Industrial Optimization


 Shana Montgomery
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1 Industrial Optimization Lessons learned from Optimization in Practice Marco Lübbecke Chair of Operations Research RWTH Aachen University, Germany SICS Stockholm Feb 11, 2013
2 Discrete Optimization: Some Applications vehicle routing container logistics course timetabling production planning materials stacking patient scheduling
3 Steel Production
4 Coil Coating
5 Coil Coating: Local Cost
6 Coil Coating: Global Cost
7 Coil Coating: A Sequencing Problem? A sequencing problem... oven finish coater oven primer coater finish coater chem coater
8 Coil Coating: A Sequencing Problem? A sequencing problem... oven test runs finish coater temperature di erences oven many more... primer coater finish coater color changes +rollerchanges height/width/... di erences chem coater roller changes width di erence over threshold? +specialcoating with a very complicated cost function.
9 Shuttle Coaters
10 Tank Assignment Problem Given a fixed sequence of coils
11 Tank Assignment Problem Given a fixed sequence of coils Setup work necessary if
12 Tank Assignment Problem Given a fixed sequence of coils Setup work necessary if I color changes ; cleaning
13 Tank Assignment Problem Given a fixed sequence of coils cleaning cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning
14 Tank Assignment Problem Given a fixed sequence of coils cleaning cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
15 Tank Assignment Problem Given a fixed sequence of coils roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
16 Tank Assignment Problem Given a fixed sequence of coils roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
17 Tank Assignment Problem Given a fixed sequence of coils 1 2 roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
18 Tank Assignment Problem Given a fixed sequence of coils 1 roller change roller change cleaning &roller change cleaning cleaning cleaning 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
19 Tank Assignment Problem Given a fixed sequence of coils tank 1 1 tank 2 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
20 Tank Assignment Problem Given a fixed sequence of coils tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
21 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
22 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
23 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
24 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
25 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
26 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
27 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
28 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
29 Tank Assignment for Several Coaters I coating line has multiple coaters oven finish coater oven primer coater finish coater chem coater
30 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2
31 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
32 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
33 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
34 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
35 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2
36 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2 I I weight(i) = time saved due to setup work avoided (vs. no shuttle) i.e. setup setup I I
37 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2 I I weight(i) = time saved due to setup work avoided (vs. no shuttle) i.e. setup setup I + saved time from concurrent setup (if possible) I i.e. setup concurrent setup I I
38 Tank Assignment Optimization Special case: one shuttle coater! select most profitable, nonoverlapping intervals! optimum tank assignment max weight independent set in interval graph! can be solved in polynomial time
39 Tank Assignment Optimization Special case: one shuttle coater! select most profitable, nonoverlapping intervals! optimum tank assignment max weight independent set in interval graph! can be solved in polynomial time General case: k shuttle coaters! need generalized intervals due to concurrent setup! special class of 2union graphs! optimum tank assignment max weight independent set in special 2union graph! NPhard! polynomial time dynamic program for fixed k
40 Tank Assignment Heuristic Practice Tank Assignment Problem with k coaters e new ideas for cient algorithm far too slow, even for small instances Theory Max Weight Indep. Set in special 2union graphs polynomialtime algorithm for fixed k ; dynamic programming strongly NPhard
41 Visualization/Verification of Solutions At a glance: Sequence, tank assignment, and cleaning schedule +adetailedexcelsheet
42 Quality of Solutions I How good are our heuristic coating plans?
43 Integer Program: Variables
44 Integer Program: Variables z s : for each possible subsequence s (global cost) z s
45 Integer Program: Variables y i, j z s : y i, j : for each possible subsequence s (global cost) between subseq.s (local cost) z s
46 Integer Program: Variables x p, j y i, j z s : y i, j : x p, j : for each possible subsequence s (global cost) between subseq.s (local cost) decide whether job j is at position p z s
47 Integer Program: The Master Problem min X s c sz s + X i,j2j c i,jy i,j X x p,j 1 j 2 J p2p X x p,j apple 1 p 2 P j2j X s3j: p(s,j)=p z s = x p,j p 2 P, j 2 J x last(t),i + x first(t+1),j apple 1+y i,j t =1,...,T 1 x p,j 2 {0, 1} p 2 P, j 2 J y i,j 2 {0, 1} i, j 2 J z s 2 {0, 1} s 2 S I solved by branchandprice
48 Results
49 Results I Reduction of idle times by about 30%! solutions verified in practice I Optimization potential for the makespan below 10%! probably less I Our schedules taught practitioners about their machines! OR/maths brings up solutions never thought of before I Went live in 2010! finally, after countless feedback cycles
50 Letter of Appreciation
51 Letter of Appreciation
52 Why (Mathematical) Optimization? I almost every process shows some improvement potential I active decision support in complex situations is rare I need relief from routine tasks, concentrate on essential I need constant/reliable quality over di erent shifts
53 Two Worlds: Views, Motivations, Interests academia/research I interesting problem! I every " counts I the problem instances may be infeasible I research takes time I clean, welldefined world industry/services I we need a solution! I we do not care about 2% I we need a solution, no matter what! I results due yesterday I nasty constraints
54 Tailormade vs. Standard Software academic solution I projectspecific support I your problem is our problem I our solution fits your process I optimization algorithms I active planning suggestions I too cheap standard software I longterm support I your problem means cash I your process fits their solution I heuristics at best I passive visualization I too expensive
55 Complementary Competences I ideal configuration may take three partners I problem owner I software/it provider I academia/research institution
56 Data
57 Are you creative? What would you improve? I objectives may be hard to formulate I don t talk to consultants (too much) I talk to mathematicians computer scientists, programmers!
58 We have many Constraints, or have we? I we have been doing this for 20 years! I distinguish habits from real constraints I mathematical solutions may look di erent from human plans I be open to the unknown
59 Humans don t know how to optimize! I don t feel bad about it! I optimization is made for computers, not humans!
60 Acceptance I talk to everybody involved I convince local expert I if possible: demonstrate potential early I convince management I improve in rounds I usually: optimization supports sta, not replaces them I your task is not easy, why should the solution be?
61 Summary and Conclusion I optimization may bring your business to the next level I academia o ers more and less I be open!
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