Collection Center Location Problem with Incentive & Distance Dependent Returns

Transcription

1 International Workshop on Distribution Logistics IWDL 2006 Brescia, ITALY October 2 nd 5 th, 2006 Collection Center Location Proble with Incentive & Distance Dependent Returns Deniz Aksen College of Adinistrative Sciences and Econoics, Koç University Necati Aras Departent of Industrial Engineering, Boğaziçi University Original slides by Ergül Taslacıoğlu Zenginer

2 Agenda Conclusions 2

3 Introduction Traditional focus of supply chains: fine-tuning the logistics of products fro raw aterial to the end custoer Modern supply chain view: increasing flow of products in the reverse direction 3

4 Definition of Reverse Logistics The process of planning, ipleenting, and controlling backward flows of raw aterial, in-process inventory, packaging, and finished goods fro a anufacturing, distribution or reuse point, to a point of origin for the purpose of recapturing value or proper disposal. (REVLOG, 2002) 4

5 Reverse Logistics Process (Fleischann et al., 2000) Collection: process of rendering used products available and physically oving the to soe point for further treatent. It ay include activities purchasing, transportation, and storage Collection Inspection/separation: costs are 30-50% the of set overall of operations EOL product for deterining anageent costs (Mulder whether et a al.,1999) given product is re-usable and in which way Reprocessing: transforation of a used product into a usable product again Disposal: done for products that cannot be re-used for technical or econoical reasons Redistribution: distributing reusable products to a potential arket 5

6 Types of Collection Strategies Curbside collection: consuers sort recyclable aterial fro other solid wastes and place in bins at curbside convenient, high return rate Drop-off centers: requires ore consuer effort, so lower return rates consuers are not offered reiburseent for aterials delivered Buy-back centers: consuers provide the initial transportation and drop-off recyclables they receive reiburseent 6

7 Coon practices for Collection (Mulder et al., 1999) Netherlands, Belgiu, and Italy unicipalities: ensure separate collection of EOL electronics fro households producers: in charge of recycling Switzerland and Sweden producers are fully responsible for organizing separate collection structures for EOL electronics Denark unicipalities are responsible for separate collection of EOL electronic products and also their proper treatent funded through local waste taxes 7

8 Multi Echelon Reverse Logistics Network (Min et al., 2006) custoers drop products to initial collection points (ICP) products are transferred fro ICPs to Central Return Centers (CRC) cost coponents: renting, inventory carrying, aterial handling, setup, shipping CRCs have a liited capacity service level requireent for ICPs Obective: finding optiu nuber and location of ICP and CRCs, and frequency of shipents fro ICP to CRCs 8

9 Proble is faced by a copany that collects used products fro consuers Sites at which collection centers can be located Consuers who have end-of-life products Drop-off odel Return decision based on the: financial incentive offered by the copany (R) travel distance of the consuers (d i ) Obective: to axiize profit by deterining sites at which collection centers ust be set up financial incentive (unit acquisition price) offered to custoers 9

10 Model-1: UCCLP the nuber and locations of CCs & incentive to be offered are decided tradeoff : high fixed cost and high return rate low fixed cost and less return rate Model-2: p-cclp UCCLP in which the nuber of collection facilities to be opened is predeterined siilar to the faous p-edian proble locations of CCs and incentive to be suggested are decided 10

11 5 9 R kd > R *3 > 20 3 R 0 : Reservation incentive (rv) R: Incentive Offered k: cost per unit distance traveled d :distance between cust. and nearest CC to it 11

12 R kd > R *3 < 20 3 R 0 : Reservation incentive (rv) R: Incentive Offered k: cost per unit distance traveled d :distance between cust. and nearest CC to it 12

13 R 0 R 0 ~ U(a,b) : easure of consuer willingness Ray et al., 2005; Woanowski et al., 2003 Probability density function of R 0 f ( R ) = 1 0 b a f(r 0 ) 1 a b R 0 Probability distribution function of R 0 F ( R 0 ) R = 0 a b a F(R 0 ) 1 a b R 0 13

14 Paraeters e i f i h s M Variables Y i δ1 : Euclidean distance between custoer zone and candidate site i : fixed cost of opening and operating a collection center at site i : nuber of product holders located at zone : unit revenue fro a return : a large nuber 1 if a collection center is located at site i = 0 otherwise 1 if product holdersat zone areassignedto thecollectioncenter at sitei X i = 0 otherwise R : aount of incentive offered by the copany P : proportion of product holders at zone who drop off their product 1 if product holders at zone do not drop off their product ( P = 0) δ 1 = 0 otherwise 1 if all product holders at zone drop off their product ( P = 1) δ 2 = 0 otherwise & auxiliary binary variables used for forulating P 14 δ 2

15 R : aount of incentive copany offers k : cost per unit distance traveled d : distance between cust. zone and nearest facility kd : cost of carrying product fro zone to nearest facility P : proportion of consuers at zone who return their product P = Pr( R kd R0 > 0) = ( R kd b a a) + P = 0 R kd a b a 1 R < kd kd + a R kd + a R < + b kd + b 15

16 Return Rate Function R 0 R 0 ~ U(a,b) P = 0 R 1 kd b a a R < kd kd + a R kd + a R < + b kd + b P 1 P 1 0 a kd +a R 1 kd +b s R 16

17 h : nuber of consuers that own the product of the copany h P : total nuber of returns fro zone s : value of a returned product (s R):profit gained fro each return Π =h P (s R): profit fro custoer zone = 0 h b a 0 2 ( R + α R β ) R < kd kd R s + a + a R < s 17

18 Obective Function - UCCLP ax n ( s R) f Y = h P = 1 i 1 i i Total expected profit Total fixed cost of opening CCs 18

19 Constraints (UCCLP) subect to (1) (2) i= 1 X i X i Y = 1 i i = 1,..., n = 1,..., ; = 1,..., n (11) R a (12) (13) (14) R s X Y i i { 0,1 } i = 1,..., ; { 0,1 } i = 1,..., = 1,..., n 19

20 δ1 = 1 and δ2 = 1 (3) (4) (5) (6) (7) (8) (9) (10) Infeasible R R R R P P P P ( ) ke X a M( ) i i i δ = 1 1 ( ) ke X a M i 1 i i + δ = 1 ( ) ke X + b + Mδ ( ) ` ke X + b M( 1 δ ) 2 i= 1 i= 1 1 δ δ 1 R ( R ( i i i= 1 ke b a i= 1 i i ke i i b a X X i i 2 2 ) a + M ) a M ( δ + δ ) 1 = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n ( δ + δ ) = 1,..., n P 1 0 a kd +a kd +b s 20 R

21 δ1 = 0 δ2 = 0 and 1 P (3) (4) (5) (6) (7) (8) (9) (10) R R R R P P P P ( ) ke X a M( ) i i i δ = 1 1 ( ) ke X a M i i i + δ = 1 1 ( ) ke X b M i 1 i i + + δ = 2 ( ) ke X + b M( 1 δ ) 2 i= 1 1 δ δ 1 R ( R ( i i= 1 ke b a i= 1 i ke i i b a X X i i 2 ) a + M ) a M ( δ + δ ) 1 = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n ( δ + δ ) = 1,..., n a kd +a kd +b s 21 R

22 P δ1 = 0 and δ2 =1 1 (3) (4) (5) (6) (7) (8) (9) (10) R R R R P P P P ( ) ke X a M( ) i i i δ = 1 1 ( ) ke X a M i i i + δ = 1 1 ( ) ke X b M i 1 i i + + δ = 2 ( ) ke X + b M( 1 δ ) 2 i= 1 1 δ δ 1 R ( R ( i i= 1 ke b a i= 1 i ke i i b a X X i i 2 ) a + M ) a M ( δ + δ ) 1 = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n ( δ + δ ) = 1,..., n a kd +a kd +b s 22 R

23 P δ1 = 1 and δ 2 = 0 1 (3) (4) (5) (6) (7) (8) (9) (10) R R R R P P P P ( ) ke X a M( ) i i i δ = 1 1 ( ) ke X a M i i i + δ = 1 1 ( ) ke X b M i 1 i i + + δ = 2 ( ) ke X + b M( 1 δ ) 2 i= 1 1 δ δ 1 R ( R ( i i= 1 ke b a i= 1 i ke i i b a X X i i 2 ) a + M ) a M ( δ + δ ) 1 = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n = 1,..., n ( δ + δ ) = 1,..., n a kd +a kd +b s 23 R

24 Extension: p-cclp Obective function ax = n = 1 h P ( s R) Additional constraint =1 Y i i = p 24

25 Begin Phase 1: Tabu Search Select CCs to be opened CCs opened Phase Phase 2: 2: Nelder-Mead Fibonacci Siplex Search Search or Hooke-Jeeves for 1 quality Pattern type Search for ultiple quality types Deterine R or R s (single vs. ultiple quality types) Obective value calculated No Does any stopping condition hold? Yes End 25

26 p-cclp: 1 st phase - Tabu Search Initially p facilities opened with the sallest total distance fro custoer zones SWAP ove operators used (syetrical 1-Swap, 2-Swap, and 3- Swap) to generate a neighborhood of the current solution For each ove operator: nu_neigh = p( p)/3 Tabu status is tracked for every facility: tabu_tenure [1, 2,, Max_Tabu_Tenure = 25] Search terinates IF EITHER ax_iter iterations have been executed, OR IF the best solution found so far does not iprove for ax_nonip_iter consecutive iterations 26

27 p-cclp & UCCLP:2 nd phase Fibonacci Search f(r) f ( λ k ) > f ( µ k ) f f( ( µ k λ + k 1) ) f ( µ k ) f ( λ k+ 1) f ( λk + 1 ) < f ( µ k + 1) a k λ k µ k R k +1 λ k +1 µ k +1 a 1 b k b k + ak +2 λ k +1 µ k + 1 b k +2 27

28 UCCLP: 1 st phase - Tabu Search initially 1 rando facility opened 1-ADD, 1-DROP, 1-SWAP ove operators to generate a neighborhood of the current solution For 1-ADD: nu_neigh = ( ρ) For 1-DROP: nu_neigh = ρ For 1-SWAP: nu_neigh = in{3, ρ ( ρ)} Tabu status is tracked for every facility: tabu_tenure [1, 2,, Max_Tabu_Tenure = 25] Search terinates IF EITHER ax_iter iterations have been executed, OR IF the best solution found so far does not iprove for ax_nonip_iter consecutive iterations 28

29 TS Heuristic vs. Exhaustive Search on p-cclp 29

30 SBB Solver of the GAMS Suite v22.0 SBB calls CPLEX 9.0 for the IP subprobles, and either MINOS or CONOPT as subsolver for NLP OQNLP and DICOPT as MINLP solvers perfor even worse. 30

31 SBB Solver vs. TS Heuristic on UCCLP instances 31

32 Effect of the variability of R 0 Width of [a,b] 32

33 Effect of the variability of R 0 Width of [a,b] 33

34 Effect of the variability of R 0 Width of [a,b] 34

35 Effect of the variability of R 0 Width of [a,b] when a = const. 35

36 p-cclp Results - Suary as p increases profit increases, but the arginal profit decreases with each additional facility return rate increases financial incentive offered decreases when s is higher incentive is higher collection rate is higher 36

37 p-cclp Effect of the Variability of R 0 As ean and standard deviation increases profit decreases return rate decreases incentive increases to soe extend 37

38 p-cclp Effect of the Variability of R 0 As standard deviation increases, ean being constant Profit increases, for s=50 and s=75 first decreases then increases for s=100 Return rate increases for s=50 decreases for s=75 and s=100 Incentive decreases 38

39 UCCLP Results - Suary when fixed cost is higher profit is lower # of opened CCs is lower return rate is lower when s is higher profit & incentive is higher # of CCs lower 39

40 Conclusions a CC location odel is proposed for collection of EOL products fro custoers nuber and locations of CCs that should be opened and financial incentive are deterined custoers are assued to aggregate at soe points a reservation price is assued for each custoer two factors affect custoers decision on returning the product: financial incentive proxiity to the nearest collection center returned product still has a value for the copany which can be extracted by subsequent reprocessing activities 40

41 Conclusions proble is forulated as a Mixed-Integer Nonlinear Facility Location (MINLP) odel to deterine the collection center locations and the financial incentive to be offered a 2-phase solution ethodology is used Tabu search & Fibonacci search 3870 experients are ade in total results are presented for two odels: p-cclp and UCCLP 41

42 Questions & Coents? Coputational Results p-cclp Sensitivity Results with respect to p and s p-cclp Sensitivity with respect to Variance and Mean Effect of the FC value in UCCLP Effect of R 0 variability in p-cclp Milano Istanbul Bergao Brescia 42

43 Effect of p on Profit 1.E+06 Profit (Logarithic Scale) 1.E+05 1.E+04 1.E+03 s=50 s=75 s=100 1.E p 43

44 Effect of p on Collection Rate Collection Rate (%) s=50 s=75 s= p 44

45 Effect of p on Incentive Incentive s=50 s=75 s= p 45

46 Effect of s on Incentive & Collection Rate Incentive Incentive Collection rate Collection Rate (%) s 0 p=1 46

47 Varying µ and σ: Effect on Profit 40,000 35,000 Profit 30,000 25,000 20,000 15,000 p=1 p=2 p=3 p=4 p=5 p=6 10,000 5,000 0 [40,60] [40,70] [40,80] [40,90] [40,100] [a,b] s=75 47

48 Varying µ and σ: Effect on Return Rate Return Rate (%) p=1 p=2 p=3 p=4 p=5 p=6 0 [40,60] [40,70] [40,80] [40,90] [40,100] [a,b] s=75 48

49 Varying µ and σ: Effect on Incentive, s= Incentive p=1 p=2 p=3 p=4 p=5 p= [40,60] [40,70] [40,80] [40,90] [40,100] [a,b] s=75 49

50 Varying µ and σ : Effect on Incentive, s= Incentive p=1 p=2 p=3 p=4 p=5 p= [40,60] [40,70] [40,80] [40,90] [40,100] [a,b] s=100 50

51 Effect of Fixed Cost on Profit Profit s=50 s=75 s= Low Mediu High Fixed Cost 51

52 Effect of Fixed Cost on Incentive and # of CCs s= s=75 s=100 Incentive Nuber of CC's Opened s=50 s=75 s=100 0 Low Mediu High 0 Fixed cost level 52

53 Effect of Fixed Cost on Return Rate Return Rate (%) s=50 s=75 s=100 0 Low Mediu High Fixed Cost 53