of a job Should be lesser than the Due Date X Formulation Understanding furniture production: Constraints In-house dried lumber (in sq. foot) + Outsourced dried lumber would be Greater than Total Demand Both the decision variables should be Positive Integers Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 8. Modelling
- 9. START Quick and Dirty Solution 2-1 exchange ? 1-2 exchange ? 1-1 exchange ? 1-0 push ? Job Reallocation Outsource Re-evaluation Success after stage 3 1000 starting points ? STOP X Heuristic Solving the dry vs buy dilemma : Understanding heuristic algorithm STAGE 1 STAGE 2 STAGE 3 Randomly Sequenced Randomly Sequenced NO NO NO Success Success Success Success Success Success NO NO NO YES YES NO SWITCHING ROUTINES RE-EVALUATION Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 10. Heuristic Algorithm Code INITIALIZATION IMPROVEMENT COST FUNCTION UTILITY FUNCTIONS Assigning Job j to Kiln k & selecting jobs to be outsourced Minimizing Drying - Buying Cost Switching Routines Checking the Feasibility and Improvement X Heuristic Solving the dry Vs buy dilemma : Understanding heuristic algorithm Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 11. Simulated Annealing Code INITIALIZATION COST FUNCTION IMPROVING THE COST FUNCTION STOPPING CRITERIA Random initial solution & Defining initial Temp Minimizing Drying - Buying Cost Defining the objective function & Cost calculation Number of Iteration X Heuristic Solving the dry Vs buy dilemma : Understanding Simulated Annealing algorithm Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 12. Conclusion
- 13. X Method Implemented 100 1000 10000 Heuristic 0.31 sec 1.09 sec 2.07 sec Simulated Annealing 0.61 sec 2.70 sec 3.40 sec Integer Programming (IP) 1.30 sec 4 sec 6.22 sec Value of N Background Comparing Solution Approaches: Heuristic, Simulated Annealing, and IP Algorithm Performance Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation
- 14. Literature Review X Problem Identification Formulation Simulated Annealing Comparative Analysis Presentation Design Conclusion Personal contribution Ankit Ranjan Biswa Ranjan Barik Himanshu Bhokarikar Vardhan Reddy Heuristic Implementation Risk Assessment Introduction Methodology Analysis Mitigation Introduction Conclusion Modelling Formulation GitHub Link