research article optimal coordinated strategy analysis for

Research ArticleOptimal Coordinated Strategy Analysis for the ProcurementLogistics of a Steel Group

Lianbo Deng1 Zhuqiang Qiu2 Pengfei Liu2 and Wenzhong Xiao1

1 School of Traffic and Transportation Engineering Central South University Changsha 410075 China2 School of Traffic and Transportation Engineering Changsha University of Science amp Technology Changsha 410114 China

Correspondence should be addressed to Lianbo Deng lbdengcsueducn

Received 17 February 2014 Accepted 19 May 2014 Published 4 June 2014

Academic Editor Andy H F Chow

Copyright copy 2014 Lianbo Deng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper focuses on the optimization of an internal coordinated procurement logistics system in a steel group and the decision onthe coordinated procurement strategy byminimizing the logistics costs Considering the coordinated procurement strategy and theprocurement logistics costs the aim of the optimization model was to maximize the degree of quality satisfaction and to minimizethe procurement logistics costs The model was transformed into a single-objective model and solved using a simulated annealingalgorithm In the algorithm the supplier of each subsidiary was selected according to the evaluation result for independentprocurement Finally the effect of different parameters on the coordinated procurement strategy was analysed The results showedthat the coordinated strategy can clearly save procurement costs that the strategy appears to be more cooperative when the qualityrequirement is not stricter and that the coordinated costs have a strong effect on the coordinated procurement strategy

This paper is dedicated to the memory of our best friend Dr Zhuqiang Qiu

1 Introduction

According to their scope coordinated procurement logisticscan be divided into two forms internal coordinated procure-ment and enterprise alliance coordinated procurement Inrecent years through eliminating outdated production capac-ity and merging and reorganizing between corporationsChinarsquos steel industry has achieved the scale productionHowever the advantage of large = scale economies has notbeen brought into full play and the internal logistics systembetween subsidiaries lacks integral coordination

Chinarsquos steel industry output accounted for 4 of GDPThe coordinated logistics of this industry shows the followingrelevant characteristics

(1) Industry characteristics the main raw materials forsteel enterprises are iron ore scrap steel coke cok-ing coal and so on There are obvious homogene-ity and substitutability requirements which provide

the operation space for coordinated procurementmanagement

(2) The competitive environment of the raw materialmarket the iron ore coal and other major upstreamindustries have a higher industrial concentration thanthe steel industry so the whole steel industry faces arelatively unfavourable situation for the negotiation ofthe prices of rawmaterialsThere is a high correlationbetween the logistics procurement cost and the degreeof synergy of the steel industry

(3) The resources and industrial layout of Chinarsquos steelindustry the demand for steel and the distributionof resources in the various regions of China arenot balanced and this leads to a high cost of steelcirculation and a low circulation efficiency Steelproduction in 2012 was 71654 million tons but thetotal transportation volume of rawmaterials and steelproduct was at least 1 billion tons Collaboration andthe integration of procurement logistics are beneficial

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 436512 7 pageshttpdxdoiorg1011552014436512

2 Mathematical Problems in Engineering

for the steel industry allowing it to reduce circulationcosts significantly and improve market competitive-ness

Increasing the level of coordinated logistics procurementand reducing the production costs of the industry have there-fore become a key strategy for the survival and developmentof Chinarsquos steel industry

2 Literature Review

Looking at the procurement logistics for a single steel enter-prise Roy and Guin [1] built a conceptual model of just-in-time purchasing for a steel company in India They con-sidered the identification and classification of raw materialsupplier availability and goods consolidation of distributionoutlets For the raw material procurement of a large steelplant considering three main factors (the selection of rawmaterial model supplier and order quantity) Gao and Tang[2] constructed a multiple objective linear programming(MOLP) model for procurement decisions Hafeez and col-leagues [3] considered factors such as human resourcesorganization and technology using the dynamic structure ofthe integrated system and described a two-level steel supplychain that achieves a minimized inventory level under thecondition of capacity constraints and limits on raw materialprocurement lead time

By analysing the procurement policy for iron ore and cokeof Japanese steel enterprises in the late twentieth centuryChang [4] argued that changing technology and institutionalstructure made Japanese procurement decisions more con-sistent and that this laid the foundations for coordinatedprocurement between enterprises Potter et al [5] made athorough study of the development process of the Britishsteel supply chain from the traditional mode to the integratedmode in the twentieth century and analysed in detail theimpact of the changes on inventory ordering lead timeand asset utilization Faes et al [6] considered that coor-dinated procurement can lead to better internal exchangeof information an improved market negotiation strategysignificant cost savings a greater impact on the monopolymarket and a better understanding of the market and coststructure Akkermans et al [7] established a theoreticalmodel for coordination and studied the important effectsof nontechnological factors on achieving synergy Essig [8]found that coordinated procurement can reduce transactioncosts allow a lower purchase price to be obtained and lead toa more efficient use of procurement staff Bishop [9] showedthat coordinated procurement can lead to the integration ofthe purchase process better continuity and coordination andeconomies of scale Tella and Virolainen [10] argued thatcoordinated procurement members wanted to reduce theirprocurement costs and achieve lower management costslower logistics costs and higher mobility of the inventoryHelo [11] proved that demand coordinationwas important forimproving the capacity of the supply chain

Turkay et al [12] established a model and made a quan-titative analysis of the cooperation between businesses inthe chemical industry Kraljicrsquos [13] model briefly described

the procurement strategy for different materials from theperspective of the profit impact and supply risk involvedin procurement Fu and Piplani [14] established a modelthat evaluated supplier coordination based on inventory tosimulate and assess distributorsrsquo performance before and aftercoordination The calculations showed that the coordinationof suppliers can improve the performance of the wholesupply chain Keskinocak and Savasaneril [15] used a gametheory method to study the coordinated procurement of twocompeting purchasers Goyal and Satir [16] used an indirectgroup strategy to seek a combination of the optimal basiccycle and order frequency to make the total relevant costa minimum to achieve optimization of multispecies coor-dinated procurement Federgruen and Zheng [17] adopteda direct group strategy and used a heuristic algorithm tooptimize the coordinated procurement Chakravarty andGoyal [18] adopted a dependent and group strategy andused dynamic programming to optimize coordinated pro-curement Gurnani [19] studied the design of a supplierquantity discount programme which is the coordinatedprocurement of two heterogeneous buyers with differentrequirement processes and cost parameters For multiperiodmultiproduct batch procurement Lu et al [20] establisheda mixed integer programming model with a constrainton transport capacity and variable transport price whichdetermined the optimal procurement quantity by using theLagrange relaxation theory Xiang et al [21] assumed that agroup regularly orders and intensively purchases under thecondition of independent demand from the subsidiaries ina group company and established an optimal order quantitymodel

This paper studies the optimization of a grouprsquos internalcoordinated procurement logistics when combined with thecharacteristics f the raw material procurement logistics ofsteel enterprises Comparing with other studies we takethe full logistics cost of coordinated procurement strategyand the quality of demand into account in the coordinatedprocurement problem On the basis of the optimizationmodel in [22] this paper improves the solution algorithm andanalyzes the effect of different parameters on the coordinatedprocurement strategy

The rest of the paper is organized as follows Section 3presents a brief description of optimization model InSection 4 we describe our approach in solution algorithmThe base example and its results are shown in Section 5Results under the conditions of different parameters areanalysed in Section 6 Lastly the conclusions of our findingsare summarized in Section 7

3 Optimization Model

This paper studies the CPS of a steel group company that isequipped with a coordinated procurement department andhas 119898 subsidiaries (or similar procurement entities) The setof subsidiaries is 119868 = 119894 119894 = 1 119898 and the order quan-tity of raw materials is 119876

119894during a period of length 119905 For

simplicity we assume that all subsidiaries in the coordinatedprocurement alliance have the same purchase frequency

Mathematical Problems in Engineering 3

In the supply market there are 119899 suppliers providing theraw materials the set of suppliers is 119869 = 119895 119895 = 1 119899We introduce 120574(119894 119895) the quality satisfaction degree (QSD) ofsubsidiary 119894 for the rawmaterial provided by supplier 119895 where120574(119894 119895) isin [0 1] 119894 = 1 119898 119895 = 1 119899 That is

120574 (119894 119895) ge 1205740 (

119894) 119894 = 1 119898 119895 = 1 119899 (1)

where 1205740(119894) is the basic requirement of subsidiary 119894 for raw

materialsThe CPS is to procure raw materials for all or some of the

subsidiaries by the coordinated procurement department Itcan be expressed as 120587 = 120587

119896= (119868119896

harr 119895119896) | 119868119896

sub 119868 119895119896

isin

119869 where 120587119896is a sub-CPS of the CPS namely the supply

relationship between the set of subsidiaries 119868119896and the supplier

119895119896 We introduce

120575119896=

11003816100381610038161003816119868119896

1003816100381610038161003816ge 2 120587

119896isin 120587

01003816100381610038161003816119868119896

1003816100381610038161003816= 1 120587

119896isin 120587

(2)

where |119868119896| is the number of the subsidiaries in 119868

119896 for sub-CPS

120587119896 When 120575

119896= 1 the CPS should be adopted when 120575

119896= 0

the independent procurement strategy (IPS) should not befollowed

The sub-CPS should satisfy

1198681198961

cap 1198681198962

= 0 1205871198961

1205871198962

isin 120587 (3)

⋃

120587119896isin120587

119868119896= 119868 (4)

119876 (120587119896) = ⋃

119894isin119868119896

119876119894

120587119896isin 120587 (5)

where 119876(120587119896) is the ordering quantity of raw material for the

sub-CPS 120587119896

Coordinated logistics procurement costs include orderpreparation costs storage costs purchase costs and trans-portation costs

Let 119888119889 be the order preparation cost of one batch 119902119896the

order quantity of one batch and 119888119904 the storage cost per unit

of raw materials in the coordinated procurementThe supply price 119901

119896and the unit transportation cost 119902

119896of

a sub-CPS 120587119896are respectively

119901119896= 119901119895119896

minus 119903119902119896 (6)

119862119910

119896= 119862119910

0minus 119862119910119902119896 (7)

where 119901119895119896

and 119903 respectively refer to the initial price and thediscount coefficient 119901

119895119896

gt 0 and 119903 ge 01198621199100and119862

119910 refer to theparameters of the transportation cost 119862119910

0gt 0 and 119862

119910ge 0

In contrast to independent procurement strategy (IPS)the additional coordination costs 119862

0(1198620gt 0) need to be paid

in CPSThus the total logistics costs for sub-CPS 120587

119896are

119862119896= 1198620120575119896+ 119876 (120587

119896) 119897119895119896

119862119910

119896+ 119876 (120587

119896) 119901119896

+

119888119889119876 (120587119896)

119902119896

+

119905

2

119888119904119902119896

(8)

Then the optimum order quantity and the optimal cost of 120587119896

are respectively

119902lowast

119896= radic

119888119889119876 (120587119896)

((1199052) 119888119904minus 119862119910119897119895119896

119876 (120587119896) minus 119903119876 (120587

119896))

119862lowast

119896= 1198620120575119896+ 119876 (120587

119896) (119862119910

0119897119895119896

+ 119901119895119896

)

+ 2radic119905

2

119888119889119888119904119876 (120587119896) minus (119862

119910119897119895119896

+ 119903) [119876 (120587119896)]2

(9)

The above-described situation can in accordance withXiao and Qiu [22] be formulated as a multiobjective opti-mization model as follows

max 1198651= sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) (10)

max 1198652=

1

sum120587119896isin120587

119862lowast

119896

(11)

st Formations (1) (3) (4) and (5) (12)

In this model the objective function equation (10) is tomaximize the QSD for the aggregated demand the objectivefunction equation (11) is to minimize total procurement costwhen all sub-CPSs take the most economic order quantity

4 Solution Algorithm

In order to solve the multiobjective model we introducea balancing factor 120572 (0 le 120572 le 1) of the QSD of totaldemand to balance the two objectives Then the objectivesare transformed into the following

max119865 = 120572 sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) +

(1 minus 120572) 120573

sum120587119896isin120587

119862lowast

119896

(13)

where 120573 is the cost conversion coefficient of 1198652

In order to obtain the optimal solution of the globalsituation we use an intelligent optimization algorithm thesimulated annealing (SA) algorithm

The annealing schedule of the SA algorithm refers toa set of process parameters used to control the algorithmincluding the generation of a neighbourhood solution thecontrol of temperature the number of iterations at eachtemperature and the termination rule

Since sub-CPS 120587119896stands for the supplier relationship

between the subsidiary sets 119868119896and the supplier 119895 we can adopt

a certain rule to select the supplier for each subsidiary thesubsidiaries which select the same supplier and their chosensupplier are composed of the sub-CPS 120587

119896 Automatically the

CPS based on the above initial solution generation methodsatisfies the constraints (3) and (4)

According to the objective function we can select suppli-ers as follows For 119894 isin 119868 let its set of alternative suppliers be119869119894= 119895 | 120574(119894 119895) ge 120574

0(119894) forall119895 isin 119869

119894 a sub-CPS which consists


of 119894 and 119895 separately is defined as 120587(119894 119895) = (119894 harr 119895) Theobjective function of this sub-CPS is

119865 (119894 119895) = 120572 sum

120587(119894119895)

120574 (119894 119895) + (120572 minus 1) sum

120587(119894119895)

1

119862lowast

120587(119894119895)

(14)

Then we choose a supplier 119895 from 119869119894according to a selection

probability 120593(119894 119895) which is

120593 (119894 119895) =

119865 (119894 119895)

sum1198951015840isin119869119894

119865 (119894 1198951015840)

(15)

According to (15) we select the corresponding supplier foreach 119894 isin 119868 and merge the sub-CPSs for the same supplier intoa new sub-CPSThe definition of 119869

119894ensures that all sub-CPSs

satisfy the constraint (1) and are feasibleOn the basis of the above analysis the algorithm is as

follows

Step 0 Initialize Set the initial temperature to1198790 the current

temperature 119879 = 1198790 the current iterations ℎ = 1 the optimal

solution 120587opt = Φ and the objective function 119865opt = infin Use(15) to calculate 120593(119894 119895) forall119894 isin 119868 119895 isin 119869

Step 1 Randomly generate a sub-CPS 120587119894 forall119894 isin 119868

Step 2 Calculate the objective function value 119865119894of each sub-

CPS 120587119894using (13)

Step 3 Update the current solution according to theMetropolis criterion if 119865 lt 119865opt let 120587opt = 120587

0and 119865opt = 119865

otherwise randomly generate a numerical value 120588 in (0 1) andif 120588 lt exp(minus(119865 minus 119865opt)119879119894) then set 120587opt = 120587

0 119865opt = 119865

Otherwise the neighbourhood solution is refused

Step 4 Judge the number of iterations at the same tem-perature The number of iterations at each temperature isrestricted by the lower limit of iterations 119871 the accepting rate120575 of the neighbourhood solution and the upper limit119867

If the iterations satisfy the restrictions then set ℎ = ℎ + 1

and move to Step 1 otherwise stop the iterations at the sametemperature and move to Step 5

Step 5 Judge the convergence rule which is a minimumtemperature 119879

119891 If it is not satisfied then update the current

temperature119879 = 120576119879 where 120576 is a constant close to 1 andmoveto Step 1 otherwise terminate the algorithm and output theoptimal solutions 120587opt and 119865opt

5 Example Analysis

51 The Base Example A steel group company has foursubsidiary companies 119894

1 1198942 1198943 and 119894

4 A certain raw material

is offered by five suppliers 1198951 1198952 1198953 1198954 and 119895

5 The coor-

dinated cost of coordinated procurement 1198620

= 10000 Thetransportation cost coefficient 119862119910

0= 2 119862119910 = 0001 The order

price discount coefficient 119903 = 001 The preparation cost ofeach batch order 119888119889 = 50 The unit storage cost for the rawmaterials 119888119904 = 10

Table 1 Demand of subsidiaries

Subsidiary 1205740(119894) Demand

1198941

060 3501198942

065 4101198943

062 2201198944

070 190

Table 2 Transportation distance and initial price

Supplier 1198951

1198952

1198953

1198954

1198955

Transportation distance 1200 1000 1500 1800 1300Initial price 35 36 30 32 38

Table 3 QSD of suppliers

Subsidiary Supplier1198951

1198952

1198953

1198954

1198955

1198941

095 092 055 095 0921198942

090 095 095 062 0951198943

050 085 087 060 0851198944

094 088 081 090 064

Table 4 Sub-CPSs for the base example

120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 0940 053 lowast 106

1205872

980 1078 0907 234 lowast 106

Table 5 Sub-IPSs of base example

120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 094 053 lowast 106

1205872

350 396 092 083 lowast 106

1205873

220 310 087 073 lowast 106

1205874

410 470 095 123 lowast 106

In the period of 119905 = 300 days the quantity and quality ofthe raw materials required are as set out in Table 1

The transportation distance from the suppliers to the steelgroup and the initial price are as set out in Table 2

The QSD of the suppliersrsquo products to meet the needs ofsubsidiaries are as set out in Table 3

52 The Results Using the balance factors for the demandsatisfaction degree 120572 = 07 and 120573 = 10119890

6 we get the CPS120587 = 120587

1= (1198944harr 1198951) 1205872= (1198941 1198942 1198943 harr 119895

2) and the optimal

objective function value is 360758ThisCPS and its sub-CPSsare seen in Figure 1 and Table 4 respectively

When we do not adopt the CPS the optimal independentprocurement strategy (IPS) 120587 = 120587

1= (1198944

harr 1198951) 1205872

=

(1198941harr 1198952) 1205873= (1198943harr 1198953) 1205874= (1198942harr 1198955) and the optimal

objective function value 119862 = 347748 This procurementstrategy and its subpolicy are shown in Figure 2 and Table 5respectively Compared with the IPS the optimal objectivefunction value of theCPS is 374higherOn the premise that


i1

i2i3

j2

j4

j1

j3

j5

i4larrrarr

1205872 = ( i1 i2 i3 j2)larrrarr 1205871 = ( i4 j2)larrrarr

Figure 1 CPS of base example

i4 i1

i2i3

j4

j1

j5

j2

j3

1205872 = ( i1 j2)larrrarr1205871 = ( i4 j1)larrrarr


Figure 2 IPS of base example

34

345

35

355

36

365

0 50 100 150 200 250 300Iterations

Obj

ectiv

e fun

ctio

n

Figure 3 Convergence efficiency

the procurement quality is met the procurement cost dropsremarkably

53 Analysis of Solving Efficiency During the solving of thebase example when the number of iterations is increasedthe optimal solution varies as shown in Figure 3 As we cansee this algorithm has a good effect and can quickly convergeto the optimal solution The convergence speed and solutionquality are both very satisfactory

6 Results under Other Conditions

Several factors including the subsidiariesrsquo requirements forthe quality of the raw materials the supply characteristics ofthe products in the market the procurement cost structureand the balance factor 120572 together have an influence on the

i3

i3

i2

i1

j3

j1 j4

j5

j2

120587 =

i1 i2 i3 i4 j2larrrarr

Figure 4 CPS under uniform QSD

Table 6


1198952

1198953

1198954

1198955

1198941

095 092 087 082 0851198942

095 092 087 082 0851198943

095 092 087 082 0851198944

095 092 087 082 085

Table 7 Sub-CPS under uniform QSD

120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

120587 1170 1657 092 279 lowast 106

Table 8 Sub-CPSs under 1198620= 0

120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

1170 1657 090 278 lowast 106

1205872

980 1077 0907 233 lowast 106

CPS Here using the base example we analyse the resultswhen various factors are changed

61 The Results with a Uniform QSD Condition In order tofind the influence of QSD on the CPS we take a uniformQSDfor each supplier as set out in Table 6

We get the optimal CPS 120587 = (1198941 1198942 1198943 1198944 harr 119895

2)

and the optimal objective function value 119862 = 365136 Theresults and the specific procurement are shown in Figure 4and Table 7 Compared with the base example the optimalobjective function value under the uniformQSD condition isincreased by 121 and the CPS has an advantage in terms ofeconomies of scale

62 Effects of the Supply Price Discount on the CPS In thissection we analyse the effects of the discount coefficient 119903 onthe CPS The supply price decreases when the order quantityincreases as (6) shows However the rawmaterials for a steelcompany are both huge in quantity and low in price the lowdiscount can be provided When 119903 = [0 025] the CPSsare the same 120587 = 120587

1= (1198944

harr 1198951) 1205872

= (1198941 1198942 1198943 harr

1198952) The average QSDs of sub-CPSs 120587

1and 120587

2are 094 and

0907 respectively and the order quantities are 119876(1205871) = 190

119876(1205872) = 980 respectively The objective function values of

the CPSs are a little different with 119862 = 360756 when 119903 = 0

and 119862 = 360761 when 119903 = 025 However the discountcoefficient 119903 has an obvious effect on the order quantity of the


Table 9 Optimal CPSs under different balance factors

120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20

0 01 02 03Discount coefficient

Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2

Figure 5 Effect of 119903 on order quantity

0

05

1

15

2

25

3

0 01 02 03

Discount coefficient

Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2

Figure 6 Effect of 119903 on procurement cost

sub-CPSs 1205871 1205872 as Figure 5 shows In contrast to the order

quantity the difference in the procurement cost of the sub-CPSs is insignificant as Figure 6 shows This is because theprice discount for the raw materials is limited At the same

time the economic order quantity has a regulating functionto the effect of price discount

Thus within a certain range (eg 119903 isin [0 025]) pricediscount has little effect on the coordinated procurementstrategy

63 Impact of the Coordinated Costs on the CPS The coor-dinated costs reflect the operation and the coordinated levelof the coordinated procurement department in the groupcompany Compared with a sub-CPS 120587

119896= 120587(119868

119896 119895) the sub-

IPSs are composed of each of the subsidiaries 119894 isin 119868119896and the

supplier 119895 the difference between the logistics costs of theCPS and the IPS is expressed as

Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)

From (16) we can see that coordinated costs have a directeffect on the CPS and that Δ119862lowast

119896ge 0 is a necessary condition

for accepting the CPS 1198620= 0 is an ideal situation with the

corresponding CPS 120587 = 1205871

= (1198941 1198942 1198943 1198944 harr 119895

2) and

objective function value 119862 = 3599 and the sub-CPSs areshown in Table 8 Although the CPS when 119862

0= 0 is still

the same as in the base sample there are some savings inprocurement costs

However when 1198620ge 400000 the optimal CPS tends to

disintegrate Every subsidiary company has its own supplierand the CPS is similar to the one shown in Figure 2

64 Effects of the Balance Factor on the CPS The balancefactor 120572 of the QSD reflects the weighting relationshipbetween the two objective functions and the procurementrequirements of the subsidiaries Under the extreme condi-tion when 120572 = 0 the company just needs to consider theprocurement costs when 120572 = 10 the company only needs to


consider the QSD With different values of 120572 the CPS variesas shown in Table 9

When 120572 is smaller the purchase logistics of the sub-sidiaries tend to lead to a higher degree of coordination andthe procurement costs are lower when 120572 = 08 the CPSshows evidence of disintegration and when 120572 = 10 everysubsidiary purchases its ownmaterials from its own suppliers

7 Conclusions

This paper focused on the optimization of coordinatedprocurement logistics for a steel groupA simulated annealingalgorithm was used to solve this problem From our analysisof the numerical sample we can draw the following conclu-sions

(1) The CPS can adapt better than the IPS to the internalprocurement logistics of the steel company and bringa significant saving in procurement costs

(2) When the QSD for the quality of the material isnot too high or there is no difference between thematerials or they are substitutable in the market theCPS appears to be highly cooperative

(3) Coordinated costs have a strong effect on the CPS soa highly advanced coordinated procurement systemis the basis for building a significantly efficient coor-dinated procurement strategy

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the Science and Technol-ogy Research Development Project of the China RailwayCorporation (Major Program 2013X004-A) the ResearchFund for the Fok Ying Tong Education Foundation of HongKong (Project no 132017) and the National Natural ScienceFoundation of China (70901076) This paper is dedicated tothe memory of the authorsrsquo best friend Dr Zhuqiang Qiu

References

[1] R N Roy and K K Guin ldquoProposed model of JIT purchasingin an integrated steel plantrdquo International Journal of ProductionEconomics vol 59 no 1 pp 179ndash187 1999

[2] Z Gao and L Tang ldquoA multi-objective model for purchasingof bulk raw materials of a large-scale integrated steel plantrdquoInternational Journal of Production Economics vol 83 no 3 pp325ndash334 2003

[3] K Hafeez M Griffiths J Griffiths and M M Naim ldquoSystemsdesign of a two-echelon steel industry supply chainrdquo Interna-tional Journal of Production Economics vol 45 no 1ndash3 pp 121ndash130 1996

[4] H-S Chang ldquoCoking coal procurement policies of the Japanesesteel mills changes and implicationsrdquo Resources Policy vol 23no 3 pp 125ndash135 1997

[5] A Potter R Mason M Naim and C Lalwani ldquoThe evolutiontowards an integrated steel supply chain a case study from theUKrdquo International Journal of Production Economics vol 89 no2 pp 207ndash216 2004

[6] W Faes P Matthyssens and K Vandenbempt ldquoThe pursuit ofglobal purchasing synergyrdquo Industrial Marketing Managementvol 29 no 6 pp 539ndash553 2000

[7] H Akkermans P Bogerd and J Van Doremalen ldquoTravailtransparency and trust a case study of computer-supportedcollaborative supply chain planning in high-tech electronicsrdquoEuropean Journal of Operational Research vol 153 no 2 pp445ndash456 2004

[8] M Essig ldquoPurchasing consortia as symbiotic relationshipsdeveloping the concept of lsquoconsortium sourcingrsquordquo EuropeanJournal of Purchasing and Supply Management vol 6 no 1 pp13ndash22 2000

[9] J E Bishop ldquoConsortium purchasingrdquo New Directions ForHigher Education vol 120 pp 81ndash88 2002

[10] E Tella and V-M Virolainen ldquoMotives behind purchasingconsortiardquo International Journal of Production Economics vol93-94 pp 161ndash168 2005

[11] P T Helo ldquoDynamic modelling of surge effect and capacitylimitation in supply chainsrdquo International Journal of ProductionResearch vol 38 no 17 pp 4521ndash4533 2000

[12] M Turkay C Oruc K Fujita and T Asakura ldquoMulti-companycollaborative supply chain management with economical andenvironmental considerationsrdquo Computers and Chemical Engi-neering vol 28 no 6-7 pp 985ndash992 2004

[13] P Kraljic ldquoPurchasing must become supply managementrdquoHarvard Business Review vol 61 no 5 pp 109ndash117 1983

[14] Y Fu and R Piplani ldquoSupply-side collaboration and its value insupply chainsrdquo European Journal of Operational Research vol152 no 1 pp 281ndash288 2004

[15] P Keskinocak and S Savasaneril ldquoCollaborative procurementamong competing buyersrdquo Naval Research Logistics vol 55 no6 pp 516ndash540 2008

[16] S K Goyal and A T Satir ldquoJoint replenishment inventorycontrol deterministic and stochastic modelsrdquo European Journalof Operational Research vol 38 no 1 pp 2ndash13 1989

[17] A Federgruen and Y-S Zheng ldquoThe joint replenishment prob-lemwith general joint cost structuresrdquoOperations Research vol40 no 2 pp 384ndash403 1992

[18] A K Chakravarty and S K Goyal ldquoMulti-item inventorygrouping with dependent set-up cost and group overhead costrdquoEngineering Costs and Production Economics vol 10 no 1 pp13ndash23 1986

[19] H Gurnani ldquoA study of quantity discount pricing modelswith different ordering structures order coordination orderconsolidation and multi-tier ordering hierarchyrdquo InternationalJournal of Production Economics vol 72 no 3 pp 203ndash2252001

[20] K Lu C-H Yang and D-M Dai ldquoA Lagrangian-based heuris-tic algorithm formulti-product capacitated lot sizing with time-varying transportation costsrdquo System Engineering Theory andPractice vol 28 no 10 pp 47ndash52 2008

[21] J Q Xiang P Q Huang and J Li ldquoOptimal order model underperiodic order policy of centralized procurement in enterprisegrouprdquo Journal of Shang Hai Jiaotong University vol 39 no 3pp 474ndash478 2005

[22] W Z Xiao and Z Q Qiu ldquoOptimization of coordinatedprocurement strategy in steel grouprdquo Journal of ComputerApplications vol 7 pp 1913ndash1918 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


for the steel industry allowing it to reduce circulationcosts significantly and improve market competitive-ness

Increasing the level of coordinated logistics procurementand reducing the production costs of the industry have there-fore become a key strategy for the survival and developmentof Chinarsquos steel industry

2 Literature Review

Looking at the procurement logistics for a single steel enter-prise Roy and Guin [1] built a conceptual model of just-in-time purchasing for a steel company in India They con-sidered the identification and classification of raw materialsupplier availability and goods consolidation of distributionoutlets For the raw material procurement of a large steelplant considering three main factors (the selection of rawmaterial model supplier and order quantity) Gao and Tang[2] constructed a multiple objective linear programming(MOLP) model for procurement decisions Hafeez and col-leagues [3] considered factors such as human resourcesorganization and technology using the dynamic structure ofthe integrated system and described a two-level steel supplychain that achieves a minimized inventory level under thecondition of capacity constraints and limits on raw materialprocurement lead time

By analysing the procurement policy for iron ore and cokeof Japanese steel enterprises in the late twentieth centuryChang [4] argued that changing technology and institutionalstructure made Japanese procurement decisions more con-sistent and that this laid the foundations for coordinatedprocurement between enterprises Potter et al [5] made athorough study of the development process of the Britishsteel supply chain from the traditional mode to the integratedmode in the twentieth century and analysed in detail theimpact of the changes on inventory ordering lead timeand asset utilization Faes et al [6] considered that coor-dinated procurement can lead to better internal exchangeof information an improved market negotiation strategysignificant cost savings a greater impact on the monopolymarket and a better understanding of the market and coststructure Akkermans et al [7] established a theoreticalmodel for coordination and studied the important effectsof nontechnological factors on achieving synergy Essig [8]found that coordinated procurement can reduce transactioncosts allow a lower purchase price to be obtained and lead toa more efficient use of procurement staff Bishop [9] showedthat coordinated procurement can lead to the integration ofthe purchase process better continuity and coordination andeconomies of scale Tella and Virolainen [10] argued thatcoordinated procurement members wanted to reduce theirprocurement costs and achieve lower management costslower logistics costs and higher mobility of the inventoryHelo [11] proved that demand coordinationwas important forimproving the capacity of the supply chain

Turkay et al [12] established a model and made a quan-titative analysis of the cooperation between businesses inthe chemical industry Kraljicrsquos [13] model briefly described

the procurement strategy for different materials from theperspective of the profit impact and supply risk involvedin procurement Fu and Piplani [14] established a modelthat evaluated supplier coordination based on inventory tosimulate and assess distributorsrsquo performance before and aftercoordination The calculations showed that the coordinationof suppliers can improve the performance of the wholesupply chain Keskinocak and Savasaneril [15] used a gametheory method to study the coordinated procurement of twocompeting purchasers Goyal and Satir [16] used an indirectgroup strategy to seek a combination of the optimal basiccycle and order frequency to make the total relevant costa minimum to achieve optimization of multispecies coor-dinated procurement Federgruen and Zheng [17] adopteda direct group strategy and used a heuristic algorithm tooptimize the coordinated procurement Chakravarty andGoyal [18] adopted a dependent and group strategy andused dynamic programming to optimize coordinated pro-curement Gurnani [19] studied the design of a supplierquantity discount programme which is the coordinatedprocurement of two heterogeneous buyers with differentrequirement processes and cost parameters For multiperiodmultiproduct batch procurement Lu et al [20] establisheda mixed integer programming model with a constrainton transport capacity and variable transport price whichdetermined the optimal procurement quantity by using theLagrange relaxation theory Xiang et al [21] assumed that agroup regularly orders and intensively purchases under thecondition of independent demand from the subsidiaries ina group company and established an optimal order quantitymodel

This paper studies the optimization of a grouprsquos internalcoordinated procurement logistics when combined with thecharacteristics f the raw material procurement logistics ofsteel enterprises Comparing with other studies we takethe full logistics cost of coordinated procurement strategyand the quality of demand into account in the coordinatedprocurement problem On the basis of the optimizationmodel in [22] this paper improves the solution algorithm andanalyzes the effect of different parameters on the coordinatedprocurement strategy

The rest of the paper is organized as follows Section 3presents a brief description of optimization model InSection 4 we describe our approach in solution algorithmThe base example and its results are shown in Section 5Results under the conditions of different parameters areanalysed in Section 6 Lastly the conclusions of our findingsare summarized in Section 7

3 Optimization Model

This paper studies the CPS of a steel group company that isequipped with a coordinated procurement department andhas 119898 subsidiaries (or similar procurement entities) The setof subsidiaries is 119868 = 119894 119894 = 1 119898 and the order quan-tity of raw materials is 119876

119894during a period of length 119905 For

simplicity we assume that all subsidiaries in the coordinatedprocurement alliance have the same purchase frequency



120574 (119894 119895) ge 1205740 (

119894) 119894 = 1 119898 119895 = 1 119899 (1)




119896= (119868119896

harr 119895119896) | 119868119896

sub 119868 119895119896

isin




120575119896=

11003816100381610038161003816119868119896

1003816100381610038161003816ge 2 120587

119896isin 120587

01003816100381610038161003816119868119896

1003816100381610038161003816= 1 120587

119896isin 120587

(2)


119896 for sub-CPS

120587119896 When 120575


119896= 0



1198681198961

cap 1198681198962

= 0 1205871198961

1205871198962

isin 120587 (3)

⋃

120587119896isin120587

119868119896= 119868 (4)

119876 (120587119896) = ⋃

119894isin119868119896

119876119894

120587119896isin 120587 (5)


sub-CPS 120587119896






119896of


119901119896= 119901119895119896

minus 119903119902119896 (6)

119862119910

119896= 119862119910

0minus 119862119910119902119896 (7)

where 119901119895119896


119895119896

gt 0 and 119903 ge 01198621199100and119862


0gt 0 and 119862

119910ge 0




119896are

119862119896= 1198620120575119896+ 119876 (120587

119896) 119897119895119896

119862119910

119896+ 119876 (120587

119896) 119901119896

+

119888119889119876 (120587119896)

119902119896

+

119905

2

119888119904119902119896

(8)


are respectively

119902lowast

119896= radic

119888119889119876 (120587119896)

((1199052) 119888119904minus 119862119910119897119895119896

119876 (120587119896) minus 119903119876 (120587

119896))

119862lowast

119896= 1198620120575119896+ 119876 (120587

119896) (119862119910

0119897119895119896

+ 119901119895119896

)

+ 2radic119905

2

119888119889119888119904119876 (120587119896) minus (119862

119910119897119895119896

+ 119903) [119876 (120587119896)]2

(9)


max 1198651= sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) (10)

max 1198652=

1

sum120587119896isin120587

119862lowast

119896

(11)





max119865 = 120572 sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) +

(1 minus 120572) 120573

sum120587119896isin120587

119862lowast

119896

(13)










0(119894) forall119895 isin 119869




119865 (119894 119895) = 120572 sum

120587(119894119895)

120574 (119894 119895) + (120572 minus 1) sum

120587(119894119895)

1

119862lowast

120587(119894119895)

(14)



120593 (119894 119895) =

119865 (119894 119895)

sum1198951015840isin119869119894

119865 (119894 1198951015840)

(15)




follows






CPS 120587119894using (13)


0and 119865opt = 119865


0 119865opt = 119865








5 Example Analysis


1 1198942 1198943 and 119894



5 The coor-



0= 2 119862119910 = 0001 The order




1198941

060 3501198942

065 4101198943

062 2201198944

070 190


Supplier 1198951

1198952

1198953

1198954

1198955




1198952

1198953

1198954

1198955

1198941

095 092 055 095 0921198942

090 095 095 062 0951198943

050 085 087 060 0851198944

094 088 081 090 064


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 0940 053 lowast 106

1205872

980 1078 0907 234 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 094 053 lowast 106

1205872

350 396 092 083 lowast 106

1205873

220 310 087 073 lowast 106

1205874

410 470 095 123 lowast 106





6 we get the CPS120587 = 120587

1= (1198944harr 1198951) 1205872= (1198941 1198942 1198943 harr 119895

2) and the optimal



1= (1198944

harr 1198951) 1205872

=




i1

i2i3

j2

j4

j1

j3

j5

i4larrrarr



i4 i1

i2i3

j4

j1

j5

j2

j3




34

345

35

355

36

365

0 50 100 150 200 250 300Iterations

Obj

ectiv

e fun

ctio

n






i3

i3

i2

i1

j3

j1 j4

j5

j2

120587 =



Table 6


1198952

1198953

1198954

1198955

1198941

095 092 087 082 0851198942

095 092 087 082 0851198943

095 092 087 082 0851198944

095 092 087 082 085


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

120587 1170 1657 092 279 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

1170 1657 090 278 lowast 106

1205872

980 1077 0907 233 lowast 106




2)



1= (1198944

harr 1198951) 1205872

= (1198941 1198942 1198943 harr


1and 120587

2are 094 and







120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2


0

05

1

15

2

25

3

0 01 02 03


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2







119896= 120587(119868

119896 119895) the sub-



Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)





= (1198941 1198942 1198943 1198944 harr 119895

2) and


0= 0 is still








7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120574 (119894 119895) ge 1205740 (

119894) 119894 = 1 119898 119895 = 1 119899 (1)




119896= (119868119896

harr 119895119896) | 119868119896

sub 119868 119895119896

isin




120575119896=

11003816100381610038161003816119868119896

1003816100381610038161003816ge 2 120587

119896isin 120587

01003816100381610038161003816119868119896

1003816100381610038161003816= 1 120587

119896isin 120587

(2)


119896 for sub-CPS

120587119896 When 120575


119896= 0



1198681198961

cap 1198681198962

= 0 1205871198961

1205871198962

isin 120587 (3)

⋃

120587119896isin120587

119868119896= 119868 (4)

119876 (120587119896) = ⋃

119894isin119868119896

119876119894

120587119896isin 120587 (5)


sub-CPS 120587119896






119896of


119901119896= 119901119895119896

minus 119903119902119896 (6)

119862119910

119896= 119862119910

0minus 119862119910119902119896 (7)

where 119901119895119896


119895119896

gt 0 and 119903 ge 01198621199100and119862


0gt 0 and 119862

119910ge 0




119896are

119862119896= 1198620120575119896+ 119876 (120587

119896) 119897119895119896

119862119910

119896+ 119876 (120587

119896) 119901119896

+

119888119889119876 (120587119896)

119902119896

+

119905

2

119888119904119902119896

(8)


are respectively

119902lowast

119896= radic

119888119889119876 (120587119896)

((1199052) 119888119904minus 119862119910119897119895119896

119876 (120587119896) minus 119903119876 (120587

119896))

119862lowast

119896= 1198620120575119896+ 119876 (120587

119896) (119862119910

0119897119895119896

+ 119901119895119896

)

+ 2radic119905

2

119888119889119888119904119876 (120587119896) minus (119862

119910119897119895119896

+ 119903) [119876 (120587119896)]2

(9)


max 1198651= sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) (10)

max 1198652=

1

sum120587119896isin120587

119862lowast

119896

(11)





max119865 = 120572 sum

120587119896isin120587

sum

119894isin120587119896

120574 (119894 119895) +

(1 minus 120572) 120573

sum120587119896isin120587

119862lowast

119896

(13)










0(119894) forall119895 isin 119869




119865 (119894 119895) = 120572 sum

120587(119894119895)

120574 (119894 119895) + (120572 minus 1) sum

120587(119894119895)

1

119862lowast

120587(119894119895)

(14)



120593 (119894 119895) =

119865 (119894 119895)

sum1198951015840isin119869119894

119865 (119894 1198951015840)

(15)




follows






CPS 120587119894using (13)


0and 119865opt = 119865


0 119865opt = 119865








5 Example Analysis


1 1198942 1198943 and 119894



5 The coor-



0= 2 119862119910 = 0001 The order




1198941

060 3501198942

065 4101198943

062 2201198944

070 190


Supplier 1198951

1198952

1198953

1198954

1198955




1198952

1198953

1198954

1198955

1198941

095 092 055 095 0921198942

090 095 095 062 0951198943

050 085 087 060 0851198944

094 088 081 090 064


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 0940 053 lowast 106

1205872

980 1078 0907 234 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 094 053 lowast 106

1205872

350 396 092 083 lowast 106

1205873

220 310 087 073 lowast 106

1205874

410 470 095 123 lowast 106





6 we get the CPS120587 = 120587

1= (1198944harr 1198951) 1205872= (1198941 1198942 1198943 harr 119895

2) and the optimal



1= (1198944

harr 1198951) 1205872

=




i1

i2i3

j2

j4

j1

j3

j5

i4larrrarr



i4 i1

i2i3

j4

j1

j5

j2

j3




34

345

35

355

36

365

0 50 100 150 200 250 300Iterations

Obj

ectiv

e fun

ctio

n






i3

i3

i2

i1

j3

j1 j4

j5

j2

120587 =



Table 6


1198952

1198953

1198954

1198955

1198941

095 092 087 082 0851198942

095 092 087 082 0851198943

095 092 087 082 0851198944

095 092 087 082 085


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

120587 1170 1657 092 279 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

1170 1657 090 278 lowast 106

1205872

980 1077 0907 233 lowast 106




2)



1= (1198944

harr 1198951) 1205872

= (1198941 1198942 1198943 harr


1and 120587

2are 094 and







120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2


0

05

1

15

2

25

3

0 01 02 03


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2







119896= 120587(119868

119896 119895) the sub-



Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)





= (1198941 1198942 1198943 1198944 harr 119895

2) and


0= 0 is still








7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119865 (119894 119895) = 120572 sum

120587(119894119895)

120574 (119894 119895) + (120572 minus 1) sum

120587(119894119895)

1

119862lowast

120587(119894119895)

(14)



120593 (119894 119895) =

119865 (119894 119895)

sum1198951015840isin119869119894

119865 (119894 1198951015840)

(15)




follows






CPS 120587119894using (13)


0and 119865opt = 119865


0 119865opt = 119865








5 Example Analysis


1 1198942 1198943 and 119894



5 The coor-



0= 2 119862119910 = 0001 The order




1198941

060 3501198942

065 4101198943

062 2201198944

070 190


Supplier 1198951

1198952

1198953

1198954

1198955




1198952

1198953

1198954

1198955

1198941

095 092 055 095 0921198942

090 095 095 062 0951198943

050 085 087 060 0851198944

094 088 081 090 064


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 0940 053 lowast 106

1205872

980 1078 0907 234 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

190 275 094 053 lowast 106

1205872

350 396 092 083 lowast 106

1205873

220 310 087 073 lowast 106

1205874

410 470 095 123 lowast 106





6 we get the CPS120587 = 120587

1= (1198944harr 1198951) 1205872= (1198941 1198942 1198943 harr 119895

2) and the optimal



1= (1198944

harr 1198951) 1205872

=




i1

i2i3

j2

j4

j1

j3

j5

i4larrrarr



i4 i1

i2i3

j4

j1

j5

j2

j3




34

345

35

355

36

365

0 50 100 150 200 250 300Iterations

Obj

ectiv

e fun

ctio

n






i3

i3

i2

i1

j3

j1 j4

j5

j2

120587 =



Table 6


1198952

1198953

1198954

1198955

1198941

095 092 087 082 0851198942

095 092 087 082 0851198943

095 092 087 082 0851198944

095 092 087 082 085


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

120587 1170 1657 092 279 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

1170 1657 090 278 lowast 106

1205872

980 1077 0907 233 lowast 106




2)



1= (1198944

harr 1198951) 1205872

= (1198941 1198942 1198943 harr


1and 120587

2are 094 and







120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2


0

05

1

15

2

25

3

0 01 02 03


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2







119896= 120587(119868

119896 119895) the sub-



Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)





= (1198941 1198942 1198943 1198944 harr 119895

2) and


0= 0 is still








7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










i1

i2i3

j2

j4

j1

j3

j5

i4larrrarr



i4 i1

i2i3

j4

j1

j5

j2

j3




34

345

35

355

36

365

0 50 100 150 200 250 300Iterations

Obj

ectiv

e fun

ctio

n






i3

i3

i2

i1

j3

j1 j4

j5

j2

120587 =



Table 6


1198952

1198953

1198954

1198955

1198941

095 092 087 082 0851198942

095 092 087 082 0851198943

095 092 087 082 0851198944

095 092 087 082 085


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

120587 1170 1657 092 279 lowast 106


120587119894

119876(120587119894) 119902

119894120574119894

119862lowast

119894

1205871

1170 1657 090 278 lowast 106

1205872

980 1077 0907 233 lowast 106




2)



1= (1198944

harr 1198951) 1205872

= (1198941 1198942 1198943 harr


1and 120587

2are 094 and







120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2


0

05

1

15

2

25

3

0 01 02 03


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2







119896= 120587(119868

119896 119895) the sub-



Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)





= (1198941 1198942 1198943 1198944 harr 119895

2) and


0= 0 is still








7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120572

CPS120587 119876

119896119902119896

120574119896

119862119896(106) 119865

00 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358452

02 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 358762

04 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359071

06 120587 = (1198941 1198942 1198943 1198944 harr 119895

2) 1170 165725 09 278977 359381

08 1205871= (1198944harr 1198951) 190 275351 094 05294 362505

1205872= (1198941 1198942 1198943 harr 119895

2) 980 107756 0907 233982

10

1205871= (1198944harr 1198951) 190 275351 094 052940

371001205872= (1198943harr 1198953) 220 309546 087 0 733107

1205873= (1198941harr 1198954) 350 4578 095 137965

1205874= (1198942harr 1198955) 410 442068 095 0 976875

0

5

10

15

20


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2


0

05

1

15

2

25

3

0 01 02 03


Ord

er q

uant

ity

Sub-CPS 1Sub-CPS 2







119896= 120587(119868

119896 119895) the sub-



Δ119862lowast

119896= 1198620120575119896+ 2radic

119905

2

119888119889119888119904sum

119894isin119868119896

119876119894minus 119888119889(119862119910119897119895119896

+ 119903) [sum

119894isin119868119896

119876119894]

2

minus sum

119894isin119868119896

2radic119905

2

119888119889119888119904119876119894minus 119888119889(119862119910119897119895119896

+ 119903)1198762

119894

(16)





= (1198941 1198942 1198943 1198944 harr 119895

2) and


0= 0 is still








7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












7 Conclusions







Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article optimal coordinated strategy analysis for

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