IMPACTS OF MINIMUM ACTIVITY LEVEL AND MULTI-SOURCING ON PRODUCT FAMILY AND SUPPLY CHAIN DESIGN

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1 21 st Internatonal Conference on Producton Research IMPACTS OF MINIMUM ACTIVITY LEVEL AND MULTI-SOURCING ON PRODUCT FAMILY AND SUPPLY CHAIN DESIGN Bertrand Baud-Lavgne, Bruno Agard and Bernard Penz Unversté de Grenoble / Grenoble INP / UJF Grenoble 1 / CNRS G-SCOP UMR5272 Grenoble, F-3831, France CIRRELT, Département de Mathématques et Géne Industrel École Polytechnque de Montréal C.P. 679, succ. Centre-Vlle, Montréal (Québec), H3C 3A7, Canada Abstract Ths study consders the problem of jont desgn of the supply chan structure and the product famly bll-of-materals through substtuton decsons: standardzaton, externalzaton and alternatve operatng sequence. The am of ths paper s to analyze the nfluence of some strategcal decsons (mnmum actvty level and mult-sourcng) on the optmal desgn of the product famly and ts supply chan. In order to avod mass lay-offs that have major economcal and mage mpact, companes may be constrant to keep producton n centers where the cost s hgh, leadng them to produce wth a sub-optmal soluton consderng producton costs. In ths context, the followng ssues are tested and dscussed: what are the consequences of the oblgaton to keep a mnmum actvty level on a center? Whch types of operaton are kept? Does mult-sourcng lead to ncrease standardzaton? How does t affect product allocaton n the supply chan? Experments are led on a case study wth several producton centers around the world. Keywords: Supply chan, Product substtuton, Mult-sourcng, Mnmum actvty, Mxed Integer Lnear Programmng 1 Introducton The nternatonalzaton of the markets compels most companes to dversfy ther offers to meet customer s demands. Ths dversty affects concepton, producton and dstrbuton processes n decreasng economes of scale. In ths condton, provdng a wde varety of products that meets customer s needs whle controllng producton and logstcal costs s of major mportance. Smultaneous desgn of the supply chan and the product famly can help to optmze these costs. Works on product famly desgn usually take nto account producton and logstcal constrants. Mass customzaton [9] s now a well spread concepton technque to acheve large varety of product desgns at mnmum cost. Ths allows focusng on the optmzaton of the product famly, consderng that assembly constrants are more flexble. Many problematcs arse as determnng the product famly varety [3] or the module optmzaton [1] to mnmze producton costs. However, product and supply chan optmzaton have not been tackled smultaneously untl recent years. The need of jont optmzaton has been hghlght by [2] and [4], showng that both decsons have mpacts on each other. [2] focuses on a producton network and compares sequental desgn wth smultaneous desgn on a case study and wth an analytc analyss. Consderng explct bll-of-materals (BOM) n supply chan desgn model s a recent feld that s yet lttle studed. A sngle-perod, mult-product and multlevel models has been proposed by [8], and a mult-perod model has been presented by [1]. In these models, BOM s fxed. Very few studes optmze smultaneously the product and the supply chan. Two approaches are lsted n the lterature. The frst approach seeks to defne the best product famly whch meets the market needs, by usng generc BOM to model the product part of the problem ([7], [12]). In these formulatons, BOM are determned so as to respect assembly constrants. The second approach consders the fnal products as fxed, but the BOM are more-or-less flexble. To model ths n an assembly-to-order context where the fnal assembly tme s constraned, [5] consdered functon and modular desgn, n whch all the assembles are possble. [6] defned several alternatve BOM, one beng selected n the optmal soluton. Ths approach needs a complete enumeraton of all product confguratons. In return, both formulaton and soluton are facltated. The only fully ntegrated model to our knowledge has been proposed by Chen n 21 [4]. The am of ths paper s to analyze the mpact of strategcal decsons wdely spread n ndustry that could redefne the optmal supply chan. Secton 2 descrbes the am of the model used for the experments, ts mathematcal formulaton and some lmtatons. Concepts of mult-sourcng and mnmum actvty are explaned and expermented n Secton 3. Secton 4 concludes the paper and gves some perspectves.

2 21 st Internatonal Conference on Producton Research 2 An optmzaton model for jont product and supply chan desgn The model used n ths study defnes smultaneously the supply chan structure and the bll-of-materals (BOM) of the product famly. The supply chan has four layers: supplers, producton centers, dstrbuton centers and customers. Product famles are represented through the BOM of each product whch shares some common subassembles and components. By defnton, all assembles can be produced and transported from a center to another. The am of the optmzaton s to determne: (a) Specfc bll-of-materals (b) Standardzaton 1. the bll-of-materals composton: selecton of the relevant components and sub-assembles, 2. the supplers selecton / producton centers locaton, 3. from where each component s suppled, 4. whch workstaton are allocated n each producton center, 5. the allocaton of each assembly to each producton center. (c) Alternatve operaton sequence Fgure 2: Bll-of-materals and substtuton llustratons. externalzaton: a sub-assembly s bought drectly from a subcontractor. Fxed costs are nearly avod whle ncreasng varable costs. In the example on Fgure 2a, the sub-assembly A or B could be replaced by a component bought from a suppler, Fgure 1: Schematc supply chan network. Products and supply chan are llustrated n Fgure 1 and 2. Fgure 1 descrbes an example of a supply chan wth four supplers, three producton centers, three dstrbuton centers and four customers. Flow contents are only components between the supplers and the plants, products between the plants and the customers and all types of part between the plants. Three types of optons can be allocated to each producton center. The example n Fgure 2a consders two products: P 1 and P 2. Each product s composed of two sub-assembles. P 1 s composed of sub-assembles A and B, whle P 2 contans A and B. Sub-assembles are composed of components 1 to 5. Substtuton possbltes can be express through explct equvalences between assembles. Three types of substtuton are consdered: standardzaton: a component (or sub-assembly) can be upgraded by another one wth more functonaltes or wth a better qualty. In one hand, ndvdual part s more expensve to buy, to produce or to transport, so varable costs ncrease. On the other hand, dversty decreases and allows better economy of scale. An llustraton s provded n Fgure 2b. Sub-assembly A can be replaced by A, B and B can be replaced by a new sub-assembly B, alternatve operatng sequence: other possble assemblng order can permt better commonalty wthout necessarly changng costs. Fgure 2c presents a sequence where sub-assembly C has a good commonalty wthout addng extra functon. Ths paper focuses on standardzaton, although these substtutons optons can be expressed by the model descrbed n the followng secton. The concept of substtuton has been reconsdered n order to model the problem wth a reasonable amount of lnear constrants. The typcal way to express substtuton would be to use the BOM as a decson varable. In our understandng, ths would conduct to quadratc constrants between BOM and producton decson varables n most supply chan desgn models. Another way proposed n [4] s to use decson varables to express exactly whch quantty of each alternatve s used for each produced assembly produced. Ths leads to a consderable amount of decson varables. Our model descrbed below has a smplfed approach: product substtuton s consdered through product transformaton. When part X s able to substtute part Y, a vrtual process can transform X nto Y. Then, quantty of Y on a plant s mxed between actual Y part and alternatves that have been transformed n Y. Ths vew of the problem allows substtuton whle keepng a lght formulaton. Indeed, the number of addtonal varables s exactly the substtuton possbltes. The problem s modelled wth flow and fxed cost constrants. Substtuton possbltes are ncluded at each level of the BOM (components, sub-assembles and fnal product). The supply chan and the product famly are optmzed smultaneously. Sets:

3 21 st Internatonal Conference on Producton Research P: products ; ndex: p, q P R P : raw materals or components, M P: manufactured products / subassembles, F P: fnshed products. N : network nodes ; ndex:, j N S N : supplers, U N : producton centers, D N : dstrbuton centers, C N : customers. T : technologes ; ndex: t T O: capacty optons ; ndex: o O Parameters: g pq : quantty of q n p. q can be a component or a sub-assembly. g represents the bll-of-materals, p M F, q R M, d p : demand of product p by customer, p M, C, c o : opton o capacty, o O, l pt : processng tme of product p on technology t, p M F, t T, l p : labour tme of product p, p M F, T p T : technologes needed by product p, p M F, P p P: products that can substtute p, p P. The decson varables are presented n table 1. Each varable s assocated wth ts proper cost. Table 1: costs. Decson varables (DV) and ther assocated Doman DV Cost Quantty of p produced on N A p α p Producton of p on {, 1} B p β p Quantty of p that substtute q on N S pq σ pq Flow of p between and j N F p j φ p j Use of flow of p between and j {, 1} T p j τ p j Use of axs between and j {, 1} L j λ j Number of opton o on N O l ω l Use of node {, 1} Z ζ Producton of p {, 1} M p The mathematcal model s as follows. Z = mn N p P N p P (A p αp Bp βp ) S qp q P p N j N \{} p P N j N \{} O o ω o N o O σ qp (F p j φp j T p j τ p j ) L j λ j Z ζ (1) N The objectve functon (1) mnmzes procurement, producton and transportaton fxed and varable costs. Constrants (2) to (6) are flow constrants. The sources are the component flows from the supplers to the plants, the snks are fnal product flows to customers. Constrant (2) consders the flow of each manufactured assembly on each producton center. A p F p j j U\{} = j U\{} F p j S qp q P p q M F g qp A q S pq q/p P q U, p M (2) Constrant (3) consders the flow of each component on each producton center. F p j j (S U)\{} = j U\{} F p j S qp q P p q M F g qp A q S pq q/p P q U, p R (3) Constrant (4) consders the flow of each component on each suppler. A p = j U F p j S, p R (4) Constrant (5) consders the flow of each fnal product on each dstrbuton center. F p j = F p j D, p F (5) j U D\{} j D C\{} Constrant (6) consders the flow of each fnal product on each producton center. A p F p j = F p j U, p F (6) j U j D C\{} Constrant (7) assures that customer s demands are satsfed. F p j = d p C, p F j D q P p S qp q/p P q S pq Constrant (8) assures that fxed costs are pad when a component s provded by a suppler or when an assembly s manufactured on a center. A p max s the upper bound of A p U. (7) A p Bp Ap max S U D, p P (8) Constrant (9) assures that fxed costs are pad when a suppler or a center s used. B p Z S U D, p P (9) Constrant (1) defnes the number of workstaton needed on a center. l pt A p O o c o U, t T (1) p/u P p o O t

4 21 st Internatonal Conference on Producton Research Constrant (11) assures that fxed costs are pad when a product s transported between two nodes. F p j T p j Ap max N, j N \{}, p P (11) Constrant (12) assures that fxed costs are pad when a lnk between two nodes s used. T p j L j N, j N \ {}, p P (12) Constrant (13) lmts substtuted products to be used wthn the center they has been created. q P p S qp 3 Experments q M\p g qp A q j C 3.1 Desgn of experment F p j U, p P (13) Experments are led by solvng the MILP presented n Secton 2 extended wth addtonal constrants presented below. ILOG CPLEX 12 Java lbrares are used on a laptop under 64 bts OS wth a 2.26 GHz Intel Core 2 Duo CPU and 2GB of memory. Because of the complexty of the model, only small nstances are expermented. The academc case study s llustrated n Fgure 3. Two markets are consdered: Unted States (US) and Europe (E). Producton s possble n each country plus on a relocated unt n North Afrca (NA), wth labour rate of respectvely 3 (US), 25(E) and 1 (NA)$ /h. Dstrbuton centers and customers are set randomly. One suppler per component type s set randomly close to each producton unt. Fgure 4: Root product from whch the product famly s generated. Table 2: Case study characterstcs. Type Parameter Value Network node Logstcal cost 15 $ /m 3 Customers Quantty 5 Prob demand.3 Max demand per product 6 Fxed costs per (axe, product) 1 $ per (component, suppler) 5 $ per (product, plant) 13, $ per supplers 1, $ per plants 5, $ per DC 2, $ Product parts Fnal products 1 Max procurement cost 2 $ Max physcal volume 1 m 3 Results are assessed through three crtera: percentage of labour allocaton n each producton center, extra costs compared to the optmal soluton wthout constrant, and the commonalty ndex of the manufactured famly product. Many ndexes have been proposed n the lterature [11]. In ths paper, the Extra Commonalty Index (ECI) s proposed to measures the commonalty brought by substtuton decsons: Fgure 3: The supply chan of the case study. Table 2 shows the parameters used n ths case study. Part transportaton cost s computed wth the part volume, the dstance between the unts and the logstcal cost. As the model consders a mono perod, all fxed costs represents the use on ths perod. Product famly s generated from the root product descrbed n Fgure 4: each fnal product s an nstantaton of ths root product wth one or none alternatve of each component. Three types of components are defned, each supplers can supply all products of a gven type. Substtutons are authorzed when a part has more or better components than another. # parts used # parts mn ECI = 1 # parts max # parts mn Parts contan components, hgh level assembles and fnal products. The mnmum number of parts refers to the soluton wth a unque fnal product, the maxmum refers to the ntal BOM. ECI s between (no extra commonalty) and 1 (total commonalty). 3.2 Mult-sourcng Mult-sourcng s a strategy that frms use to lower rsk n procurement of key components. It conssts n multplyng supplers to avod dsrupton f one suppler s defcent. At the opposte, a company can prefer to lmt ts supplers. For each component p R, the number of dfferent supplers that provde p s between b p mn and bp max.

5 21 st Internatonal Conference on Producton Research Constrant (14) defnes decson varables M p. B p M p p R (14) S Constrant (15) assures that the mnmum and the maxmum number of supplers for each component s satsfed f the component s used. M p b p mn S B p M p b p max p R (15) Constrant (16) avod supplers to provde less than Q p mn unts for part p. B p Qp mn Ap p P, S (16) These constrants can also be expressed for producton: a crtcal assembly can be forced to be produced n multple producton centers. In ths paper, only constrants on supplers are consdered. Experments consst n consderng dfferent levels of sourcng: only one suppler per component, up to 2, exactly 2, up to 3, 2 or 3, and exactly 3. Constrants are even for each component. Results are presented n Fgure 5. Producton n each unt (n hour) Number of supplers authorzed Europe Unted States North Afrca ECI Extra costs Fgure 5: Allocaton repartton, extra commonalty ndex and extra costs accordng to mult-sourcng strategy. Experments shows that, when number of supplers s constraned to be up to three (1-3 on Fgure 5), there s not addtonal constrants on the problem as there can be one suppler per component type per unt, thus the result s the optmal. In ths condton, some parts of the products (2%) are manufactured n the North-Afrcan unt whle the rest of the producton n done on the local unts (43% n Europe, 37% n US). The allocaton s the same when the number of supplers s constraned to be hgher: then all unts must have a suppler for each type of product and substtutons are more mportant n both Amercan and European unts. On the contrary, when supplers are constraned up to two, the European unt s unused and ts producton s absorbed by the North-Afrcan unt. When only one suppler s allowed, the North-Afrcan unt produces extra modules for the Amercan unt and product standardzaton s very low. In ths only case, the soluton s sgnfcantly more expensve (4%). A trend can be noted between standardzaton level and local producton level. When producton s concentrated far ECI & Extra costs from the market, product standardzaton s low, whereas many substtuton happen when local producton unts are mportant. Ths comes from economes of scale when producton s concentrated n one unt. 3.3 Mnmum actvty levels For some reasons, management can decde to keep a mnmum actvty level on some producton center. Ths constrant can arse from legslatve decsons, through subventons, or to avod mass lay-offs that have major economcal and mage mpacts that are hardly assessable. Ths can lead to contnue producton n center where t would be sub-optmal. In ths case, whch type of operaton s kept? When dealng wth relocaton, hgh-value added processes can be allocated to countres where labour rate s hgh but whch are near the market, and hgh labour processes to cheaper countres. Constrant (17) assures the desred mnmum actvty level on each producton center. p M F l p A p a U (17) Experments consst n forcng a mnmum actvty on the European unt, from to the maxmum quantty of work needed for the whole producton. The case study s slghtly dfferent wth transportaton cost of 1 nstead of 15 and demands of 2/3 lower to have more pertnent results. Results are presented n Fgure 6. Producton n each unt (n hour) Mnmum actvty on the European unt (n hour) Europe Unted States North Afrca ECI Extra costs Fgure 6: Allocaton repartton, extra commonalty ndex and extra costs accordng to mnmum actvty constrants on European unt. Wthout any constrant, the European unt should close n the optmal soluton. Whle constranng a mnmum actvty on ths unt, two phenomena arse: tll 5 hours, whch represents the producton for the European market, producton s relocated from the North-Afrcan unt to the European one wthout a sgnfcant ncrease of the producton costs. At 1 hours, the constrant s barely satsfed: only a lttle sub-assembly s produced then shpped to the Amercan unt. At 25 hours, only one fnal product and ts assembles are manufactured n the North-Afrcan unt, the European unt produced all the others product to response ts demand. Beyond 5 hours, the European unt have to produce for the Amercan market, thus costs ECI & Extra costs

6 21 st Internatonal Conference on Producton Research are ncreasng drastcally, up to 152% of the optmal soluton. The less producton are kept n the Amercan unt, the more substtutons ncrease n ths unt whle substtutons are stable n the European unt. 4 Concluson In ths paper, we provde tools and a framework to analyze and quantfy the nfluence of exogenous strategy on the mathematcal optmzaton of the product and the supply chan. When dealng wth qualtatve ssues, ther economc mpact assessment s relevant n the decson process and can rebuld all the decsons concernng the supply chan and the way the products are manufactured. A perspectve s to nternalze these strateges to become part of the decson process. REFERENCES [1] B. Agard and B. Penz. A smulated annealng method based on a clusterng approach to determne blls of materals for a large product famly. Internatonal Journal of Producton Economcs, 117(2):389 41, 29. [2] B. Baud-Lavgne, B. Agard, and B. Penz. Mutual mpacts of product standardzaton and supply chan desgn. Internatonal Journal of Producton Economcs, do : 1.116/j.jpe , 21. [3] O. Brant and D. Naddef. The optmal dversty management problem. Operatons Research, 52(4): , 24. [4] H.-Y.S. Chen. The mpact of tem substtutons on producton-dstrbuton networks for supply chans. Transportaton Research Part E: Logstcs and Transportaton Revew, 46(6):83 819, 21. [5] R. El Hadj Khalaf, B. Agard, and B. Penz. An expermental study for the selecton of modules and facltes n a mass customzaton context. Journal of Intellgent Manufacturng, 21(6):73 716, 21. [6] H.A. ElMaraghy and N. Mahmoud. Concurrent desgn of product modules structure and global supply chan confguratons. Internatonal Journal of Computer Integrated Manufacturng, 22(6): , 29. [7] J. Lamothe, K. Hadj-Hamou, and M. Aldanondo. An optmzaton model for selectng a product famly and desgnng ts supply chan. European Journal of Operatonal Research, 169(3):13 147, 26. [8] M. Paquet, A. Martel, and G. Desaulners. Includng technology selecton decsons n manufacturng network desgn models. Internatonal Journal of Computer Integrated Manufacturng, 17(2): , 24. [9] B. J. Pne. Mass customzaton: The new fronter n busness competton. Harvard busness school press, [1] P. N. Thanh, N. Bostel, and O. Peton. A dynamc model for faclty locaton n the desgn of complex supply chans. Internatonal Journal of Producton Economcs, 113(2): , 28. [11] H.J. Thevenot and T.W. Smpson. Commonalty ndces for assessng product famles. In Product platform and product famly desgn: methods and applcatons. Sprnger, New York, 26. [12] X. Zhang, G. Q. Huang, and M. J. Rungtusanatham. Smultaneous confguraton of platform products and manufacturng supply chans. Internatonal Journal of Producton Research, 46(21): , 28.