Optimization Problems and Algorithms in Supply-Chain Management

Transcription

1 Optimization Problems and Algorithms in Supply-Chain Management 1 Botond Bertok, 1 Robert Adonyi, 2 Sandor Bodrogi, and 1 Zoltan Kovacs 1 University of Pannonia, Faculty of Information Technology Department of Computer Science 2 Ministry of Defence, Electronics, Logistics and Property Management Co. Ltd. Electronics Directorate VOCAL 2006 December 13-15, 2006

2 2 Outline Project Asset tracking Technological Elements of the Proposed System Levels of Decision Support Supply-chain Synthesis Route Planning Shipment Planning Space Filling

3 3 Project Title: On-line Optimization of Asset Traffic Satisfying Safety Regulations Partners: University of Pannonia, Faculty of Information Technology University of Szeged, Faculty of Science Ministry of Defence, Electronics, Logistics and Property Management Co. Ltd. Sponsored by: National Research and Development Programme 2004 Duration:

4 On-line Optimization of Asset Traffic Satisfying Safety Regulations 4 Keywords Asset Tracking Optimization and Decision Support Safety Regulations On-line

5 5 Asset tracking Traffic control center Server NAVSTAR GPS GSM GSM Plant Repository WAN IBU Barcode reader PC PC Asset Asset Asset Intelligent Board Unit

6 6 Technological Elements of the Proposed System Automatic tracking of assets, using barcodes and RFIDs (Radio Frequency Identification) in the whole supply chain Intelligent Board Unit on vehicles Automatic asset identification Video and sound processing Automated information interchange through EDI (Electronic Data Interchange) between the partners having EAN/UCC identification Automatic recognition of the critical differences between tracking information and plans Real-time revision of the route plan when unexpected event is detected Multilevel decision support and optimization system

7 7 Levels of Decision Support Decisions supported by the system Supply-chain synthesis Route planning Shipment planning Strategic Control Strategic Decision Makers Traffic Control Traffic Control Center Space filling, Loading order Local Decisions Repository Vehicle

8 8 Supply Chain Synthesis: Problem Synthesize optimal network of purchase, production, and transportation Multi-objective optimization: minimize cost, makespan, risk regarding cost, makespan, risk

9 9 Supply Chain Synthesis: Methodology P-graph approach for process synthesis Exploring transportation needs Modeling timing constraints Adopting algorithms Modeling reliability Search strategy

10 10 Process Network Synthesis (PNS) Inputs: A set of demands (to be satisfied), A set of resources (available or can be purchased) A set of functional units (manufacturing, transportation) Cost data and capacity constraints Output: A ranked list of the n-best network

11 PNS: Mathematical Model (Friedler et al., 1992, 1993, 1995) 11 Structural model: P-graph representation m j inputs r i,j input/output ratio functional unit O i Design variables: y i : existence of unit O outputs x i : size or capacity of unit O i

12 capacity PNS: Mathematical Model (Friedler et al., 1992, 1993, 1995) 12 Mass balance constraints: x 1 r 1,j + x 2 r 2,j x 3 r 3,j x 1 r 1,j r 2,j x 2 m j Cost: a 1 x 1 + b 1 y 1 + a 2 x 2 + b 2 y 2... y i {0,1} cost r 3,j x 3 In the relaxed model: x i M y i and y i [0,1]

13 13 Axioms of Combinatorialy Feasible Process Structures (Friedler et al., 1992) (S1) Every final product is represented in the structure. (S2) A material represented in the structure is a raw material if and only if it is not an output of any operating unit represented in the structure. (S3) Every operating unit represented in the structure is defined in the synthesis problem. (S4) Any operating unit represented in the structure has at least one path leading to a product. (S5) If a material belongs to the structure, it must be an input to or output from at least one operating unit represented in the structure

14 14 PNS: Reduction of the Search Space Search Space Combinatorically Feasible Structures Feasible Structures

15 PNS: Combinatorial Algorithms (Friedler et al., 1992, 1993, 1995) 15 Algorithm SSG (Solution-Structure Generator) generates each combinatorially feasible structure exactly once Algorithm MSG (Maximal Structure Generation) generates the superstructure: the union of the combinatorially feasible structure Algorithm ABB generates the n-best solution of the problem while examines the set of combinatorially feasible structure in the worst case

16 PNS: Combinatorial Acceleration (Friedler et al., 1995) 16 F G H I F G H I F G H I C D E C D E C D E B B B A A A included in each structure (based on decisions) included in each structure (based on maximal neutral extension) excluded from each structure included in at least one structure

17 Supply Chain Synthesis: Exploring transportation needs 17 production at place B production at place A consumption at place C

18 Supply Chain Synthesis: Exploring transportation needs 18 transportation: B -> C transportation: A -> C

19 19 Supply Chain Synthesis: Modeling timing constraints Timing constraints: t k t j + d i x i + e i y i t j m j O i t k time m k amount

20 20 Supply Chain Synthesis: Adopting Algorithms Algorithm SUIT: Search Units reachable In Time timefix = 4 t = 9 timefix = 6 t = 11 timefix = 3 t = 8 timefix = 5 t = 5 timefix = 6 t = 6 demand

21 21 Supply Chain Synthesis: Modeling reliability Without redundancy overall reliability = exp sum of the logarithms of the reliabilities of the elements of the network With redundancy p 12 = p 1 + p 2 p 1 p 2i Relaxed model: p 1 p 1MAX y 1, p 2 p 2MAX y 2 p O1 p 1 p 2 p O2 p 12MAX = p 1MAX + p 2MAX p 1MAX p 2MAX p 12 p 12MAX p 12 p 12 p 1 + p 2 p O3

22 22 Supply Chain Synthesis: Search Strategy initialization Route planning for estimating costs of potential transportations search finalization Shipment planning based on the designed capacities of transportations

23 23 Supply Chain Synthesis: Route Planning Route planning Generate shortest, fastest, cheapest, and most reliable path Vehicle profile - e.g., size, weight, speed, fuel consumption Employee profile - e.g., wage, working hours

24 24 Supply Chain Synthesis: Shipment Planning Designing optimal flow of mass volume vehicles transportation needs routes of vehicles

25 Supply Chain Synthesis: Shipment Planning (Cont'd) 25 Space filling variable sized 3-dimensional bin packing problem (volume) (first algorithm published in 2004 by Epstein, van Stee) vector packing (mass) safety regulations heuristic methods - forming larger blocks decreasing the dimension of the packing problem Scheduling single vehicles

26 26 Supply Chain Synthesis: Search Strategy initialization Route planning for estimating costs of potential transportations search finalization Shipment planning based on the designed capacities of transportations

27 27 Conclusion On-line supply chain optimization requires integration of modern solutions of information and telecommunication technologies effective optimization methods for - network synthesis, - route planning, - shipment planning, and - space filling