Abstract Number : Optimal Blending Model for Paper Manufacturing With Competing Input Materials. Rupesh Kumar Pati,

Transcription

1 Abstract Number : Optimal Blening Moel for Paper Manufacturing With ompeting Input Materials Rupesh Kumar Pati, Inian Space Research Organization, Srihariota, Anhra Praesh, Inia- rupesh_pati@reiffmail.com, Phone No.: Prem Vrat (orresponing Author) Vice hancellor, U.P Techanical University, Lucno, Uttar Praesh, Inia-60 pvrat@hotmail.com, vc@uptu.ac.in, Phone no.: POMS 8th Annual onference Dallas, Texas, U.S.A. May to May 7, 007

2 Optimal Blening Moel for Paper Manufacturing With ompeting Input Materials Rupesh Kumar Pati an Prem Vrat Abstract: The stringent environmental regulations, groing shortages of ra materials have brought the concept of reverse supply chain into limelight. This paper presents a linear programming moel for minimizing the cost of paper manufacturing by optimal blening of to competing input materials viz. oo as ell as by recycling astepaper. The objective function inclues forar an reverse supply chain costs encountere uring paper manufacturing from the manufacture's viepoint. The moel also inclues the economic implications of using the alternative input materials on the environment, paper quality along ith the possible reuse of the non-relevant astepaper collecte uring the segregation stage. The moel can assist the manufacturer to etermine the optimal amount of oo as ell as astepaper require to satisfy the maret eman uner a given situation. To gain further insight into the system behaviour, sensitivity analyses have been carrie out hich highlights various strategies uner ifferent conitions. Key Wors: Optimal blening, Supply chain, Paper manufacturing, Linear Programming. Introuction Availability of natural resources an its exploitation have impact on economic evelopment of a country. The quest of man for higher stanar of living has multiplie the emans exorbitantly, an the earth s non resources have starte epleting along ith generation of soli aste at an alarming rate. The groing size an cost of the Municipal Soli Waste (MSW) (mainly of plastics, papers, metal scraps etc.) isposal problem is also

3 raing attention all over the orl. The costs, public apprehension, health an environmental concerns have mae lanfill an incineration methos unesirable. Incineration facilities are not very popular ue to air pollution problems an lanfills are preicte to become the most expensive isposal metho because of iminishing availability of space an stringent environmental stanars [Tilman an Sanhu (998)]. Alternative management methos are being sought by recycling or reusing the ingreients of the municipal soli aste as far as possible. The paper inustry is one such sector hich extensively epletes a natural resource i.e. forest cover by consumption of oo in an iniscriminate manner an aversely affecting the environment. Also the groth in the literacy as ell as urbanization has le to increase use of paper proucts, consequently leaing to increase in aste paper content in MSW. This clearly highlights the nee for conservation of available resources i.e. forest cover by effective astepaper management through recycling/reusing. The focus on the recycling issue in recent years is mainly on (a) the municipal soli aste (or supply) of paper recycling an (b) on the policy aspects of the issue [Smith (997)]. Samaovlis (00) re-evaluates the hierarchy of paper aste management policies in a ynamic general equilibrium moel. Grace et al. (978) an Yohne (979) performe economic stuies of the supply an eman or trae, ith aste paper. Recent publications on aste paper recycling concentrate on the high volatility of aste paper prices [Acerman an Gallagher (00)], examine inter-country ifferences in aste paper recovery an utilization rates [Bystrom an Lonnstet (99), Berglun et al. (00)] or iscuss hether astepaper shoul be recycle or incinerate [Hanley an Slar (99), Leach et al. (997), Bystrom an Lonnstet (997), Samaovlis (00)]. Various stuies are reporte on the environmental

4 issues in astepaper recycling. Bloemhof-Ruaar et al. (996) evelope an environmental life cycle optimization moel for the European pulp an paper sector. The objective of the moel as to minimize environmental impacts of virgin paper prouction, recycle paper prouction, astepaper incineration an transport. Hoever, literature on the economic analyses for manufacturing paper by blening of to competing ra materials i.e. oo an recyclable astepaper ith ue consieration to environment as ell as the quality issues coul not be trace. This paper attempts to fill the gap by eveloping a linear programming moel to minimize system ie paper manufacturing cost by blening to competing ra materials. Further, the sensitivity analysis etermines the effect of the quality of input ra material as ell as the quality of the finishe paper on the system. The effect of environmental costs (representing the egree of concern of manufacturer for the environmental) on the system has also been stuie.. Functional Moel of Inian Paper Inustry Figure represents a functional supply chain moel ith various entities involve in manufacturing of paper in Inia by blening competing ra materials. The members involve in paper manufacturing (upto manufacturer) are consumer (a term use to represent a customer ho sells the use paper for recycling to ealer), segregator, an supplier of segregate relevant astepaper to manufacturer. The supplier of oo to the manufacturer is another important entity of the paper supply chain. The associate costs are collection cost of ra material, transportation, inventory (carrying, shortage an orering), segregation an isposal, an manufacturing (ra material, poer an miscellaneous) as ell as reuse cost of certain varieties of astepaper hich are not fit for recycling. The astepaper collecte by the

5 SUPPLIER OF WOOD (=) Material flo irection Flo of oo for paper manufacturing ollection cost of oo Shortage cost of oo MANUFATURER (=) Information/eman flo irection Inboun transportation cost of oo an astepaper for blening Inventory cost of oo an astepaper (orering cost, carrying cost an shortage cost) Manufacturing cost (oo an astepaper ra material cost, energy cost an miscellaneous cost) Environmental cost (upgraation by using astepaper an egraation by using oo) ost of quality ( upgraation by using oo an egraation be using astepaper) SUPPLIER OF WASTEPAPER (=) Flo of astepaper for paper manufacturing Inboun transportation cost of segregate recyclable astepaper Wastepaper inventory cost (orering cost, carrying cost, shortage cost) ONSUMER DEALER (=) ost of collection of astepaper/use paper Inboun transportation cost of collecte astepaper Wastepaper inventory cost (carrying cost, shortage cost) SEGREGATOR (=) Inboun transportation cost of astepaper prior to segregation Segregation cost of recyclable as ell as reusable astepaper collecte. Disposal cost of unrelevant astepaper Wastepaper inventory cost (orering cost, carrying cost, shortage cost). Reusable astepaper cost Figure-: Schematic Diagram of Inian Paper ycle from Manufacturer s Viepoint (ith etaile cost involve). inicates the echelon number in the entire supply chain

6 ealer from the consumer broaly consists of three varieties of astepaper i.e. relevant recyclable astepaper, reusable astepaper (not fit for recycling but can be reuse) an finally, unrelevant astepaper (neither fit for recycling nor reusing). These costs have been shon at the require echelon the figure. An aitional feature consiere in the above moel (at the requisite echelon) is the inclusion of cost of quality an the cost of impact on environment by the use of competing ra materials i.e. oo an relevant astepaper for recycling. The figure also inicates the irection of the flo of ra materials (bol arros) an eman information (otte arros) beteen the echelons. To facilitate the moel formulation, the folloing assumptions are postulate: Initial inventory an the maximum storage capacity for each variety of collecte aste/ra material at each stage uner consieration are non. The emans for the respective prouct/ra material at each echelon are non. In practice; these emans can be measure reaily from orer entries of each stage. The cost of internal istribution is ignore. orresponingly, only the inboun transportation cost is taen into account in moel formulation. There is no loss of any variety of at any echelon in system. There is enough eman for finishe paper prouct i.e. hatever is prouce at manufacturer stage is immeiately sent to the maret ith no storage. The segregate astepaper recovere for reuse is not store but reuse immeiately ith no storage or any other associate cost after segregation. No orering cost at the ealer stage has been accounte as they collect the unsegregate astepaper from society.

7 Unit energy cost an miscellaneous cost are constant for any type of output prouct (finishe paper) at manufacturer stage.. Optimal Blening Moel for Paper Manufacturing The objective of the propose linear optimization moel is to minimize the total system cost for paper manufacturing by blening the to competing ra materials i.e. oo an recyclable astepaper subjecte to various constraints. The moel has the provision for varying egree of shortage of the prouct in eman at each echelon. The objective of the moel is represente by equation (0). The concern of manufacturer for the quality of finishe paper an environment has been reflecte in the moel by assigning appropriate environmental an quality opportunity costs component in the objective function. Woo in comparison to recyclable astepaper has higher fiber strength, thus leaing to improve quality characteristics. Hence, a negative quality cost is assigne in the moel for the proportion of oo in the blen an a positive cost hen astepaper is use. In contrary, the use of oo epletes the natural resources as ell as leas to ecological imbalance, hereas, the use of astepaper improves the environment by reucing the content of soli aste. Thus, a negative environmental opportunity cost is assigne for the use of astepaper an positive cost for the use of oo. A negative cost has also been assigne for reusing the proportion of astepaper segregate at the segregator stage. Various constraints consiere in the formulation of the moel are eman constraints, storage capacity constraints, astepaper mix constraint, an non-negativity constraints (from equation 0-). The moel can solve for the optimal flo of ra materials

8 in the netor an also etermine the system cost for various egrees of shortages. The explanation of the notation use in moel formulation is given in Appenix I. The total cost of paper prouction by blening oo an astepaper can be represente as: Total cost =[collection cost of astepaper by ealer from venor customer][collection cost of oo at supplier of oo stage][transportation cost of astepaper from ealer to manufacturing plant covering segregator, supplier stage an transportation cost of oo from supplier of oo to manufacturer stage][segregation cost of recyclable relevant astepaper an reusable astepaper at segregator stage][isposal cost at segregator stage][cost of reusing the reusable astepaper][inventory carrying cost of ra materials (oo as ell as astepaper) for all relevant stages from ealer to manufacturer][orering cost for oo an astepaper at all echelons except supplier of oo an ealer stages] [shortage cost at all stages for require eman][manufacturing cost incluing ra material, energy an miscellaneous costs][quality cost at manufacturer][environmental cost assigne at manufacturer] The mathematical representation of the propose moel is as follos: Minimize ( ) ( ) [ ] ( ) ( ) [ ] [ ] D RU RU g g c c D S S l T l T = = [ ] ( ) ( ) rc f f RU RU h Y W b h Y W b 0 0 )) ( ( (0) ) ( (0) = = * * * (0) (0) O O O h b h b ( ) ( ) ( ) ( ) = S S S S S S S S

9 R W f R ( W f ) P OM Y Yrc R ( Wf ) q R Wf q Yrc Y ED W Y ( W ) 0 f ED f Yrc 0 0 Subject to: b ( 0) ( S) -- (0) -- (0) b ( 0) ( S ) =, -- (0) ( -- (0) b 0) ( S) Wf Y Deman constraint b (0) ( S) ( W f ) -- (0) Y rc 0 ( S) -- (06) ( S) -- (07) D WD -- (08) RU WRU Wastepaper mix -- (09) constraint RU D = -- (0) b ( 0) B -- () b (0) B, -- () = W Storage constraint -- () 0 f b (0) B Y 0 ( W f ) b (0) B -- () Y rc RU D,,,,,,, 0, 0 Non-negativity constraint -- ()

10 Equation (0-0) represents the satisfaction of eman for the astepaper at ealer, segregator an supplier of astepaper stage, hereas, Equation (0-0) are the eman for ra materials i.e. oo an astepaper respectively at the manufacturer stage to fulfill its eman for finishe paper. Equations (06-07) represent the satisfaction of the eman for the finishe paper an oo at manufacturer an supplier of oo stage respectively. Equations (08-0) signify the presence of relevant recyclable aste, reusable paper (not fit for recycling) in the mix of astepaper s collecte from consumers. It is assume that the proportion of reusable astepaper an isposable astepaper is alays W RU an W D respectively of total aste collection from consumers. Equations (-) enote the maximum available storage capacity at ealer, segregator, supplier of astepaper an manufacturer stages for astepaper an/or oo. Equation () correspons to the estimates of the ecision variables. All the estimates shoul be subjecte to the non-negative omain in orer to meet the basic requirements of feasible solutions.. Sensitivity analysis To emonstrate the applicability of the propose blening moel, inputs ere collecte from Uttaranchal (a state in Inia, ith consierable number of small an largescale paper manufacturing plants). LINDO- (version 6.) softare as utilize to etermine the optimum flo of ra materials as ell as system ie cost in the paper supply chain for a given set of maret situation/conition. The present section iscusses the results of analysis being performe on the blening moel for paper manufacturing (from competitive ra material sources). The strategies have been suggeste ith the objective of minimizing the system-ie costs for manufacturing of paper prouct uner ifferent maret situation.

11 The section confers about the effects of yiel of input ra materials an quality of finishe paper on the system through yiel an quality analysis respectively. The sensitivity of the system cost toars the shortages of the competing ra material an environmental opportunity cost has also been stuie. The behavior of the moel as compare ith the anticipate intuitive behavior of the system.. Yiel analysis of competing ra materials Yiel at the manufacturer stage is one of the important factors contributing to the quality of input ra material i.e. a high quality ra material ill have a higher yiel, hereas, a loer quality ill have lo yiel. The input ra material yiel (or its quality) also has an impact on the eman for ra materials beteen the echelons. The loer yiel ra material ill eman more ra materials from the system to satisfy the eman for the finishe prouct at the manufacturer. For a esire quality of finishe paper (ith constant proportion of oo fiber i.e. W f ), yiel sensitivity analysis of competing ra material (i.e. oo an Unit cost of paper supply chain (INR/g) Yrc=0% Yrc=0% Yrc=0% Yrc=70% Yrc=90% Yiel of oo for manufacturing paper (Y in %) Figure : Yiel analysis of competing ra material for paper prouction

12 relevant recyclable astepaper) as conucte to etermine the optimal yiel of the input ra material in ifferent maret situation hich leas to minimum system ie cost (Figure ). Uner all the conitions of constant yiel of astepaper (Y rc ), unit cost of paper manufacturing as foun to ecrease ith the increase in yiel of oo (Y ). This can be attribute to the reuce quantity of input oo, improve quality of finishe paper as ell as the increase in positive cost component associate ith environmental upgraation ue to less consumption of oo. Similarly, tren as observe uner constant Y an varying Y rc.. uality analysis of finishe paper on the paper supply chain The quality of fiber prouce from oo is superior in comparison to the quality of fibre prouce from astepaper. Hence, the quality of the finishe paper prouct greatly epens on the proportion of oo fibre present in a unit of finishe paper (W f ). Sensitivity analysis as performe on the moel to stuy the impact of W f on the system s supply chain cost uner a given quality of input competing ra materials (in terms of yiel). The outcome unit cost on paper supply chain (INR/g) Proportion of oo fibre in finishe paper (Wf) Figure : uality analysis of finishe paper in terms of oo fibre content

13 of the analysis is shon in figure. It is seen that ith increase in the proportion of oo fiber (W f ), the unit cost of the supply chain ecreases. This can be attribute to ecrease in the quantity of astepaper flo as ell as associate costs in the system, an increase in quality of finishe paper prouct. The ecrease in cost compensates for the increase in environmental egraation costs (ue to increase use of oo an reuce use of astepaper).. Environmental cost sensitivity analysis onstant egraation of the environment (ue to increase in soli aste an reuction in natural resources ue to human usage) has force governments to enforce strict environmental regulation, an the consumers also eman manufacturers to follo environmental frienly methos. Hence, the propose moel also consiers the environmental component in its objective function. This is an opportunistic cost highlighting the concern of the manufacturer toars the environment. The behavior of the system toars the environmental concern as analyze by varying the unit environmental cost of using oo Unit cost of paper supply chain (INR/g) EDrc=0% EDrc=0% EDrc=0% EDrc=70% EDrc=90% % increase in the environmental cost ue to use of oo as ra material Figure : Environmental cost sensitivity analysis * Note: EDrc = % increase in unit opportunity environmental cost

14 ( ) an astepaper ( W ED ED shon in figure. It is notice that ith the increase in paper supply chain increases. In contrast, ith increase in ) as competing ra material. The outcome of the analysis is W ED at constant ED at constant ED the cost of the W ED the cost of the paper supply chain ecreases. Hence, the manufacturer having higher concern for the environment shoul increase the proportion of astepaper an reuce that of oo for manufacturing paper.. onclusion Reverse logistics is an area of groing importance. In this paper a linear cost optimization blening moel as formulate ith to competing ra material sources i.e. oo an astepaper for manufacturing of finishe paper prouct. The objective function of the blening moel inclue commonly accounte costs of collection, transportation, inventory, manufacturing, segregation an isposal along ith the opportunity quality an environmental cost. The moel thus taes care of the globally relevant topic of manufacturing eco-frienly quality proucts. The results of the sensitivity analysis on the moel are in line ith the intuitive behavior of the system. It is seen from the yiel analysis (section.) that ith improve quality of input ra materials (in terms of yiel increases) the system ie cost of manufacturing paper by blening ecreases. Hence, the manufacturer shoul opt for better input ra materials. The quality analysis (section.) inicates that increasing proportion of oo fibre in the finishe paper ecreases the system ie cost even at the cost of egraation to the environment. Thus, it is upto the manufacturer to convey its egree of environmental concern to the government an society by assigning higher environmental

15 costs in the moel. Higher emphasis on using increase content of recycle paper (by assigning higher environmental) ecreases the system ie cost, hereas, higher emphasis on using oo (by assigning loer environmental cost) increases the system ie cost. It envisage that the quantitative analysis presente in this paper can play a vital role in the ecision process of a paper manufacturer for etermining an optimal blen of quality an quantity of competing input ra materials. The choice for the supply chain strategy coul be justifie base on the quantitative reasons. Hoever, limitations of the present stuy pertain to ignoring the effect of internal istributions on system ie supply chain cost an assumption of no loss conition of any variety. Difficulty in obtaining the estimates of the environmental cost is also a major limitation of the stuy. The linear moel presente can possibly be extene to inclue non-linearities, stochasticity of parameters an multiplicity of objectives in future stuies on this topic. Appenix I: Nomenclature of the propose optimal blening moel c c Unit collection cost of astepaper at ealer stage (INR/T) Unit collection cost of oo (INR/T) uantity of unsegregate astepaper collecte by ealer stage uantity of oo supplie by supplier of oo stage(=) to the manufacturer stage(=) T umulative unit transportation cost of relevant recyclable aste moving form () to stage (INR/m/T) T umulative unit inboun transportation cost for unsegregate astepaper at th stage (INR/m/T) l l Total istance travele by ra material astepaper before entering th stage from () stage Total istance travele by oo from = stage before entering = stage. uantity of oo moving out of supplier of oo stage an entering manufacturer stage uantity of unsegregate astepaper moving out of th stage an entering (-) stage

16 uantity of recyclable (relevant) astepaper in moving from th stage to (-) stage. RU uantity of reusable astepaper (not fit for recycling) in mixture moving from ealer to segregator stage D uantity of isposable astepaper (not fit for recycling as ell as reuse) in mixture moving from ealer to segregator stage S Unit segregation cost incurre for segregating relevant recyclable astepaper from the unsegregate g aste collecte from ealer stage (INR/T) RU S Unit segregation cost incurre for segregating reusable astepaper from unsegregate aste collecte g (INR/T) D Unit isposal cost of unrelevant astepaper after regregating from recyclable & reusable astepaper s RU Unit cost of using reusable astepaper collecte after segregation. b Initial inventory (at t=0) for oo at the manufacturer stage (0) b (0) Initial inventory (at t=0) for unsegregate astepaper at ealer stage (=) 0 uantity of finishe paper moving out of manufacturer stage to fulfill its eman. W f Y Y rc h Desire proportion of oo fibre in the finishe prouct Yiel percentage for oo at manufacturer to get a unit eight of esire finishe paper Yiel percentage of recyclable astepaper at manufacturer to get unit eight of esire finishe paper Unit inventory carrying cost for oo at manufacturer stage (INR/T) h Unit inventory carrying cost for relevant recyclable astepaper at stage (INR/T) h Unit inventory carrying cost for unsegregate astepaper at ealer stage (INR/T) b (0) Initial inventory (tt=0) of relevant recyclable astepaper at stage. Orering cost of unsegregate astepaper at segregator stage. O Orering cost of oo at the manufacturer stage O Orering cost of relevant recyclable astepaper at stage O Deman for total unsegregate astepaper by segregator stage from ealer stage Deman for oo by manufacturer stage from supplier of oo stage Deman for relevant recyclable astepaper by the stage from () stage. * Economic orer quantity (EO) for unsegregate astepaper at the segregator stage

17 * * S EO for oo at manufacturer stage EO for relevant recyclable aste paper at stage Percentage shortage in material emane at the stage Deman for finishe paper at manufacturer stage Unit shortage cost of the material (astepaper an finishe paper) at the stage. S Unit shortage cost of oo at the supplier of oo stage. S P Unit energy cost for manufacturing paper (INR/T) Unit miscellaneous cost for manufacturing paper (INR/T) OM R Unit cost of oo use as ra material (INR/T) Unit cost of relevant recyclable astepaper use as ra material R Unit environmental egraation cost ue of use of oo for proucing paper ED Unit environmental up graation cost ue to use of relevant astepaper for proucing paper ED It is a measure of the impact of use of recyclable astepaper on quality cost an is estimate as a q proportion cost of astepaper use. q W D It is a measure of the impact of use of oo on quality cost an is estimate as a proportion cost of oo use. Proportion of nonrelevant astepaper (neither fit for reusing or recycling) collecte ith unsegregate aste W Proportion of reusable astepaper (not fit for recycling) collecte ith unsegregate aste RU B Maximum storage capacity of unsegregate astepaper at the ealer stage. B Maximum storage capacity of relevant recyclable astepaper at stage. B Maximum storage capacity of oo at the manufacturer stage. Reference:. Acerman, F., Gallagher, K., Mixe signals: maret incentives, recycling, an the price spie of 99. Resources, onservation an Recycling,, 7-9, 00.

18 . Berglun,., Soerholm, P., Nilsson, M., A note on intercountry ifferences in aste paper recovery an utilization. Resources, onservation an Recycling,, 7-9, 00.. Bloemhof-Ruaar, J.M., van Wassenhove, L. N., Gabel, H.L., Weaver, P.M., An Environmental Life ycle Optimization Moel for the European Pulp an Paper Inustry. Omega- International Journal of Management Science, (6), 6-69, 996. Bystrom, S., Lonnstet, L., Waste paper usage an fiber flo in Western Europe. Resources, onservation an Recycling,,, 99.. Bystrom, S., Lonnstet, L., Paper recycling: environmental an economic impact. Resources, onservation an Recycling,, 09-7, Grace, R., Turner, R.K., Waler, I., Seconary materials an international trae. Journal of Environmental Economics an Management,, 7-86, Hanley, N., Slar, R., ost-benefit analysis of paper recycling: a case stuy an some general principles. Journal of Environmental Planning an Management, 7, 89-97, Leach, M.A., Bauen, A., Lucas, N.J.D., A systems approach to material flos in sustainable cities: a case stuy of paper. Journal of Environmental Planning an Management, 0, 70-7, Samaovlis, E., The relationship beteen aste paper an other inputs in the Seish paper inustry. Environmental an Resource Economics,, 9-, Samaovlis, E., Revaluing the hierarchy of paper recycling. Energy Economics, 6,0-, 00.

19 . Smith, M., The US Paper Inustry an Sustainable Prouction. ambrige, MA: MIT Press, Tilman,., Sanhu, R., A moel recycling programme fro Alabama, Resources, onservation an Recycling,, 8-90, Yohne, G.W., Seconary materials an international trae: a comment on the omestic maret. Journal of Environmental Economics an Management, 6, 99-0, 979.