An MILP model for planning of batch plants operating in a campaign-mode

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "An MILP model for planning of batch plants operating in a campaign-mode"

Transcription

1 An MILP model for plannng of batch plants operatng n a campagn-mode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN Gabrela Corsano Insttuto de Desarrollo y Dseño CONICET UTN santafe-concet.gov.ar Jorge M. Montagna Insttuto de Desarrollo y Dseño CONICET UTN santafe-concet.gov.ar Abstract A mxed nteger lnear programmng for the detaled producton plannng of multproduct batch plants s proposed n ths work. New tmng decsons are ncorporated to the model takng nto account that an operaton mode based n campagns s adopted. For plants operatng n a regular fashon along a tme horzon, ths operaton mode assures a more effcent producton management. In addton, sequencedependent changeover tmes and dfferent unt szes for parallel unts n each stage are consdered. Gven the plant confguraton and unt szes, the total amount of each product to be produced and the product recpes, the proposed model determnes the number of batches that compose the producton campagn and ther szes, the assgnment and sequencng of batches n each unt, and the tmng of batches n each unt n order to mnmze the campagn cycle tme. The proposed model provdes a useful tool for solvng the optmal campagn plannng of nstalled facltes. Keywords: multproduct batch plants; producton campagn; plannng; schedulng; MILP model. 1 Introducton Multproduct batch plants are characterzed by ther flexblty to manufacture multple products usng the same equpment. These plants consst of a collecton of processng unts where batches of the varous products are produced by executng a set of operatons. These operatons can be characterzed by a processng tme and they do not nvolve both smultaneous feed and removal of products from the unt durng ths processng tme. Unts that perform the same operaton are grouped n a producton stage, and they can operate n parallel mode (n phase or out of phase). In multproduct batch plants, every product follows the same sequence through all the processng stages (Voudours and Grossmann, 1992). Assumng a gven plant,.e., ts confguraton and the unt szes are known, dfferent producton problems can be posed dependng of the contemplated scenaro. In partcular, when products demands can be accurately forecasted durng a relatvely long tme horzon due to a stable context, more effcent management and control of the producton resources can be attaned f the plant s operated n a perodc

2 or cyclc way,.e. n a campagn-mode. In ths case, the campagn conssts of several batches of dfferent products that are gong to be manufactured and the same pattern s repeated at a constant frequency over a tme horzon. Ths campagn-based operaton mode has several advantages, for example, more standardzed producton durng certan perods of tme, easer and proftable operatons decsons, more effcent operaton control, and adequate nventory levels wthout generatng excessve costs and mnmzng the possblty of stock-outs. Under ths context, a cyclc schedulng problem must be addressed. Ths type of schedulng s used for products manufacturng wth relatvely constant demand durng a plannng horzon, whch lead to a more regular producton mode and t s more approprate for a make-to-stock producton polcy. From the computatonal pont of vew, the cyclc schedulng allows reducng the sze of the overall schedulng problem, whch s often ntractable. On the other hand, from the modelng pont of vew, one of the man dfferences between cyclc schedulng based on mxed product campagns (MPCs) and short-term schedulng s the adopted objectve functon. Whle the most of approaches for short-term schedulng dealt wth makespan mnmzaton, tardness or earlness, the most approprate performance measure for the schedulng problem usng MPCs of cyclc repetton s the mnmzaton of the campagn cycle tme (Fumero et al., 2012). Takng n mnd that n a plannng context the campagn wll be repeated over the tme horzon, consecutve campagns have to be overlapped n order to reduce dle tmes between them as much as possble. Accordng to Maravelas (2012), the schedulng problem n the context of batch process nvolves the followng decsons: () selecton and szng of batches to be carred out; () assgnment of batches to process unts; () sequencng of batches on unts; and (v) tmng of batches. Takng nto account the combnatoral nature of the problem, most of the exstng approaches n the process systems engneerng lterature consder a specal case of the problem, where the number and sze of batches s fxed,.e. the lot-szng problem s solved frst and then obtaned batches are used as nputs n the schedulng model. The schedulng problem usng MPCs was scarcely addressed n the lterature. Besdes the paper of Fumero et al. (2012), Brewar and Grossmann (1989) developed slot-based formulatons MILP for schedulng of multproduct batch plants usng producton campagns, consderng dfferent transfer polces (unlmted ntermedate storage, UIS, and zero wat, ZW) and where the number and sze of batches are data problem. They determned the optmal campagn cycle tme, for smple plants ncludng only one unt per processng stage. In Fumero et al. (2011) two MILP models for the smultaneous desgn and schedulng of a mult-stage batch plant are proposed. The parallel unts are consdered dentcal and no changeover tmes are taken nto account. The rest of the papers that menton the use of campagns, do not refer to the determnaton of batches and ts cyclc sequencng, as t s managed n ths work. In ths work, the detaled plannng problem of multstage batch plants wth an operaton based on MPCs s addressed usng a MILP model. It s assumed that the plant manager must produce known demands usng a cyclc campagn durng a tme horzon. Nondentcal parallel unts, ZW transfer polcy and sequence-dependent changeover tmes are consdered. Gven the plant confguraton and unt szes, the total amount of each product to be produced n the campagn and the product recpes, the approach determnes the number of batches that compose the producton campagn and ther szes, the batches assgnment to unts, the sequencng of batches n each unt for each stage, and the ntal and fnal tmes of the batches processed n each unt n order to mnmze the campagn cycle tme. Wth the am of reducng the combnatoral complexty assocated to the schedulng decsons, addtonal constrants are consdered n order to elmnate equvalent symmetrc solutons. Then, the schedulng approach through MPCs consderng sequence-dependent changeover tmes for multstage batch plants wth nondentcal parallel unts s effcently solved. 2 Problem descrpton

3 The problem addressed n ths artcle deals wth a multproduct batch plant where J denotes the set of processng stages that compose the plant and K the set of all unts n the plant. K j represents the set of nondentcal parallel batch unts that operate out-of-phase n stage j, so K = K 1 K 2 K J. A set I of products must be manufactured n the plant followng the same sequence of stages. The total amount requred of each product n the campagn, Q ( I), whch allows mantanng adequate stocks levels takng nto account the estmated demands, s a model parameter. Q can be fulflled wth one or more batches, therefore an ndex b s ntroduced to denote the bth batch requred to meet producton of the correspondng product. In each stage, there are not restrctons about parallel unt szes and, therefore, dfferent unt szes are admtted. Then, V k s used to denote the sze of unt k. The processng tme of each batch of product n unt k, t k, and the sze factor SF j that denotes the requred capacty of unts n stage j to produce one mass unt of fnal product, are problem data. Consderng the demand of product, the non-dentcal parallel unt szes for each stage, the equpment utlzaton mnmum rate for product at each unt, denoted by α k, and the sze factors of product n each stage, the mnmum and maxmum numbers of batches requred to fulfll the demand of product can be calculated n order to ensure soluton optmalty. Thus, the mnmum and maxmum numbers of batches of product for the campagn are calculated, respectvely, as followng: LOW Q UP Q NBC = max and NBC = mn B B max mn where B = mn max and B = max mn α k are the maxmum and mnmum j J k K j SF j J k K j j SFj feasble batch szes for product. The upper bound for the number of batches of each product n the UP NBC campagn allows to propose a set of generc batches assocated to that product, IB, where IB =. Intermedate storage tanks are not allowed. Therefore, takng nto account the confguraton of the plant, there s no batch splttng or mxng,.e. each batch s treated as a dscrete entty throughout the whole process. It s assumed that a batch cannot wat n a unt after fnshng ts processng. Therefore, the ZW transfer polcy between stages s adopted,.e., after beng processed n stage j, a batch b s mmedately transferred to the next stage j+1. Besdes, batch transfer tmes between unts are assumed very small compared to process operaton tmes and, consequently, they are ncluded n the processng tmes. Sequence-dependent changeover tmes, c k, are consdered between consecutve batches processed n the same unt k, even of the same product. Ths transton tme corresponds to the preparaton or cleanng of the equpment to perform the followng batch processng. It s necessary for varous reasons: ensure products qualty, mantan the equpment, safety reasons, etc. For schedulng decsons, an asynchronous slot-based contnuous-tme representaton has been used. The slots correspond to tme ntervals of varable length where batches wll be assgned. In each slot l of a specfc unt k at most one batch b of product can be processed and, f no product s assgned to slot l, ts length wll be zero. The number of slots that must be postulated for unt k of stage j, denoted by L kj, can be approxmated consderng the estmaton on the maxmum number of batches of each product at the campagn. Then, the number of slots postulated for all unts of each stage s the same and t s gven by: UP L NBC k, j = I Although ths value s an overestmaton, a major approxmaton cannot be proposed takng nto account that the parallel unts are dfferent and, on the other hand, the number and szes of batches to be scheduled are optmzaton varables, unlke the most of schedulng approaches presented n the lterature where they are consdered as parameters. However, the lower bound on the number of batches of product at the

4 campagn, NBC LOW, strongly reduces the number of possble combnatons and consequently mproves the computatonal performance of the model. As prevously stated, the problem conssts of solvng smultaneously two decson levels often addressed sequentally. Through a holstc approach, the selecton and szng of batches of each product, the assgnment of batches to unts n each stage, the producton sequence of assgned batches n each unt and ntal and fnal processng tmes for batches that compose the campagn n each processng unt are jontly determned. 3 Mathematcal formulaton 3.1 Batches selecton and szng constrants The number of batches of product that must be manufactured n the campagn s a model varable. Then, a bnary varable z b s ntroduced, whch takes value 1 f batch b of product s selected to satsfy the demand requrements of that product and 0 otherwse. Let B b be the sze of batch b of product and Q the demand of product that must be fulflled, then: Q B I (1) = b IB b Takng nto account that the sze of unt k denoted by V k and the sze factor SF j are model parameters, f batch b of product s processed n unt k of stage j the followng nequaltes lmt the sze B b of batch b between the mnmum and maxmum processng capactes of unt k: α k Bb I,b IB,k {unts of stage j used to process batch b} (2) SF SF j j where α k s the mnmum flled rate requred to process product n unt k. Due to the unts selected to process the batches of each product are optmzaton varables and ther szes are dfferent, Eq. (2) must be expressed through a varable that ndcates ths selecton, as t wll see later. Besdes, wthout loss the generalty and n order to reduce the number of alternatve solutons, the selecton of batches of a same product as well as the assgned szes to them are made n ascendng and descendng numercal order, respectvely, that s: zb+ 1 zb I,b IB,b + 1 IB (3) Bb+ 1 Bb I,b IB,b + 1 IB (4) 3.2 Assgnment and Sequencng constrants Selected batches must be assgned, n each stage, to specfc slots n the unts. Then, the bnary varable Y bkl s ntroduced, whch takes value 1 f batch b s assgned to slot l n unt k and 0 otherwse. Although ths varable s enough for formulatng the schedulng problem, the bnary varable X kl, whch specfes the slots set utlzed n unt k for processng batches, wll be also used n order to reduce the search space and, therefore, to mprove the computatonal performance. Logcal relatons can be defned among bnary varables z b, X kl and Y bkl. In fact, f slot l of unt k s not utlzed, then none of the proposed batches s processed n t. Moreover, f slot l of unt k s utlzed, then only one of the proposed batches s processed n t. Then, the followng constrant s mposed: Y = X j J,k K, 1 l L (5) I b IB bkl kl j On the other hand, f batch b of product s selected (.e. z b = 1), then ths batch s processed, n each stage j, n only one slot of some of the avalable unts at the stage. Ths condton s guaranteed by:

5 Y bkl k K 1 l L j = z b j J, I,b IB Wthout loss of generalty and n order to reduce the search space, t s assumed that slots of each unt are consecutvely used n ascendng numercal order. Hence, the slots of zero length take place at the end of each unt. Eq. (7) establshes that for each unt k, slot l+1 s only used f slot l has been already allocated: X kl X kl+ 1, j J,k K j, 1 l L (7) Fnally, varable Y bkl allow correctly expressng the nequaltes posed n (2) as: α k Ybkl Bb I,b I, 1 l L (8) SF B b j SF j + M (1 Y ) I,b IB 1 bkl (9) 1 l L where scalar M 1 s a suffcently large number Tmng constrants Nonnegatve contnuous varables, TI kl and TF kl, are used to represent the ntal and fnal processng tmes, respectvely, of the proposed slots n each unt k. When slot l s not the last slot used n unt k of stage j for processng one batch, that s, f Y b kl+1 take value 1 for some b, fnal processng tme TF kl of slot l n unt k s constraned by: TFkl TI kl + (tk + c'k )Y bkl Yb'kl + 1 j J,k K j, 1 l < L (10) = I ' I b IB b' IB ' b b' A nonnegatve varable YY blb l k s defned to elmnate the blnear products, whch takes value 1 f Y bkl = 1 and Y b' kl + 1 = 1, and 0 otherwse, so (10) s represent usng Bg-M expressons: TFkl TIkl ( tk + c' k ) YY blb' l + 1 k M 2( X kl + 1 ) j J,k K j, 1 l < L (11a) 1 I ' I b IB b' IB' b b' 1 TFkl + TIkl + ( tk + c' k ) YY blb' l + 1 k M 2( X kl + 1 1) j J,k K j, l < L (11b) I ' I b IB b' IB' b b' On the other hand, when the sequence of slots used n unt k s 1, 2,... l,.e. slot l s the last slot used at unt k of stage j to process some batch, takng nto account that the campagn can be cyclcal repeated over a tme horzon, the fnal processng tme TF kl s calculated consderng the changeover tme requred for processng the batch assgned to slot 1 n unt k of stage j. Constrants analogous to (11a) and (11b) are posed for ths case. Constrants to avod the overlappng between the processng tmes of dfferent slots n a unt as well as to match the ntal tmes of empty slots wth the fnal tme of the prevous slot are added to the formulaton. In order to assure ZW transfer polcy, constrants of Bg-M type are ncluded, dependng f slot l s or s not the last slot used at unt k for processng one batch. Due to space reasons, ths set of constrants s not provded n ths manuscrpt, but nterested readers can request t to authors. Fnally, takng nto account that slots of each unt are used n ascendng numercal order, the expresson for the cycle tme of the campagn, CT, s gven by: CT TFkL TI k1, j J,k K j (12) 3.4. Objectve functon The problem goal s to mnmze the cycle tme of the producton campagn that fulflls the demands requrements, subject to prevous constrants. (6)

6 4 Example The consdered batch plant conssts of three stages wth nondentcal parallel unts wth known szes that operate out-of-phase, as s llustrated n Fgure 1. Avalable unts at each stage are denoted by the sets: K 1 = {1}, K 2 = {2, 3}, and K 3 = {4, 5}, respectvely. Products A, B, and C have to be processed through all stages before beng converted nto fnal products. The requred amounts n the campagn are Q A = 10500, Q B = 6000 and Q C = Data on processng tmes and sze factors of each product are shown n Table 1, whle the sequence-dependent changeover tmes are gven n Table 2. Consderng the non-dentcal parallel unt szes at each stage, the sze factors for each product n each stage and assumng that the equpment utlzaton mnmum rate s 0.50 for all products and equpment tems, the mnmum feasble batch szes for products A, B and C are: B mn = 0. 5max 5714 kg, 5000 kg,5000 kg = 2857 { } kg { 6666 kg, 4285kg,5555kg} 3333kg { 5714 kg, 4615 kg, 4545 kg} 2857 kg A, B mn B = 0. 5max =, B mn C = 0. 5max =. Stage 1 Stage 2 Stage L 4200 L 3000 L 3000 L 2500 L Fgure 1. Plant structure Table 1. Processng tmes and sze factors of products Processng tme: t k (h) Sze factor: SF j (L/kg) Product Stage 1 Stage 2 Stage 3 Stage 1 Stage 2 Stage k = 1 k = 2, 3 k = 4, 5 A B C Table 2. Sequence-dependent changeover tmes Product Sequence-dependent changeover tme: c k (h) Stage 1 Stage 2 Stage 3 k = 1 k = 2, 3 k = 4, 5 A B C A B C A B C A B C

7 Then, consderng the campagn demands for all products, the maxmum number of batches of each product at the campagn s four, two and four for products A, B and C, respectvely. Thus, the sets of proposed batches are {b 1, b 2, b 3, b 4 }, {b 5, b 6 }, and {b 7, b 8, b 9, b 10 } for products A, B and C, respectvely, and consequently a total of ten batches must be postulated to guarantee the global optmalty of the soluton. Also, the maxmum feasble batch szes for all products allow determnng the mnmum number of batches of every product at the campagn. In ths case, the maxmum feasble batch szes for all products are: B max A B max B = mn = mn { 5714 kg, 7000 kg, 6000 kg} = 5714 kg { 6666 kg, 6000 kg, 6666 kg} = 6000 kg { 5714 kg, 6461 kg, 5454 kg} = 5454 kg B max C = mn then, the requred mnmum number of batches for products A and C s two, whle for product B s one. The model under these assumptons comprses constrants, 9167 contnuous varables and 555 bnary varables. It was mplemented and solved usng GAMS, va CPLEX 12.5 solver, n CPU seconds wth a 0% of optmalty gap. The optmal campagn cycle tme s equal to 70.4 hours and t nvolves two batches of product A (b 1, b 2 ), one of B (b 5 ), and two of C (b 7, b8),.e. the demands of all products are fulfll wth the mnmum number of batches. The optmal producton sequence obtaned n each batch unt for the dfferent stages, consderng sequence-dependent changeover tmes, s llustrated n the Gantt chart of Fgure 2. Takng nto account that the optmal campagn s cyclcally repeated over a tme horzon, the changeover tmes between products processed n the last and frst slot of each unt must be ncluded n the optmzaton n order to acheve the accurate overlap of successve campagns. For ths example, as t can be seen from Fgure 2, changeover tmes between pars of campagns are: c AC1 = 0.3 h for unt of stage 1; c AC2 = c AC3 = 0.4 h for unts of stage 2; and c AC4 = c AC5 = 0.6 h for unts of stage 3. Unts Campagn cycle tme = 70.4 h Stage 1 1 b7 b5 b8 b1 b2 Stage b7 b5 b8 b1 b2 Stage b7 b5 b8 b1 b Product A Product B Product C Changeovers tmes Tme (h) Fgure 2. Gantt chart of the producton campagn Batches b 1 and b 2 satsfy the total requred demand of product A wth szes of 5500 kg and 5000 kg, respectvely; batch b 5 wth sze equal to 6000 kg s only selected to accomplsh the campagn demand of product B; whle batches b 7 and b 8 are requred to acheve the producton of C wth szes equal to 4955 kg and 4545 kg, respectvely. The capactes used n each unt of the dfferent stages for processng the selected batches are resumed n Table 3. The batches that reach the maxmum capactes are hghlghted n boxes shaded n gray. Batch b 2 of product A s processed n unts 1, 3 and 5 and ts sze s the maxmum possble to be processed n unts 3 and 5 of stages 2 and 3, respectvely. Then, batch b 1 fulflls the requred amount of that product occupyng approxmately 96%, 79% and 92% of the capacty of unts 1, 2 and 4, respectvely. Batch b 5 of product B s processed n unts 1, 2 and 4 and ts sze s the maxmum

8 possble to be processed n unt 2 of stage 2. On the other hand, two batches of product C are processed for meetng ts demand. Batch b 8 s processed n unts 1, 3 and 5 usng 80%, 98.5% and 100% of ther capactes, respectvely; whle batch b 7 fulflls the requred amount of that product n the campagn. Table 3. Capactes used n each unt of each stage Stage 1 Stage 2 Stage 3 Product Batch k = 1 k = 2 k = 3 k = 4 k = 5 A b b B b C b b Conclusons In ths work, the optmal producton plannng of multstage batch plants wth nondentcal parallel unts that operate n campagn-mode s faced. Schedulng s modeled accordng to campagn-based operaton mode n such way that the campagn cycle tme mnmzaton s an approprate optmzaton crteron. Sequence-dependent changeover tmes are consdered for each ordered par of products n each unt of the dfferent stages. Takng nto account the complexty of the smultaneous nvolved decsons, some addtonal constrants that elmnate equvalent symmetrc solutons mantanng the model generalty are consdered, n order to reduce the search space and therefore mprove the computatonal performance. Also, varous equatons are reformulated n order to keep the problem lnear and assure the global optmalty of the soluton. Through the example the capabltes of the proposed formulaton are shown. Wth the proposed formulaton, an nterestng problem has been solved. Many tmes, n made-to-stock contexts, the campagn-based operaton mode s an approprate alternatve that allows takng advantage of the avalable resources wth an ordered producton management. The proposed model smultaneously solves lot-szng and schedulng problems n reasonable computng tme. Thus, ths approach can be appled n real producton systems that operate n campagn-mode takng nto account the assumed suppostons as far as dfferent unt szes, changeovers, etc. References 1. C. T. Maravelas. General framework and modelng approach classfcaton for chemcal producton schedulng. AIChE Journal 2012, 58(6): , D. Brewar and I. E. Grossmann. Incorporatng schedulng n the optmal desgn of multproduct batch plants. Computers and Chemcal Engneerng, 13, , V.T. Voudours, I.E. Grossmann. Mxed-Integer Lnear Programmng Reformulatons for Batch Process Desgn wth Dscrete Equpment Szes. Ind. Eng. Chem. Res. 1992,31, Y. Fumero, G. Corsano, J. M. Montagna. Schedulng of multstage multproduct batch plants operatng n a campagn-mode. Industral Engneerng and Chemcal Research, 5: , Y. Fumero, G. Corsano, J. M. Montagna. Detaled Desgn of Multproduct Batch Plants Consderng Prodcton Schedulng. Industral Engneerng and Chemcal Research, 50 (10), , 2011.

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa

More information

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)

More information

2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet

2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet 2008/8 An ntegrated model for warehouse and nventory plannng Géraldne Strack and Yves Pochet CORE Voe du Roman Pays 34 B-1348 Louvan-la-Neuve, Belgum. Tel (32 10) 47 43 04 Fax (32 10) 47 43 01 E-mal: corestat-lbrary@uclouvan.be

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

Optimization of network mesh topologies and link capacities for congestion relief

Optimization of network mesh topologies and link capacities for congestion relief Optmzaton of networ mesh topologes and ln capactes for congeston relef D. de Vllers * J.M. Hattngh School of Computer-, Statstcal- and Mathematcal Scences Potchefstroom Unversty for CHE * E-mal: rwddv@pu.ac.za

More information

1 Approximation Algorithms

1 Approximation Algorithms CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons

More information

The Greedy Method. Introduction. 0/1 Knapsack Problem

The Greedy Method. Introduction. 0/1 Knapsack Problem The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING

APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING Journal Journal of Chemcal of Chemcal Technology and and Metallurgy, 50, 6, 50, 2015, 6, 2015 638-643 APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING Abdrakhman

More information

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION

More information

On the Optimal Control of a Cascade of Hydro-Electric Power Stations

On the Optimal Control of a Cascade of Hydro-Electric Power Stations On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;

More information

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,

More information

Method for Production Planning and Inventory Control in Oil

Method for Production Planning and Inventory Control in Oil Memors of the Faculty of Engneerng, Okayama Unversty, Vol.41, pp.20-30, January, 2007 Method for Producton Plannng and Inventory Control n Ol Refnery TakujImamura,MasamKonshandJunIma Dvson of Electronc

More information

Activity Scheduling for Cost-Time Investment Optimization in Project Management

Activity Scheduling for Cost-Time Investment Optimization in Project Management PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta- San Sebastán, September 8 th -10 th 010 Actvty Schedulng

More information

SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.

SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976-76-10-00

More information

A method for a robust optimization of joint product and supply chain design

A method for a robust optimization of joint product and supply chain design DOI 10.1007/s10845-014-0908-5 A method for a robust optmzaton of jont product and supply chan desgn Bertrand Baud-Lavgne Samuel Bassetto Bruno Agard Receved: 10 September 2013 / Accepted: 21 March 2014

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告

行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告 行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告 畫 類 別 : 個 別 型 計 畫 半 導 體 產 業 大 型 廠 房 之 設 施 規 劃 計 畫 編 號 :NSC 96-2628-E-009-026-MY3 執 行 期 間 : 2007 年 8 月 1 日 至 2010 年 7 月 31 日 計 畫 主 持 人 : 巫 木 誠 共 同

More information

Stochastic Inventory Management for Tactical Process Planning under Uncertainties: MINLP Models and Algorithms

Stochastic Inventory Management for Tactical Process Planning under Uncertainties: MINLP Models and Algorithms Stochastc Inventory Management for Tactcal Process Plannng under Uncertantes: MINLP Models and Algorthms Fengq You, Ignaco E. Grossmann Department of Chemcal Engneerng, Carnege Mellon Unversty Pttsburgh,

More information

Preventive Maintenance and Replacement Scheduling: Models and Algorithms

Preventive Maintenance and Replacement Scheduling: Models and Algorithms Preventve Mantenance and Replacement Schedulng: Models and Algorthms By Kamran S. Moghaddam B.S. Unversty of Tehran 200 M.S. Tehran Polytechnc 2003 A Dssertaton Proposal Submtted to the Faculty of the

More information

AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE

AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE Yu-L Huang Industral Engneerng Department New Mexco State Unversty Las Cruces, New Mexco 88003, U.S.A. Abstract Patent

More information

Omega 39 (2011) 313 322. Contents lists available at ScienceDirect. Omega. journal homepage: www.elsevier.com/locate/omega

Omega 39 (2011) 313 322. Contents lists available at ScienceDirect. Omega. journal homepage: www.elsevier.com/locate/omega Omega 39 (2011) 313 322 Contents lsts avalable at ScenceDrect Omega journal homepage: www.elsever.com/locate/omega Supply chan confguraton for dffuson of new products: An ntegrated optmzaton approach Mehd

More information

Joint Scheduling of Processing and Shuffle Phases in MapReduce Systems

Joint Scheduling of Processing and Shuffle Phases in MapReduce Systems Jont Schedulng of Processng and Shuffle Phases n MapReduce Systems Fangfe Chen, Mural Kodalam, T. V. Lakshman Department of Computer Scence and Engneerng, The Penn State Unversty Bell Laboratores, Alcatel-Lucent

More information

Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT

Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the

More information

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure

More information

Ants Can Schedule Software Projects

Ants Can Schedule Software Projects Ants Can Schedule Software Proects Broderck Crawford 1,2, Rcardo Soto 1,3, Frankln Johnson 4, and Erc Monfroy 5 1 Pontfca Unversdad Católca de Valparaíso, Chle FrstName.Name@ucv.cl 2 Unversdad Fns Terrae,

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem

A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem Journal o Economc and Socal Research 5 (2), -2 A Bnary Partcle Swarm Optmzaton Algorthm or Lot Szng Problem M. Fath Taşgetren & Yun-Cha Lang Abstract. Ths paper presents a bnary partcle swarm optmzaton

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

Fault tolerance in cloud technologies presented as a service

Fault tolerance in cloud technologies presented as a service Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance

More information

Enabling P2P One-view Multi-party Video Conferencing

Enabling P2P One-view Multi-party Video Conferencing Enablng P2P One-vew Mult-party Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract Mult-Party Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P

More information

Simulation and optimization of supply chains: alternative or complementary approaches?

Simulation and optimization of supply chains: alternative or complementary approaches? Smulaton and optmzaton of supply chans: alternatve or complementary approaches? Chrstan Almeder Margaretha Preusser Rchard F. Hartl Orgnally publshed n: OR Spectrum (2009) 31:95 119 DOI 10.1007/s00291-007-0118-z

More information

Period and Deadline Selection for Schedulability in Real-Time Systems

Period and Deadline Selection for Schedulability in Real-Time Systems Perod and Deadlne Selecton for Schedulablty n Real-Tme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng

More information

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Artcle ID 867836 pages http://dxdoorg/055/204/867836 Research Artcle Enhanced Two-Step Method va Relaxed Order of α-satsfactory Degrees for Fuzzy

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

Heuristic Static Load-Balancing Algorithm Applied to CESM

Heuristic Static Load-Balancing Algorithm Applied to CESM Heurstc Statc Load-Balancng Algorthm Appled to CESM 1 Yur Alexeev, 1 Sher Mckelson, 1 Sven Leyffer, 1 Robert Jacob, 2 Anthony Crag 1 Argonne Natonal Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439,

More information

Software project management with GAs

Software project management with GAs Informaton Scences 177 (27) 238 241 www.elsever.com/locate/ns Software project management wth GAs Enrque Alba *, J. Francsco Chcano Unversty of Málaga, Grupo GISUM, Departamento de Lenguajes y Cencas de

More information

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel

More information

Nathalie Perrier Bruno Agard Pierre Baptiste Jean-Marc Frayret André Langevin Robert Pellerin Diane Riopel Martin Trépanier.

Nathalie Perrier Bruno Agard Pierre Baptiste Jean-Marc Frayret André Langevin Robert Pellerin Diane Riopel Martin Trépanier. A Survey of Models and Algorthms for Emergency Response Logstcs n Electrc Dstrbuton Systems - Part I: Relablty Plannng wth Fault Consderatons Nathale Perrer Bruno Agard Perre Baptste Jean-Marc Frayret

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

Optimal Joint Replenishment, Delivery and Inventory Management Policies for Perishable Products

Optimal Joint Replenishment, Delivery and Inventory Management Policies for Perishable Products Optmal Jont Replenshment, Delvery and Inventory Management Polces for Pershable Products Leandro C. Coelho Glbert Laporte May 2013 CIRRELT-2013-32 Bureaux de Montréal : Bureaux de Québec : Unversté de

More information

An Integrated Approach for Maintenance and Delivery Scheduling in Military Supply Chains

An Integrated Approach for Maintenance and Delivery Scheduling in Military Supply Chains An Integrated Approach for Mantenance and Delvery Schedulng n Mltary Supply Chans Dmtry Tsadkovch 1*, Eugene Levner 2, Hanan Tell 2 and Frank Werner 3 2 1 Bar Ilan Unversty, Department of Management, Ramat

More information

Scatter search approach for solving a home care nurses routing and scheduling problem

Scatter search approach for solving a home care nurses routing and scheduling problem Scatter search approach for solvng a home care nurses routng and schedulng problem Bouazza Elbenan 1, Jacques A. Ferland 2 and Vvane Gascon 3* 1 Département de mathématque et nformatque, Faculté des scences,

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

Multi-Period Resource Allocation for Estimating Project Costs in Competitive Bidding

Multi-Period Resource Allocation for Estimating Project Costs in Competitive Bidding Department of Industral Engneerng and Management Techncall Report No. 2014-6 Mult-Perod Resource Allocaton for Estmatng Project Costs n Compettve dng Yuch Takano, Nobuak Ish, and Masaak Murak September,

More information

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedo-cho

More information

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson

More information

NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY

NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY A Dssertaton Presented to the Faculty of the Graduate School of Cornell Unversty In Partal Fulfllment of the Requrements

More information

Alternate Approximation of Concave Cost Functions for

Alternate Approximation of Concave Cost Functions for Alternate Approxmaton of Concave Cost Functons for Process Desgn and Supply Chan Optmzaton Problems Dego C. Cafaro * and Ignaco E. Grossmann INTEC (UNL CONICET), Güemes 3450, 3000 Santa Fe, ARGENTINA Department

More information

Robust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School

Robust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation of Deutsch's Algorithm Using Mathcad Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

More information

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network *

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network * JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819-840 (2008) Data Broadcast on a Mult-System Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,

More information

A multi-start local search heuristic for ship scheduling a computational study

A multi-start local search heuristic for ship scheduling a computational study Computers & Operatons Research 34 (2007) 900 917 www.elsever.com/locate/cor A mult-start local search heurstc for shp schedulng a computatonal study Ger BrZnmo a,b,, Marelle Chrstansen b, Kjetl Fagerholt

More information

Solutions to the exam in SF2862, June 2009

Solutions to the exam in SF2862, June 2009 Solutons to the exam n SF86, June 009 Exercse 1. Ths s a determnstc perodc-revew nventory model. Let n = the number of consdered wees,.e. n = 4 n ths exercse, and r = the demand at wee,.e. r 1 = r = r

More information

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo.

RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo. ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) yaoq.feng@yahoo.com Abstract

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.

More information

Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network

Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network Dynamc Constraned Economc/Emsson Dspatch Schedulng Usng Neural Network Fard BENHAMIDA 1, Rachd BELHACHEM 1 1 Department of Electrcal Engneerng, IRECOM Laboratory, Unversty of Djllal Labes, 220 00, Sd Bel

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

Research Note APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES * Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77-866 Logcal Development Of Vogel s Approxmaton Method (LD- An Approach To Fnd Basc Feasble Soluton Of Transportaton

More information

A Simple Approach to Clustering in Excel

A Simple Approach to Clustering in Excel A Smple Approach to Clusterng n Excel Aravnd H Center for Computatonal Engneerng and Networng Amrta Vshwa Vdyapeetham, Combatore, Inda C Rajgopal Center for Computatonal Engneerng and Networng Amrta Vshwa

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Extending Probabilistic Dynamic Epistemic Logic

Extending Probabilistic Dynamic Epistemic Logic Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set

More information

Research Article A Time Scheduling Model of Logistics Service Supply Chain with Mass Customized Logistics Service

Research Article A Time Scheduling Model of Logistics Service Supply Chain with Mass Customized Logistics Service Hndaw Publshng Corporaton Dscrete Dynamcs n Nature and Socety Volume 01, Artcle ID 48978, 18 pages do:10.1155/01/48978 Research Artcle A Tme Schedulng Model of Logstcs Servce Supply Chan wth Mass Customzed

More information

An efficient constraint handling methodology for multi-objective evolutionary algorithms

An efficient constraint handling methodology for multi-objective evolutionary algorithms Rev. Fac. Ing. Unv. Antoqua N. 49. pp. 141-150. Septembre, 009 An effcent constrant handlng methodology for mult-objectve evolutonary algorthms Una metodología efcente para manejo de restrccones en algortmos

More information

Efficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ

Efficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ Effcent Strpng Technques for Varable Bt Rate Contnuous Meda Fle Servers æ Prashant J. Shenoy Harrck M. Vn Department of Computer Scence, Department of Computer Scences, Unversty of Massachusetts at Amherst

More information

A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION

A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION A GENERAL APPROACH FOR SECURITY MONITORING AND PREVENTIVE CONTROL OF NETWORKS WITH LARGE WIND POWER PRODUCTION Helena Vasconcelos INESC Porto hvasconcelos@nescportopt J N Fdalgo INESC Porto and FEUP jfdalgo@nescportopt

More information

Dynamic Resource Allocation and Power Management in Virtualized Data Centers

Dynamic Resource Allocation and Power Management in Virtualized Data Centers Dynamc Resource Allocaton and Power Management n Vrtualzed Data Centers Rahul Urgaonkar, Ulas C. Kozat, Ken Igarash, Mchael J. Neely urgaonka@usc.edu, {kozat, garash}@docomolabs-usa.com, mjneely@usc.edu

More information

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo

More information

greatest common divisor

greatest common divisor 4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no

More information

Credit Limit Optimization (CLO) for Credit Cards

Credit Limit Optimization (CLO) for Credit Cards Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt

More information

An ILP Formulation for Task Mapping and Scheduling on Multi-core Architectures

An ILP Formulation for Task Mapping and Scheduling on Multi-core Architectures An ILP Formulaton for Task Mappng and Schedulng on Mult-core Archtectures Yng Y, We Han, Xn Zhao, Ahmet T. Erdogan and Tughrul Arslan Unversty of Ednburgh, The Kng's Buldngs, Mayfeld Road, Ednburgh, EH9

More information

Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to

Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to Vol. 45, No. 3, August 2011, pp. 435 449 ssn 0041-1655 essn 1526-5447 11 4503 0435 do 10.1287/trsc.1100.0346 2011 INFORMS Tme Slot Management n Attended Home Delvery Nels Agatz Department of Decson and

More information

Fragility Based Rehabilitation Decision Analysis

Fragility Based Rehabilitation Decision Analysis .171. Fraglty Based Rehabltaton Decson Analyss Cagdas Kafal Graduate Student, School of Cvl and Envronmental Engneerng, Cornell Unversty Research Supervsor: rcea Grgoru, Professor Summary A method s presented

More information

Considering manufacturing cost and scheduling performance on a CNC turning machine

Considering manufacturing cost and scheduling performance on a CNC turning machine European Journal of Operatonal Research 77 (2007) 325 343 Producton, Manufacturng and Logstcs Consderng manufacturng cost and schedulng performance on a CNC turnng machne Snan Gurel, M Selm Akturk * Department

More information

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,

More information

Rate Monotonic (RM) Disadvantages of cyclic. TDDB47 Real Time Systems. Lecture 2: RM & EDF. Priority-based scheduling. States of a process

Rate Monotonic (RM) Disadvantages of cyclic. TDDB47 Real Time Systems. Lecture 2: RM & EDF. Priority-based scheduling. States of a process Dsadvantages of cyclc TDDB47 Real Tme Systems Manual scheduler constructon Cannot deal wth any runtme changes What happens f we add a task to the set? Real-Tme Systems Laboratory Department of Computer

More information

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and POLYSA: A Polynomal Algorthm for Non-bnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n

More information

A Performance Analysis of View Maintenance Techniques for Data Warehouses

A Performance Analysis of View Maintenance Techniques for Data Warehouses A Performance Analyss of Vew Mantenance Technques for Data Warehouses Xng Wang Dell Computer Corporaton Round Roc, Texas Le Gruenwald The nversty of Olahoma School of Computer Scence orman, OK 739 Guangtao

More information

Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Conversion between the vector and raster data structures using Fuzzy Geographical Entities Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,

More information

GENETIC ALGORITHM FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY

GENETIC ALGORITHM FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY Int. J. Mech. Eng. & Rob. Res. 03 Fady Safwat et al., 03 Research Paper ISS 78 049 www.jmerr.com Vol., o. 3, July 03 03 IJMERR. All Rghts Reserved GEETIC ALGORITHM FOR PROJECT SCHEDULIG AD RESOURCE ALLOCATIO

More information

INSTITUT FÜR INFORMATIK

INSTITUT FÜR INFORMATIK INSTITUT FÜR INFORMATIK Schedulng jobs on unform processors revsted Klaus Jansen Chrstna Robene Bercht Nr. 1109 November 2011 ISSN 2192-6247 CHRISTIAN-ALBRECHTS-UNIVERSITÄT ZU KIEL Insttut für Informat

More information

Optimization under uncertainty. Antonio J. Conejo The Ohio State University 2014

Optimization under uncertainty. Antonio J. Conejo The Ohio State University 2014 Optmzaton under uncertant Antono J. Conejo The Oho State Unverst 2014 Contents Stochastc programmng (SP) Robust optmzaton (RO) Power sstem applcatons A. J. Conejo The Oho State Unverst 2 Stochastc Programmng

More information

The Stochastic Guaranteed Service Model with Recourse for Multi-Echelon Warehouse Management

The Stochastic Guaranteed Service Model with Recourse for Multi-Echelon Warehouse Management The Stochastc Guaranteed Servce Model wth Recourse for Mult-Echelon Warehouse Management Jörg Rambau, Konrad Schade 1 Lehrstuhl für Wrtschaftsmathematk Unverstät Bayreuth Bayreuth, Germany Abstract The

More information

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000 Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from

More information

Conferencing protocols and Petri net analysis

Conferencing protocols and Petri net analysis Conferencng protocols and Petr net analyss E. ANTONIDAKIS Department of Electroncs, Technologcal Educatonal Insttute of Crete, GREECE ena@chana.tecrete.gr Abstract: Durng a computer conference, users desre

More information

Study on Model of Risks Assessment of Standard Operation in Rural Power Network

Study on Model of Risks Assessment of Standard Operation in Rural Power Network Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,

More information

J. Parallel Distrib. Comput.

J. Parallel Distrib. Comput. J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n

More information

Lecture 3: Force of Interest, Real Interest Rate, Annuity

Lecture 3: Force of Interest, Real Interest Rate, Annuity Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and

More information

Solving Factored MDPs with Continuous and Discrete Variables

Solving Factored MDPs with Continuous and Discrete Variables Solvng Factored MPs wth Contnuous and screte Varables Carlos Guestrn Berkeley Research Center Intel Corporaton Mlos Hauskrecht epartment of Computer Scence Unversty of Pttsburgh Branslav Kveton Intellgent

More information

Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis

Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis OPERATIONS RESEARCH Vol. 54, No. 5, September October 6, pp. 94 93 ssn 3-364X essn 56-5463 6 545 94 nforms do.87/opre.6.35 6 INFORMS Revenue Management for a Multclass Sngle-Server Queue va a Flud Model

More information

Optimal Map Reduce Job Capacity Allocation in Cloud Systems

Optimal Map Reduce Job Capacity Allocation in Cloud Systems Optmal Map Reduce Job Capacty Allocaton n Cloud Systems Marzeh Malemajd Sharf Unversty of Technology, Iran malemajd@ce.sharf.edu Danlo Ardagna Poltecnco d Mlano, Italy danlo.ardagna@polm.t Mchele Cavotta

More information

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,

More information

Can Auto Liability Insurance Purchases Signal Risk Attitude?

Can Auto Liability Insurance Purchases Signal Risk Attitude? Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

Retailers must constantly strive for excellence in operations; extremely narrow profit margins

Retailers must constantly strive for excellence in operations; extremely narrow profit margins Managng a Retaler s Shelf Space, Inventory, and Transportaton Gerard Cachon 300 SH/DH, The Wharton School, Unversty of Pennsylvana, Phladelpha, Pennsylvana 90 cachon@wharton.upenn.edu http://opm.wharton.upenn.edu/cachon/

More information

Outsourcing inventory management decisions in healthcare: Models and application

Outsourcing inventory management decisions in healthcare: Models and application European Journal of Operatonal Research 154 (24) 271 29 O.R. Applcatons Outsourcng nventory management decsons n healthcare: Models and applcaton www.elsever.com/locate/dsw Lawrence Ncholson a, Asoo J.

More information

Abstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING

Abstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING 260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore

More information

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently. Corporate Polces & Procedures Human Resources - Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:

More information