Minimizing The Cost Of Leverage Items In Supply Chain:A Mathematical Approach

Transcription

1 Tehran International Congress on Manufacturing Engineering (TICME2005) ecember 2-5, 2005, Tehran, Iran Minimizing The Cost Of Leverage Items In Supply Chain:A Mathematical Approach J. Razmi, Parisa Akbary 2 and M.R.Taghizadeh 3 Research Instute in Energy Management and Planning, Industrial Engineering epartment, Faculty of Engineering, Universy of Tehran, Tehran, Iran Corresponding Author mrtaghizadeh@engmail.ut.ac.ir Abstract Ltle attention is given in the lerature to decisions on the appropriate selection of suppliers, and on assigning order quantes to these supplier, in the case of multiple sourcing, wh multiple creria and wh suppliers' capacy constraints. In order to be competive organizations in the new environment (globalization) one has to consider not only the cost of product, but also manage their suppliers in supply chain and select the best of them. In this paper a goal programming model is presented, multiple sourcing, multiple leverage ems, multiple time periods, which takes in to net price for purchasing em. Keywords: Supply chain Management, supplier selection, goal programming Introduction In most industries the cost of raw materials and component parts constutes the main cost of a product, such that in some cases can a ccount for up to 70% []. In such circumstances the purchasing department can play a key role in cost reduction, and supplier selection is one of the important function of purchasing management. Basically there are two kinds of supplier selection problems: ) Supplier selection when there is no constraint. 2) Supplier selection when there are some limations in supplier's capacy, qualy, etc, in othe words, no one supplier can satisfy the buyer's total requirements and the buyer needs to purchase some part of his /her demand from one supplier and the other part from another one supplier to compensate for the shortage of capacy or low qualy of the first supplier. Gaball [2] is the first author who applied a mixed integrprogramming model to minimize the total discounted price of allocated ems to the vendors, under constraints of vendor's capacy and demand satistaction. Anthony and Buffa [2] developed a single objective linear programming model to minimize total cost by considering limations of purchasing budegt, vendor capacies and buyer's demand. Narasimhan and stoynoff [3] applied a single - Assistant professor, epartment of Industrial Engineering, Faculty of Engineering, Universy of Tehran, Tehran, Iran. 2 - Research Scholar, epartment of Industrial Engineering, Faculty of Engineering, Universy of Tehran, Tehran, Iran. 3 - Research Scholar, epartment of Industrial Engineering, Faculty of Engineering, Universy of Tehran, Tehran, Iran.

2 ecember 2-5, 2005, Tehran, Iran objective, mixed integer programming model to optimize the allocation of procurement for a group of vendors. Chaudhry et al (993) have used liner and mixed binary integer programming models to solve cost minimzing problems of vendor selection wh price breaks. Rosenthat et al.(995) developed a mixed integer linear program that would find the purchasing strategy for the buyer to minmize the total purchase cost. Ghodsypour and O'Brien (200) presented a mixed integer non-linear programming model to solve the multiple sourcing problem, which took into account the total cost logistics, including net price, storage, transportation and ordering costs. Kumaret al.(2003) used a fuzzy mixed integer goal programming for vendor selection problem. For first time Kraljic (983) developeod a conceptual model in order to determine the purchasing strategies for an organization. This simple model was a two dimensional figure which on the first side prof impact has been allocated and the other side supply risk has been allocated. Several large companies like Shell, Alcatel, Philips, Akzo, Nobel and Simens have applied this model. ubios and Pederson (2002) divide the total material into four different parts of "Routine" ems, "Leverage" ems, "Strategic" ems and Bottelneck ems. Those group must be controled in different policy. Figure Introduced a 2 2 matrix and a classification in four categories: Bottleneck, Routine, Leverage and Strategic Items. Prof impoct Leverage em: Usually a raw material category Many supplier a lternative Large demand from a high capacy market Routine Item Figure. Kraljic's categories Strategic Item Bottleneck Item The evaluation and selection process differs in whether the product is classified as "qualy" or "commody". A qualy product is one that is some what crical in the manufacturing process. These products are usually candidates for long-term supplier partnerships. A commody product (or service) is generally non-crical in the manufacturing or has a routine nature in process or market. Figure2. introduced a Hierarchy of strategic importance in view of Kraljic's categories. 2

3 ecember 2-5, 2005, Tehran, Iran Figure 2. A Hierarchy of strategic importance In this paper, a goal programming is applied for leverage ems in orther to solve selection problem that includes the following primary goals: Minimzing net price, minimzing net rejection, and minimzing on time deliveries: subject to realistic constraints regarding buyer s demand, vendor s capacy, and the buyer s limations on budget, qualy, on time delivery, etc. This model considered vendor selection for multiple ems and multiple time periods and multiple sourcing. 2 Formulating model Before describing the model the following notations are considered. Assumptions: () emand of the em is constant and known whh certainty (2) Only one supplier must provides one em. (3) Multiple sourcing, multiple ems, multiple time periods. Indices : i: index for product, for all i=..n j. index for supplier for all j=..s i t. index for time Parameteres: : demand of h em in period t (constant). C : jth supplier s cappacy for Rendei th em in period t. q ia : minimum accepted perfect rate of incomingi th em (constant for All time periods) q : perfect rate of jth supplier for h em in period t. P : price of jth supplier for h em in periodt. S i : number of suppliers competing for selection h em. U : (It is determinat and constant)maximum accepted earliest dudate rate for h em in period t. K : (It is determinat and constant)maximum accepted delay time rate for h em in period t. M : earliest due date or delay time rate of jth supplier for h em in period t. 3

4 ecember 2-5, 2005, Tehran, Iran :percent of assigned to jth supplier over aperiod t. 2. Constraints The most important constraints of the problem are: buyer s emand and qualy, supplier Capacy and leadtime. These constraints are formulated as follows 2.. Capacy Constraint The vendor j can provide up to c j uns of the product over a period t.therefore: C for all i,j,t 2..2 emand Constraint AS demand is equal to and is assumed that S i vendors can meet the buyer s emand then: si j= = for all i,t = s i 2..3 Qualy Constraint As q ia is minimum accepted perfect rate of incoming i th em and q is perfect rate of jth supplier for h em in period t and purchased volume is,the qualy constraint can be shown as si q q ia si q 2..4 Lead time Constraint q ia U is maximum accepted earliest dudate rate for h em in period t and K is maximum accepted delay time rate for h em in period t. M is earliest due date or delay time rate of jth supplier for h em in period t.the leadtime constraint can be shown as: j M Z U + ( Z ) K IfM ( earliestduedate) Z = 0IfM ( delaytimerate) After constructing all constraints, It is necessary to be sure of The integer variable s condions, which are if X is zero, is also zero and if X is, is less than are greater than one. The following constraints can satisfy these condions: ( εx ) for all i,j,t ( X ) Where ε is slightly greater than zero Model formulation min z = ΣiΣ jσt P + ΣiΣtdpi t + ΣiΣ jσt ( dnij2t ) C si s i q q ia q it + dn it dp it = q ia for all i,t 4

5 ecember 2-5, 2005, Tehran, Iran s i ( ( j Z j = for all i,t morethanzeroifx = zeroifx = 0 ε X ) X ) P IfM = 0IfM TBP = ( earliestduedate) ( delaytimerate) M + dn dp = Z U + ( Z ) K ij 2 t ij 2t 2.2 Numerical example The objective is to find the best choice of suppliers if there are three suations. Table Supplier s information in period () for em (A) =000, K =0.7, U =0.,TB =6000,q a=0.92 price Perfect rate M capacy Sup /6(delay time rate) 600 Sup /4(earliest due date rate) 700 Sup /4(delay time rate) 500 Table 2 Supplier s information in period (2) for em (A) 2 =800, K 2 =0.6, U 2 =0.4,TB 2 =6800,q a=0.92 price Perfect rate M capacy Sup. 28 0/95 0/5(delay time rate) 400 Sup.2 4 0/92 0(on-time) 600 Sup.3 8 0/90 0/4(earliest due date rate) 700 Table 3 Supplier s information in period () for em (B) 2 =500, K 2 =0.7, U 2 =0.,TB 2 =5000 price Perfect rate M capacy Sup /6(delay time rate) 400 Sup (on-time) 300 5

6 ecember 2-5, 2005, Tehran, Iran Table 4 Supplier s information in period (2) for em (B) 22 =600, K 22 =0.6, U 22 =0.,TB 22 =8000,q 2 a=0.93 price Perfect rate M capacy Sup.4 3 0/98 0/5(delay time rate) 500 Sup.5 9 0/92 0/5(earliest due date rate) Review of cases As three suppliers should be evaluated for em (A),there are 8 possibilies of integer variable. only three possibilies of them evaluated. For em(b),there are 4 possibilties of integer variable. only two possibilies of them evaluated. Table 5. Three posibilies of integer variable when s suation is feasible Case s X X 2 X 3 Capac y X 2 X 22 X 32 Capac y X 24 X 25 Capac y X 242 X 252 Capac y For example in the first case, GP model can shown as: Min=9* *000+6* 2 *000+32* 3 *000+28* 2 *800+4* 22 *800+8* 32 *800 +4* 24 *500+2* 25 *500+3* 242 *600+dp +dp 2 +dp 2 +dn 2 +dn 22 +dn 32 + dn 22 +dn 322 +dn 242 +dn 2522 St : * * *0.98+dn -dp = * * *0.9+dn 2 -dp 2 = * *0.96+dn 2 -dp 2 = = = 252 = 9* *00+6* 2 *000+32* 3 *000<= * 2 *800+4* 22 *800+8* 32 *800<=6800 4* 24 *500+2* 25 *500<=5000 9* 252 *600<=8000 6

7 ecember 2-5, 2005, Tehran, Iran 0.6* +dn 2 -dp 2 = * 2 +dn 22 -dp 22 =0. 0.4* 3 +dn 32 -dp 32 = * 2 +dn 22 -dp 22 = * 32 +dn 322 -dp 322 =0. 0.6* 24 +dn 242 -dp 242 = * 252 +dn dp 2522 =0. Table 6. Optimum solution for three cases Cases Z unfeasibl e The optimum answers for all the cases are shown in table 6. It should be noticed that case three is unfeasible. As table 6 shows, case has the minimum cost and therefore is the optimum solution. 3 conclusions Supplier selection is one of the most important a ctivies of purchasing managers in which cost, qualy, delivery perforemances, etc. should be considered in selecting the best suppliers. Regarding the leverage ems, most of the researchers suggest that the most important creria in controlling these ems is minimizing the cost of procurement. This paper illustrates a mathematical (goal programming) model to minimize this cost as well as considering multiple creria such as cost, qualy, order lead time, and total budget constraint. This model will be coded as a rule-based expert system and also other materials circumstances (strategic Items, bottleneck ems, and ordinary ems) have been taken into account. An example has been shown in order to illustrate how the proposed model works. For future research is suggested to develop a newral network model for the define problem. The newral network can cope this problem better and probabily provide more practical solution. References [] A. Ghobbadian & A. Stainer, T. kiss (993), A computerized venoder rating system, proceedings of the first international symposium on logistics the universy of nottingham, not tingham, uk, july, [2] A.A. Gaball (974), Minimum cost allocation of tendera, operational research quarterly 25(3) [3] T.F. Anthony & f.p. Buffa (977), strategic purchasing scheduling, journal of purchasing and materials management 3(3) 27-3 [4] R. Narasimhan & K. Stoynoff (986), optimising aggregate procurement allo cation decisions, joumal of purchasing and materials mangement 22() [5] Ghodsypour & S.H O Brien, C. (200) «the total cost of logistics in supplier selection, under condions of multiple sourcing, multiple creria and capacy constrains» international journal of production economics, 73,5-27. [6] Bhutta & K.S, Hug, F. (2002), : «supplier selection problem: a comparison of total cost of ownership and analytical hierachy process approach» supply chain management: An International Journal, 7 (3), pp

8 ecember 2-5, 2005, Tehran, Iran [7] Kraljic (983) purchasing must become supply management. Harvard Business Review, 6(5), [8] Bensaou M. (999) porfolios of buyer supplier relationships, solan management review, 40(4), [9] A. C Pan, (989) Allocation of order quanty among suppliers. [0] Journal of purchasing and materials mangemen 25(3) wiess. M. & kulikowski C.A (983) A sytem for developing consul tation. [] models, proceeding of IJCAI ( ). [2] Moller, M&J. Momme (2000) supplier segmentation in theory and practice towards a competence perspective, proceedings of the 9th International IPSERA conference, London, Canada (508-59) 8