Optimal Allocation of Mould Manufacturing Resources Under Manufacturing Network Environments based on a Bi-Level Programming Model

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1 Available olie at Vol. 13, No. 7, November 2017, pp DOI: /ipe p Optimal Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model Hogya Hao a,b, *, Faxi Kog a,b a Jiagsu Key Laboratory of Advaced Structural Materials ad Applicatio Techology, Naig, , Chia b School of Material Egieerig, Naig Istitute of Techology, Naig, ,Chia Abstract I order to achieve the optimal selectio ad allocatio of various mould maufacturig resources uder a maufacturig etwork eviromet, this study developed a bi-level programmig model ad proposed a related solutio. Based o a thorough aalysis of the allocatio process of mould maufacturig resources, the calculatio formulas of the task s satisfactio with resource service quality ad the load balace rate of resources were derived, ad a bi-level programmig mathematical model for the optimal allocatio of mould maufacturig resources was established. Moreover, a hierarchical discrete particle swarm optimizatio (HDPSO) algorithm, which was based o the priciple of o-domiated sortig i a multi-obective optimizatio, was desiged for solvig the model. Fially, a mould maufacturig proect was selected for experimetally validatig the feasibility of the proposed bi-level programmig model for the optimal allocatio of resources ad the effectiveess of the proposed HDPSO algorithm. Keywords: maufacturig etwork; bi-level programmig; HDPSO algorithm; optimal allocatio of resources (Submitted o August 29, 2017; Revised o September 30, 2017; Accepted o October 18, 2017) 2017 Totem Publisher, Ic. All rights reserved. 1. Itroductio Due to the curret globalizatio of the maufacturig idustry, mould eterprises, which are classic examples of resourceorieted ad order-drive orgaizatios, should be able to respod quickly to market demads ad complete customer orders promptly. However, most of the mould eterprises i Chia are small ad medium-sized eterprises, ad do ot possess the various resources for maufacturig all types of mould. This meas that may eterprises eed to break dow barriers, share resources ad achieve the dyamic optimizatio ad itegratio of maufacturig resources. Accordigly, ot oly would orders be fulfilled o schedule, but also resources could be utilized fully, so as to maximize ecoomic beefits ad icrease profits. A maufacturig etwork, which is a ew etworked productio model, was developed for precisely these reasos, ad had the aim of poolig idle ad superior maufacturig resources, which were origially scattered i differet geographical locatios, thereby achievig the effective utilizatio of resources. Therefore, gaiig a i-depth kowledge of the optimal allocatio of maufacturig resources uder a maufacturig etwork eviromet is of great sigificace with regard to the implemetatio ad developmet of a maufacturig etwork. To date, a great amout of research has bee coducted regardig the optimal allocatio of maufacturig resources. For example, Fu Jigzhi et al. adopted some performace parameters icludig time (T), quality (Q), cost (C) ad service (S) as the importat evaluatio idexes of the allocatio of, ad search for, maufacturig resources i a etwork eviromet, ad the ivestigated the optimal maufacturig resources that satisfied the requiremets of maufacturig tasks [1-5]. Furthermore, Zhou Chagchu et al. also selected T, Q, C ad S as the evaluatio idexes that satisfied users resource requiremets, ad made a feasible selectio ad optimal allocatio of maufacturig resources usig a two-stage fuzzy comprehesive evaluatio [18]. Zhag Xiagbi et al. aimed at the miimizatio of the total cost of task completio * Correspodig author. address: haohogya@it.edu.c.

2 1148 Hogya Hao ad Faxi Kog ad established the optimal allocatio model of resources [19]. Liu Lila et al. used idexes of the resources quality of service (QoS) attributes, amely, time (T), price (P), quality (Q) ad service (S), as the evaluatio criterio of resources, ad proposed a resource schedulig method based o the QoS s group decisio-makig fuzzy-aalytic hierarchy model [7, 8]. Ma Xuefe et al. established a optimal allocatio model of maufacturig resources, i which product delivery time, cost ad maufacturig quality were employed as three obectives, ad the solved this model usig a geetic algorithm (GA) [11]. Sog Shuqiag et al. used cost ad time as the optimizatio obectives of maufacturig resources ad itroduced a quatum-behaved particle swarm optimizatio (QPSO) algorithm for the solutio [13]. Based o the aalytic hierarchy process (AHP), Shi Zhabei et al. costructed a etwork ode selectio method, which used T, Q, C ad S as the optimizatio criterio of maufacturig resources, ad attempted to select some optimal resource odes [14]. Fei Tao et al. proposed a maufacturig grid resource service QoS model (icludig time, cost, reliability, ad satisfactio) ad QoSbased resource search method [15-17]. To summarize, previous studies maily established evaluatio models of maufacturig resources that oly icluded time, quality, cost ad service, which were related to maufacturig tasks, ad the adopted several algorithms, which maily icluded the PSO [8,11,13], GA [2, 4, 11], AHP [7,14] ad two-stage fuzzy comprehesive evaluatio [18], to solve the models. However, the load balace of mould maufacturig resources was ot take ito accout i these studies, which accordigly always yielded a local optimizatio scheme as opposed to a systematical optimizatio scheme that cosidered the maufacturig task ad resources. Therefore, this study first reviewed research results from all over the world, ad explored the feasibility of usig a bi-level programmig model to solve the optimal allocatio problem of mould maufacturig resources i a etwork eviromet. The, usig the degree to which the task s requiremets were satisfied (the task s satisfactio degree) with regard to resource service quality ad the load balace of the maufacturig eterprise s resources as the upper-level ad lower-level programmig obectives respectively, a bi-level programmig model for the optimal allocatio of maufacturig resources was established, ad a improved PSO algorithm embeddig the bi-level iteratio rule was proposed as a solutio. 2. Aalysis of the Allocatio Process of Mould Maufacturig Resources This study assumed that a mould maufacturig proect existed i a maufacturig etwork eviromet, which icluded multiple maufacturig tasks. For each maufacturig task, may differet maufacturig service resources ca satisfy the task requiremets. A lot of iformatio, icludig delivery date, productio cost ad quality requiremets, was first released for the maufacturig task via the etwork odes. The, the related assessmet ad screeig activities took place uder the costrait coditios of various criteria (T, C, Q ad S) i accordace with the feedback results of the resource maager; ext, the cadidate resource sets of various maufacturig tasks were acquired, ad the iformatio icludig delivery date, maufacturig cost ad completio quality that was promised from the eterprise resposible for the maufacturig task were ascertaied; fially, the optimizatio model of maufacturig resource selectio was established so that each maufacturig task was assiged to the most appropriate maufacturig resource. Accordigly, the optimal allocatio scheme of maufacturig resources that achieved the load balace of maufacturig resources ad simultaeously maximized the task satisfactio degree of resource service quality was obtaied. As show i Fig. 1, a problem should be firstly addressed i the optimal allocatio of resources, i.e., how to select the most appropriate service resource set from multiple cadidate service resource sets for each task. 3. The Bi-level Programmig Model of the Optimal Allocatio of Mould Maufacturig Resources 3.1. A mathematical descriptio It is assumed that the maufacturig process of a set of moulds uder a maufacturig etwork eviromet ca be decomposed ito m maufacturig tasks, deoted as t t 1, t 2,, t m, ad these maufacturig tasks iclude may subtasks t t, t,, t ); the set of cadidate maufacturig (for the i-th maufacturig task, its subtask set ca be deoted as resource odes ca be deoted as G G, G,, m 1 2 G. The subtasks, with a total umber of M u i i1 i i 1 i 2 iu i, were completed by cadidate resource odes, i order to achieve the task s satisfactio degree with regard to resource service quality ad the load balace of maufacturig resources Hypotheses Hypothesis 1 - All cadidate resource odes that participate i mould maufacturig are equal.

3 Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model 1149 Hypothesis 2 - Accordig to the priciple that a sigle task caot be decomposed, a task ca oly be processed at a resource service ode. Hypothesis 3 - The time of a cadidate resource ode required for fulfillig a maufacturig task icludes the actual processig time ad the logistics time for the trasportatio to the resource ode. Hypothesis 4 - The cost of a cadidate maufacturig resource ode required for fulfillig a maufacturig task icludes the productio cost ad logistics cost. Hypothesis 5 - The maufacturig etwork service caot be iterrupted. Oce a maufacturig task is iitialized, it caot be stopped; i other words, the maufacturig service ability provided by the service odes i the maufacturig etwork is cotiuous. Mould productio proect Maufacturig task iformatio Delivery deadlie Product cost Quality requiremet Decompositio of maufacturig task Maufacturig etwork platform Mappig betwee maufacturig task ad maufacturig etwork resource Cadidate resource ode Cadidate resource set 2 Cadidate resource set 1 Cadidate resource set Optimal resource allocatio scheme Satisfactio degree with resource service quality Whether the resource load was balaced? Establishmet of the optimizatio model of maufacturig resources Iformatio of various maufacturig iformatio icludig delivery date, productio cost ad quality Figure 1. The optimal allocatio process of maufacturig resources 3.3. Defiitios of the task s satisfactio degree with resource service quality ad the load balace of maufacturig resources ad the related calculatio formulas Whe optimizig the allocatio of maufacturig resources uder a maufacturig etwork eviromet, the eterprises offerig these resources should maximize the maufacturig task s satisfactio degree with regard to resource service quality, ad simultaeously maitai the load balace of these resources as much as possible. However, maitaiig the load balace of the eterprise s maufacturig resources would affect that task s satisfactio degree with resource service quality, while the task s satisfactio degree with resource service quality would also affect the load balace of the resources provided by maufacturig eterprises. Therefore, these two factors show mutual iterdepedece ad iteractio. Accordigly, the optimal allocatio of maufacturig resources ca be regarded as a hierarchical programmig problem, which is geerally described ad solved usig a bi-level programmig model. Bi-level programmig icludes two levels of obectives ad is a hierarchical optimizatio problem. The upper-level obective serves as the domiator while the lowerlevel obective serves as the subordiate. The obective fuctio ad costrait coditios i the upper level are ot oly related to the variables i this level, but are also affected by the optimal solutio or optimal value i the lower-level programmig; furthermore, the optimal solutio i the lower-level programmig is also subected to the effects of the decisios made i the upper-level programmig. I a decisio-makig process related to the optimal allocatio of maufacturig resources, the satisfactio rage of a maufacturig task with resource service quality should first be determied, ad the acceptable rage of various factors that affect the degree of satisfactio should be listed. Moreover, the eterprises offerig maufacturig resources should seek the optimal scheme for the allocatio of these resources. Defiitio 1: A task s satisfactio degree with resource service quality A task s satisfactio degree with resource service quality is also referred to as a task s satisfactio idex with resource service quality, which is reflected by the compariso value betwee the actual feelig of the task s recipiet i acceptig resource services ad their expectatio, i.e., the differece betwee the perceptio quality ad cogitio quality. There are a

4 1150 Hogya Hao ad Faxi Kog umber of evaluatio methods regardig the task s satisfactio degree with resource service quality; however, the idex measuremet method was employed i this study for determiig the key factors that affected the task s satisfactio degree with resource service quality. Subsequetly, the weights of various factors ( C CH, C C ) were obtaied, ad the task s L satisfactio idex with resource service quality was calculated through the weighted summatio: p = CSI = 1W X (1) where p deotes the umber of key factors that affect the task s satisfactio degree with resource service quality, W deotes the weight of the -th factor ad X deotes the score of the -th factor. I this study, oly the ifluece factors of the customizig task s satisfactio degree with resource service quality, amely, delivery date (T), implemetatio cost (C) ad completio quality (Q), were cosidered, ad their weights were determied based o experiece. Accordigly, CSI ca be expressed as a fuctio of T, C ad Q: CSI = f ( T, C, Q) (2) Next, we focus o the relatioships betwee the task s satisfactio degree with resource service quality ad delivery date, implemetatio cost ad completio quality. (1) The relatioship betwee the task s satisfactio degree with resource service quality ad delivery date For a task, the allowable delivery date is a certai time slot rather tha a fixed time poit. Therefore, the closer the actual delivery date is to the earliest delivery deadlie, the higher the task s satisfactio degree. A advace ad delayed delivery is ot allowed; i these two cases, the task s satisfactio degree is equal to 0. Withi the task s allowable delivery date, the eterprises that offer maufacturig resources should deliver as early as possible, as the task s satisfactio degree with resource service quality will be greater; otherwise, the later the delivery, the lower the task s satisfactio degree with resource service quality. It was assumed that the task s satisfactio degree was the greatest ad equal to 1 whe the products were delivered o the earliest allowable delivery date, ad the task s satisfactio degree was the lowest ad equal to 0 whe the products were delivered o the latest allowable delivery date. The followig piecewise decreasig fuctio was selected for describig the relatioship betwee the task s satisfactio degree with resource service quality ad delivery date: 0 f1( Ti ) TiH Ti TiH TiL Ti TiH, Ti TiL i = 1,2,, m (3) T T T il i ih where T ih ad T il deote the specified earliest ad latest delivery dates respectively, i.e., the task s allowable delivery rage was [T il, T ih]. (2) The relatioship betwee the task s satisfactio degree with resource service quality ad implemetatio cost The implemetatio cost should first exceed the miimum cost of maufacturig the mould parts bore by maufacturig eterprise; otherwise, the eterprise will make o profit ad thus forgo the order. Secodly, if the implemetatio cost is too high, the customer will go elsewhere ad the eterprise will have ot have a order to implemet. Therefore, the implemetatio cost must have a acceptable rage, deoted as [C L, C H], where C L deotes the miimum acceptable cost of the maufacturig eterprise ad C H deotes the maximum implemetatio cost that the customer will accept. Withi the acceptable implemetatio cost rage, the task s satisfactio degree with resource service quality is i iverse proportio to the implemetatio cost, suggestig that the task s satisfactio degree with resource service quality decreased gradually with the icrease of the implemetatio cost. Specifically, as the implemetatio cost rose, the task s satisfactio degree with resource service quality first dropped rapidly; whe the implemetatio cost icreased to a certai value, the maufacturig task s satisfactio degree with resource service quality almost disappeared. Therefore, the relatioship betwee the task s satisfactio degree with resource service quality ad the implemetatio cost ca be described as a covex fuctio that is covex to the poit of origi. Accordigly, this study selected the followig expoetial fuctio to describe this relatioship:

5 Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model f2( C) 1 C e C C C C L H, L (4) C C C H where coefficiet. λ > 0 deotes the user s sesitivity degree to the implemetatio cost ad is also referred to as the cost sesitivity (3) The relatioship betwee the task s satisfactio degree with resource service quality ad completio quality Assumig that some maufacturig errors will occur durig the fabricatio process, the completio quality of the maufacturig task demaded by the customer shows a certai tolerace, i.e., the highest quality requiremet for part fabricatio is ot ecessarily set for the maufacturig task. I this study, the tolerace limit of the completio quality of the maufacturig task was defied as the miimum tolerace of completio quality ad deoted as Q L, ad the part quality was geerally characterized by the qualificatio rate of the processed part i the mould part s actual maufacturig process. Assumig that Q i deotes the qualificatio rate of a part, the task s satisfactio degree with resource service quality ad the part s completio quality satisfies the followig fuctio: 0 Qi Qi H, Qi Q f3( Qi ) Qi QiL Qi Qi H il i = 1,2,,m (5) where Q L ad Q H deote the miimum quality tolerace ad the maximum qualificatio rate respectively. For a lower part qualificatio rate, the completio quality is lower, ad the task s satisfactio degree with resource service quality is lower; alteratively, the higher the part s qualificatio rate, the higher the satisfactio degree. Whe the part s qualificatio rate is lower tha the miimum tolerace Q L, the satisfactio degree is equal to 0; by cotrast, the satisfactio degree reaches the maximum, i.e., 1, whe the qualificatio rate is 100%. Withi the rage betwee Q L ad 100%, the satisfactio degree icreases gradually with the risig qualificatio rate. From the above-described relatioships betwee the task s satisfactio degree with resource service quality ad delivery date, implemetatio cost ad completio quality, the comprehesive fuctio of the satisfactio degree of the subtask t ik with the service quality of the maufacturig resource ode G ca be writte as: CSI 1 T i, k, W 2 W Qi, k i, k, W1 f1( Ti, k, ) W 2 f2( Ci, k, ) W3 f3( Qi, k, ) W1 f1 3 C, i, k, e (6) Defiitio 2: The load balace of maufacturig resources For a optimal allocatio of resources icludig m M maufacturig tasks ad maufacturig resource odes, the load rate of the maufacturig resource, deoted as, ca be writte as: m u i i ec xi, k, ti, k, 1 k 1 100% Tp (7) where deotes the load rate of the cadidate resource ode G (i actual productio, is geerally ot greater tha 80%); m u i i1 k1 x t ec i, k, i, k, deotes the load of the cadidate resource ode G ad represets the sum of the labor hours of various sub-tasks after the resource odes were selected for the maufacturig task;, deotes the relatioship betwee the k-th sub-task i the i-th task t i ad cadidate resource odes (if the cadidate resource ode G was selected for the k-th x i k, sub-task i the i-th task, the decisio factor is equal to 1; otherwise, the decisio factor is equal to 0); t ec i, k, deotes the predicted processig time of the k-th sub-task i the i-th task t i at the cadidate resource ode G ; ad Tp deotes the rated labor hours of the cadidate resource ode G. The variace of the resource load rates, deoted as, ca be used for

6 1152 Hogya Hao ad Faxi Kog describig the balace state of the resource load. S ca be calculated by: S 1 2 avg avg (8) (9) where avg deotes the overall utilizatio rate of the cadidate resource ode (the greater the value of overall utilizatio rate). At a smaller odes became more balaced. S avg, the larger the, the differece betwee resource odes was smaller ad the load of resource 3.4. The establishmet of the bi-level programmig model of the optimal allocatio of maufacturig resources uder a maufacturig etwork eviromet Accordig to the problem descriptio, defiitios ad calculatio formulas outlied above, the bi-level programmig model of the optimal allocatio of maufacturig resources uder a maufacturig etwork eviromet ca be described as: ui m TiH xi, k, Ti, k, ui ui k1 1 1 xi, k, Q (10) i. k. ( U) maxcsi W1 W2 xi, k, W Ci, k, 3 m i1 TiH TiL k1 1 e k1 1 ui i1 T t t (11) ec lg i, k, i, k, i, k,, g C c c (12) ec lg i, k, i, k, i, k,, g ui s.t. Ti mi Ti, k, xi, k, T (13) i max ui k1 1 C C x C (14) i mi i, k, i, k, i max k1 1 ui Q Q x 0 (15) i max i, k, i, k, k1 1 xi, k, 0,1 xi, k, 1 1 (16) i 1,2,, m k1,2,, ui (L) max F S( ) (17) s.t. 80% 0 (18) x 0,1 x 1 i, k, i, k, 1 i k 1,2,, m 1,2,, u i (19) where: t lg i, k,, g deotes the logistics time betwee the k-th sub-task i the task t i at the cadidate resource ode G ad the (k+1)-th sub-task i the task t i at the cadidate resource ode G g; c ec i k,, deotes the processig cost of the k-th sub-task i the

7 Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model 1153 task t i at the cadidate resource ode G ; lg c i, k,, g deotes the logistics cost betwee the k-th sub-task i the task t i at the cadidate resource ode G ad the (k+1)-th sub-task i the task t i at the cadidate resource ode G g; ad x i, k, deotes the relatioship betwee the k-th sub-task i the task t i ad cadidate resource odes. If the cadidate resource ode G was selected for the k-th sub-task i the task t i, the decisio factor is equal to 1; otherwise, the decisio factor is equal to 0. Eq. (10) ad Eq. (17) represet the obective fuctios i the upper-level ad lower-level programmig models; Eqs. (13)~(16) represet the upper-level costraits; Eq. (18) ad Eq. (19) represet the lower-level costraits. Specifically, Eqs. (13)~(15) represet the costraits o delivery date, implemetatio cost ad completio quality, respectively. As show i Eq. (16) ad Eq. (19), a sub-task ca oly be assiged to a cadidate resource ode uder a maufacturig etwork eviromet; Eq. (18) represets the costrait o a resource s load rate. 4. A solutio to the model The bi-level programmig model for the optimal allocatio of maufacturig resources is a typical NP-Hard problem, whose solutio space icreases rapidly with the icrease of the umbers of maufacturig tasks ad resources. It is very difficult to obtai the optimal solutio to the large-scale optimal allocatio of maufacturig resources withi a reasoable time period. For this problem, it is more practical to acquire the approximate optimal solutio withi a reasoable time period. For the established bi-level programmig model of the optimal allocatio of maufacturig resources uder a maufacturig etwork eviromet, this study developed a hierarchical discrete PSO (HDPSO) o the basis of the discrete PSO (DPSO) [9, 10, 20]. A HDPSO itegrates two DPSOs for solvig both upper-level ad lower-lever programmig models, ad the follows the basic idea of o-domiated sortig i a multi-obective optimizatio. Fially, it solves the bilevel programmig model for the optimal allocatio of maufacturig resources through game-based iteractive iteratio amog the populatios at differet levels. A PSO is a kid of global adaptive radom search techique based o swarm itelligece ad is ow used maily for optimal solutios i a cotiuous domai. There are a umber of difficulties i solvig complex discrete problems, such as the optimal allocatio of resources. To seek the optimal solutio i a discrete space, a PSO should be discretized [6]. The DPSO algorithm that aims for optimizatio i a discrete domai was described i detail i Ref. [12], ad is ot repeated i this article. A HDPSO is a DPSO-based optimizatio algorithm obtaied via ested iteratios. I each iteratio, both the upperlevel ad lower-level models were solved usig a DPSO. Firstly, the decisio variable i the upper-level model, deoted as X, was used i the lower-level model for obtaiig the optimal solutio Y * ; the, the optimal solutio Y * was fed back to the upper-level model, ad the upper-level model sought the overall optimal solutio X * withi the possible rage based o the optimal solutio Y * i the lower-level model. Through iteractive iteratio betwee the two levels, both levels i the bi-level programmig were optimized simultaeously. Fially, the approximate global optimal solutio to the bi-level programmig model, deoted as Y, was acquired. Fig. 2 illustrates the procedure of the developed HDPSO algorithm. The specific procedure for solvig a bi-level programmig problem usig a HDPSO algorithm is ow described. Step 1: The decisio variable, populatio X, withi the rage of the decisio variables i the upper-level model was iitialized. Step 2: For each idividual i the iitial upper-level populatio, the lower-level populatio Y * costituted by the optimal solutios i the lower-level programmig model was solved usig a DPSO algorithm; the, the lower-lever populatio Y * was passed to the upper-level model ad used as the basis for the implemetatio of the algorithm i the upper-level DPSO. Step 3: For each idividual i the upper-level populatio, the upper-level programmig model was solved usig a DPSO, ad the upper-level populatio X *, which was costituted by the optimal solutio i the upper-level programmig model correspodig to each idividual i the lower-level populatio, was formed. Step 4: For the populatios i both the upper- ad lower-level models, their fitess degrees were evaluated ad a Cartesia set was formed. The Cartesia, icludig two optimizatio obectives i both levels, should be processed by meas of a multi-obective optimizatio techique. This study employed a Pareto-frotier level measuremet operator for sortig the idividuals accordig to the o-domiated relatioship i a multi-obective optimizatio. Step 5 The HSPSO eded the assessmet process. Oe of these two idexes, amely, whether the outer loop reached the maximum umber of iteratios or whether the populatio s average fitess variatio amplitude

8 1154 Hogya Hao ad Faxi Kog satisfied the preset precisio rage, was used as the algorithm s ed coditios. If oe of the above-described coditios was satisfied, the idividuals i the frotier set costituted the set of optimal solutios. Fially, a idividual i the frotier set was selected accordig to the actual coditios ad adopted as the ultimate solutio. If these two coditios were ot satisfied, the algorithm retured to Step 2 ad repeated. Set the parameters ad variable rages Iitial the decisio variable populatio X i the upper-level model Calculate the optimal solutio populatio Y * based o the acquired decisio variable populatio X i the upper-level model Calculate the optimal solutio populatio X * based o the acquired decisio variable populatio Y * i the upper-level model Costitute a Cartesia set usig the obective fuctio values i bi-level model i accordace with the evaluatio criterio of populatio s fitess, ad the, coduct o-domiated sortig Costitute the ext geeratio of set by reservig the superior idividuals i the populatio Satisfy the ed coditio 5. A experimetal validatio ad aalysis of the results 5.1. A case study Ed the algorithm Figure 2. A flowchart of the HDPSO algorithm Next, by takig the productio order of 20 sets of moulds received by a large-scale mould-maufacturig eterprise as a example, the proposed bi-level programmig model for the optimal allocatio of mould maufacturig resources ad HDPSO algorithm were validated. The maufacturig of each set of moulds icluded 10 maufacturig tasks, deoted as t 1, t 2, t 3, t 4, t 5, t 6, t 7, t 8, t 9 ad t 10; the, each maufacturig task was further decomposed ito several maufacturig sub-tasks. Each maufacturig sub-task had 10 cadidate maufacturig resources, deoted as G 1, G 2, G 3, G 4, G 5, G 6, G 7, G 8, G 9 ad G 10, ad the most appropriate maufacturig resource is selected to fiish the maufacturig task. Moreover, the maufacturig task should be fiished withi the allowable delivery date, with a acceptable implemetatio cost ad completio quality; i additio, the overall cost should be as low as possible while the load rate of maufacturig resources should be as balaced as possible. 10 maufacturig etwork odes i total provided the required maufacturig resources, ad the related iformatio is listed i Tables 1~3. Table 1. Iformatio about the maufacturig task Task Delivery date rage Acceptable cost rage Miimum qualificatio rate (T, with a uit of h) (Q, with a uit of yua) (S) t 1 [80,130] [400,900] 0.85 t 2 [70,100] [800,1000] 0.92 t 3 [240,280] [1400,2000] 0.85 t 4 [120,180] [700,1000] 0.86 t 5 [220,280] [1000,1400] 0.85 t 6 [60,90] [800,1200] 0.80

9 Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model 1155 t 7 [80,1420] [1000,1500] 0.95 t 8 [170,220] [900,1300] 0.80 t 9 [150,190] [800,1200] 0.94 t 10 [60,100] [700,1000] 0.90 Table 2. The relevat data of the cadidate resource odes Task Subtask Resource C T ec C ec Resource T ec ec (RMB Q Task Subtask (RMBy Q Task Subtask Resource C T ec ec (RMBy Q ode (h) ode (h) ode (h) yua) ua) ua) t ,1 t ,1 t , t ,2 t ,2 t , t t 1 t t t 4,3 t ,3 1, t t 7,4 t , , t ,1 t ,1 t , t ,2 t 2 t ,2 t , t 8 t ,3 t ,3 t , t t t , , t 5, t , t 9, t 5, t 3, t t t ,2 3 t ,1 t , t t 6,2 t ,3 t , t t 10, , t t 10 3, t , Table 3. The relevat data of the cadidate resource odes resource T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg T lg C lg The establishmet of the optimizatio model ad implemetatio of the algorithm were compiled o MATLABR2010a. The parameters were iitialized as follows. The weight coefficiets of delivery date, implemetatio cost ad completio quality i the task s satisfactio degree with resource service quality were set as: w 1=0.3, w 2=0.4 ad w 3=0.3 respectively; the umber of particles, m, was set as 30; the legth of the particles i a discrete particle group was set as the umber of tasks; the particle rage was a variable with a rage of 0~1; V Max deotes the maximum velocity ad determies the maximum movig distace of a particle i a loop, which is geerally set as the particle s rage width; the learig factors were set as: C1=C2=2; the maximum umber of iteratios was set as 200; the rated labor hours at each cadidate resource ode was set as 4,000 h ad the sesitivity coefficiet for the implemetatio cost was set as λ= Sice the priciple of multi-obective o-domiated rakig was used i the desig of the proposed HDPSO, the fial optimal allocatio schemes of resources were ot uique ad costituted a frotier set of Pareto optimal solutios. Fig. 3 shows the frotier set of the acquired Pareto optimal solutios usig the proposed HDPSO algorithm, ad Table 4 lists the optimal allocatio results of maufacturig resources i the first order, i which the correspodig optimal solutios i the

10 1156 Hogya Hao ad Faxi Kog upper-level ad lower-level models were ad (U * = ad L * =0.0375) respectively. As show i Fig. 4, the average load rate of resource odes was 61.60%. It ca also be observed from Fig. 4 that the maximum utilizatio rate ad the miimum utilizatio rate of resource odes were 77.5% ad 38.5% respectively, suggestig that the load balace amog these resource odes had improved sigificatly. Figure 3. The frotier set of the Pareto optimal solutio Table 4. The optimal resource allocatio results i the first order Task Subtask Resource ode Task Subtask Resource ode Task Subtask Resource ode t 1,1 4 t 4,1 10 t 7,1 9 t 1 t 1,2 3 t t 4,2 6 t 4 t 7,2 3 t 7 1,3 1 t 4,3 7 t 7,3 6 t 1,4 5 t 4,4 8 t 7,4 8 t 2,1 1 t 5,1 2 t 8,1 4 t 2 t 2,2 7 t 5,2 5 t t 8,2 6 t t 8 2,3 8 5 t 5,3 4 t 8,3 8 t 3,1 1 t 5,4 5 t 8,4 7 t 3,2 10 t 5,5 2 t 9,1 1 t 3 t 3,3 3 t 6,1 5 t 9 t 9,2 4 t 3,4 8 t 6 t 6,2 6 t 9,3 9 t 3,5 9 t 6,3 3 t t 10,1 2 t 10 3,6 3 t 10,2 10 Resource ode load rate 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Resource ode Figure 4. Resource ode load rates usig two differet algorithms Without cosiderig the load balacig hierarchical discrete particle swarm optimizatio 5.2. A compariso betwee the results usig two differet algorithms Fig. 4 compares the resource load rates usig two differet algorithms, amely, the algorithm without the cosideratio of the balace of resource load ad the proposed HDPSO algorithm. Usig the algorithm that did ot take the balace of resource load ito accout, the maximum load rate at the resource ode was 99.0% while the miimum load rate was

11 Allocatio of Mould Maufacturig Resources Uder Maufacturig Network Eviromets based o a Bi-Level Programmig Model %; by cotrast, usig the proposed HDPSO, the miimum load rate ad the miimum load rate were 77.5% ad 38.5% respectively, ad the distributio was more balaced. It should be oted that some researchers have adopted other itelliget optimizatio algorithms to solve bi-level programmig problems but geerally opted for oe optimal solutio. Usig the proposed algorithm, the frotier set of optimal solutios (also kow as the set of optimal solutios) ca be acquired, which ca provide greater flexibility for the related bi-level programmig ad decisio-makig. 6. Coclusios This study first established a bi-level programmig model for describig the optimal allocatio of mould maufacturig resources, ad the employed a HDPSO algorithm for solvig this model. Specifically, the upper-level programmig model described the satisfactio degree of the maufacturig task with the various service requiremets, while the upper-level programmig model described the load balace of maufacturig resources. Fially, through a case study, the feasibility of the established model ad proposed algorithm was validated. Accordig to the validatio results, the algorithm shows a favorable robustess ad high calculatio efficiecy ad thus has high practical applicatio values i solvig problems relatig to the large-scale optimal allocatio of maufacturig resources. However, uder a maufacturig etwork eviromet, the task s satisfactio degree with resource service quality does ot ust iclude delivery date, cost ad quality. Therefore, i future work, we will focus o the multi-obective optimal allocatio model uder a maufacturig etwork eviromet as well as the related optimizatio methods. Ackowledgemets The work is fiacially supported by Key Uiversity Sciece Research Proect of Jiagsu provice of Chia (13KJA460002), Scietific Foudatio of Naig Istitute of Techology (Grat CKJB201305), ad Outstadig Scietific ad Techological Iovatio Team i Colleges ad Uiversities of Jiagsu Provice. Refereces 1. J. Z. Fu, Y. L. Zhag, Study o the optimal dispositio method of resources geared to the eeds of maufacturig grid, Joural of Machie Desig, vol. 23, o. 10, pp , J. Z. Fu, Y. L. Zhag, Resource select io ad optimisatio i maufacturig grid based o geetic algorithm, Joural of Chiese Computer Systems, vol. 28, o. 4, pp , J. Z. Fu, A practical resource-searchig method for maufacturig grid, The Iteratioal Joural of Advaced Maufacturig Techology, vol. 74, pp , J. Z. Fu, J. D. Liu, Research o iterval trasformatio of resource i maufacturig grid ad multi-obective optimizatio selectio method, Joural of Naig Uiversity of Iformatio Sciece ad Techology (Natural Sciece Editio), vol. 5, o. 2, pp , J. Z. Fu, A efficiet resource-searchig method i maufacturig grid, The Iteratioal Joural of Advaced Maufacturig Techology, vol. 66, pp , W. Ha, X. Q. Zhag, A multisatellite task plaig algorithm based o discrete particle swarm, Radio Egieerig, vol. 45, o. 1, pp. 1-5, L. L. Liu, T. Yu, ad Z. B. Shi, Research o QoS -based resource schedulig i maufacturig grid, Computer Itegrated Maufacturig Systems, vol. 11, o. 4, pp , L. L. Liu, Z. S. Shu, Resource allocatio ad etwork evolutio cosiderig ecoomics ad robustess i maufacturig grid, The Iteratioal Joural of Advaced Maufacturig Techology, vol. 57, pp , L. J. Li, Z. B. Huag, ad F. Liu, A heuristic particle swarm optimizatio method for truss structures with discrute variables, Computers ad Structures, vol. 87, pp , C. B. Li, F. M. Zhag, Bi-level programmig locatio strategy of logistics distributio ceter based o hierarchical particle swarm algorithm, Joural of Lazhou Uiversity of Techology, vol. 39, o. 4, pp , X. F. Ma, X. D. Dai, ad S. D. Su, Optimizatio deploymet of etworked maufacturig resources, Computer Itegrated Maufacturig Systems, vol. 10, o. 5, pp , Q.K. Pa, M. Fatih Tasgetire, ad Y. C. Liag, A discrete particle swarm optimizatio algorithm for the o-wait flowshop schedulig problem, Computers ad operatios research, vol. 35, o. 9, pp , S. Q. Sog, C. M. Ye, Research o the maufacturig grid resource schedulig problem based o quatum particle swarm algorithm, Maufacturig Automatio, vol. 30, o. 10, pp , Z. B. Shi, L. L. Liu, Maufacturig grid ad its resource cofiguratio algorithm, Computer Egieerig, vol. 30, o. 5, pp , F. Tao, L. Zhag, ad K. Lu, Research o maufacturig grid resource service optimal-selectio ad compositio framework, Eterprise Iformatio Systems, vol. 6, o. 2, pp , F. Tao, Y. f. Hu, ad D. M. Zhao, Study o resource service match ad search i maufacturig grid system, The Iteratioal Joural of Advaced Maufacturig Techology, vol. 43, pp ,2009

12 1158 Hogya Hao ad Faxi Kog 17. F. Tao, Y. F. Hu, D. M. Zhao, Z. D. Zhou, H. J. Zhag, ad Z. Z. Lei, Study o maufacturig grid resource service QoS modelig ad evaluatio, The Iteratioal Joural of Advaced Maufacturig Techology, vol. 41, pp , C. C. Zhou, G. F. Yi, ad Y. C. Wu, Study o the tactics of maufacturig resource optimal allocatio orieted to maufacturig grid, Joural of Sichua Uiversity (Egieerig Sciece Editio), vol. 41, o. 2, pp , X. B. Zhag, Y.Y. Ni, A iterval programmig model of maufacture resources optimal allocatio i grid, Mathematics i Practice ad Theory, vol. 42, o. 6, pp , Z. G. Zhao, W. Q. Wag, ad S.Y. Huag, Bi-level programmig problem based o improved particle swarm algorithm, Computer Sciece, vol. 40, o. 11A, pp , 2013 Hogya Hao graduated from the School of Mechaical maufacturig ad automatio, Southeast Uiversity, for the degree of Bachelor, Master ad Ph. D. Now she is a associate professor of the School of materials egieerig, Naig Istitute of Techology. Faxi Kog graduated from the School of Material processig egieerig, Southeast Uiversity, for the degree of Bachelor, Master's degree. Now he is a professor of the School of materials egieerig, Naig Istitute of Techology.