Hybrid Model Predictive Control Applied to Production-Inventory Systems

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Hybrid Model Predictive Control Applied to Production-Inventory Systems"

Transcription

1 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy Hybri Moel Preictive Control Applie to Prouction-Inventory Systems Naresh N. Nanola Daniel E. Rivera Control Systems Engineering Laboratory, School for Engineering of Matter, Transport an Energy, Arizona State University, Tempe, AZ , USA ( an Abstract: Hybri prouction-inventory systems are characterize by iscrete ecisions on prouction levels an/or capacity. These systems have broa applicability to important, emerging applications of process control concepts, among them time-varying aaptive behavioral interventions an supply chain management. This paper examines the usefulness of hybri moel preictive control (HMPC) in these two novel application settings. In a hypothetical aaptive behavioral intervention inspire by Fast Track (a preventive intervention for reucing conuct isorer in at-risk chilren), HMPC is presente as a means to improve the assignment of frequency of home-base counseling visits to families with low parental function. In supply chain management, the usefulness of HMPC for assigning prouction capacity in an inventory control problem uner conitions of varying customer eman is presente. These problems are moele as mixe logical ynamical (MLD) systems, with HMPC consisting of a Mixe Integer Quaratic Program (MIQP) that employs a three-egree-of-freeom parametrization for achieving ease of tuning an facilitating robust performance uner uncertainty. Keywors: Hybri systems; Moel Preictive Control; prouction-inventory systems; aaptive behavioral interventions; supply chain management 1. INTRODUCTION Hybri systems are characterize by interactions between continuous an iscrete ynamics. The term hybri has also been applie to escribe processes that involve continuous ynamics an iscrete (logical) ecisions (Bempora an Morari, 1999; Nanola an Bhartiya, 28). Hybri systems occur in many iverse settings; these inclue manufacturing, automotive systems, an process control. In recent years, significant emphasis has been given to moeling, ientification, control an optimization of linear an nonlinear hybri systems (Nanola, 29). The review paper by Camacho et al. (21) notes that espite the consierable interest within the control engineering community for moel preictive control for hybri systems, the fiel has not been fully evelope, an many open challenges remain. One of these is the application to new areas outsie of the inustrial community, an the the nee for novel formulations that can be effectively use in noisy, uncertain environments. This paper emonstrates the application of hybri MPC to two non-traitional areas that can be conceptualize as prouction-inventory systems: aaptive interventions in behavioral health, an inventory management in supply chains. These problems are hybri in nature an isplay performance requirements that eman a flexible control formulation. We consier a novel Three-Degree-of-Freeom (3-DoF) Moel Preictive Control formulation evelope by Nanola an Rivera (21), Support for this work has been provie by the Office of Behavioral an Social Sciences Research (OBSSR) of the National Institutes of Health an the National Institute on Drug Abuse (NIDA) through grants K25 DA21173 an R21 DA Naresh N. Nanola is currently with ABB Corporate Research Center, Bangalore, Inia. [ which offers performance an ease of tuning that is amenable for robustification in hybri systems. Prouction-inventory control is a classical problem in enterprise systems that has application in many problem arenas. Fig. 1 shows a iagram of a prouction-inventory system uner combine feeback-feeforwar control action. Two prouction noes are represente by two separate pipes, while the inventory component consists of flui in a tank. The goal is to manipulate the inflow to the prouction noes (i.e., starts) in orer to replenish an inventory that satisfies exogeneous eman. The eman signal can be broken own into forecaste an unforecaste components. A substantial literature exists that examines prouction-inventory systems from a control engineering stanpoint (Schwartz an Rivera, 21). Schwartz an Rivera (21) examine both Internal Moel Control (IMC) an Moel Preictive Control (MPC) for a linear prouction-inventory system with continuous inputs. The hybri prouction-inventory system, in which prouction occurs at iscrete levels (or is ecie by iscrete-event ecisions) is an important yet less stuie problem; we consier it the focus of this paper. The paper highlights two application areas that map into the hybri prouction-inventory problem space. The first is aaptive interventions in behavioral health, which is a topic receiving increasing attention as a means to aress the prevention an treatment of chronic, relapsing isorers, such as rug abuse (Collins et al., 24). In an aaptive intervention, osages of intervention components (such as frequency of counseling visits or meication) are assigne to participants base on the values of tailoring variables that reflect some measure of outcome or aherence. Recent work has shown the relationship between forms of aaptive interventions an feeback control of prouction-inventory systems (Rivera et al., 27). In prac-

2 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy (k) K 1 (Yiel) (Throughput Time) Net Stock (Controlle) y(k) K 2 (Yiel) θ 1 θ 2 (Throughput Time) LT Actual (k) θ (Delivery Time) Controller u 2 (k) F (k) Forecast θ F Forecast Horizon Deman (Disturbance) Fig. 1. Diagrammatic representation of a prouction-inventory system consisting of two prouction noes (one primary, one seconary) an a single inventory, with combine feeback-feeforwar control. tice, these problems are hybri in nature because osages of intervention components correspon to iscrete values. These interventions have to be implemente on a participant population that may isplay significant levels of interiniviual variability. Hence a novel problem formulation is necessary that insures that the ecision policy makes appropriate ecisions for all members of a population, without emaning excessive moeling effort for each iniviual participant. Inventory management in supply chains also represents a rich application area for hybri prouction-inventory systems. Consier a scenario where an enterprise is require to make the ecisions on startup / shutown of an auxiliary manufacturing facility in orer to achieve operational goals uner changing market eman. These problems are hybri in nature, an the ynamics of these systems can be highly uncertain (Wang an Rivera, 28). This necessitates a novel problem formulation to insure efficient use of resources an an optimal operating policy for the supply chain management problem, while taking account of the changing market eman. The paper is organize as follows: Section 2 summarize the MPC formulation with the multi-egree-of-freeom tuning for MLD systems. Two case stuies, namely a hypothetical aaptive intervention base on Fast Track program, an the supply chain management problem escribe previously are iscusse in Section 3. Summary, conclusions, an irections for future research are presente in Section MODEL PREDICTIVE CONTROL FOR HYBRID SYSTEMS Moel preictive control (MPC) is wiely accepte in the process inustries ue to its ability to systematically inclue constraints, the capability to hanle plants with multiple inputs an outputs, the flexibility given to the user to efine a cost function, an its isturbance rejection properties. 2.1 Controller Moel The MPC controller presente in this paper relies on the following moel framework (Nanola an Rivera, 21), x(k + 1) = Ax(k) + B 1 u(k) + B 2 δ(k) + B 3 z(k) + B (k) (1) y(k + 1) = Cx(k + 1) + (k + 1) + ν(k + 1) (2) E 5 E 2 δ(k) + E 3 z(k) E 4 y(k) E 1 u(k) + E (k)(3) where x an u represent states (both iscrete an continuous) an inputs (both iscrete an continuous) of the system. y is a vector of outputs, an, an ν represent measure isturbances, unmeasure isturbances an measurement noise signals, respectively. δ an z are iscrete an continuous auxiliary variables that are introuce in orer to convert logical/iscrete ecisions into their equivalent linear inequality constraints summarize in (3) (for etails, see Bempora an Morari (1999) ). The framework permits the user to inclue an prioritize constraints, an incorporate heuristic rules in the escription of the moel. Because isturbances are an inherent part of any process, it is necessary to incorporate these in the controller moel that efines the control system. Equations (1)-(3) are the MLD framework shown in (Bempora an Morari, 1999), which is moifie by incorporating measure an unmeasure isturbances. The moel lumps the effect of all unmeasure isturbances on the outputs only, which is a common practice in the process control literature (Wang an Rivera, 28; Lee an Yu, 1994). We consier, the unmeasure isturbance, as a stochastic signal, escribe as follows, x w (k + 1) = A w x w (k) + B w w(k), (k + 1) = C w x w (k + 1)(4) where A w has all eigenvalues insie the unit circle an w(k) is a vector of integrate white noise. Here, it is assume that the isturbance effect is uncorrelate. Thus, B w = C w = I an A w = iag{α 1, α 1,, α ny } where n y is number of outputs. In orer to take avantage of well unerstoo properties of white noise signal consiering ifference form of isturbance an system moels an augmenting them as follows, X(k + 1) = A X(k) + B 1 u(k) + B 2 δ(k) + B 3 z(k) +B (k) + B w w(k) (5) y(k + 1) = C X(k + 1) + ν(k + 1) (6) Here X(k) = [ x T (k) x T w(k) y T (k)] T, (k) = (k) (k 1) an w(k) is white noise sequence. Augmente matrices A, B i an C are given in Nanola an Rivera (21). 2.2 MPC Problem In this work, we use a quaratic cost function of the form, min {[u(k+i)] m 1 i=, [δ(k+i)]p 1 i=, [z(k+i)]p 1 m 1 + i= p 1 + i= i= } J = Q u ( u(k + i)) 2 m i= Q (δ(k + i) δ r ) 2 p p i=1 Q y (y(k + i) y r ) 2 2 Q u (u(k + i) u r ) 2 2 i= Q z (z(k + i) z r ) 2 2 (7) subjecte to mixe integer constraints of (3) an various process an safety constraints such as boun constraints on inputs, outputs an move. Here p is the preiction horizon, m is the control horizon, ( ) r stans for reference trajectory an 2 is for 2-norm. Q y, Q u, Q u, Q, an Q z are penalty weights on the control error, move size, control signal, auxiliary binary variables an auxiliary continuous variables, respectively. The aforementione MPC problem is governe by both binary an continuous ecision variables hence it is a mixe integer quaratic program (miqp). Moreover, it requires future preictions of the outputs an the mixe integer constraints in (3),

3 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy which can be obtain by propagating (3), (5) an (6) for p steps in future. These multi-step preictions are then use to convert aforementione MPC problem to a stanar miqp (for etails, see Nanola an Rivera (21)). This problem can be solve using any miqp solver available in the market. In this work, we have use the Tomlab-CPLEX solver. It shoul be note that the algorithm also requires externally generate reference trajectories, an externally generate forecast of the measure isturbance an estimate of (isturbance free) initial states X(k) that influence the robust performance of the MPC. The output reference trajectory is generate using an asymptotically step (a Type-I filter per Morari an Zafiriou (1989)) as: y r (k + i) = (1 α r j )q y target q αr j, 1 j n y, 1 i p (8) The setpoint tracking spee can be ajuste by choosing αr j between [,1) for each output. The smaller the value, the faster the response for particular setpoint tracking. Thus, setpoint tracking spee can be ajuste for each output iniviually. The spee require to reject each measure isturbance can be ajuste inepenently by using a filter, f (q,α j ), 1 j n ist, for each measure isturbance. Here n ist is the number of measure isturbances an α j is a tuning parameter between [,1), for the jth measure isturbance. Smaller the α j, faster the spee of particular isturbance rejection. Thus, filtere signal can be use as an anticipate unmeasure isturbance. The transfer function f (q,α j ) can be assume as an asymptotically step or an asymptotically ramp (i.e. Type-I or Type-II signal as per Morari an Zafiriou (1989)), as per the nature of the system ynamics. Type-I filter structure is given in (8) an Type-II filter structure can be given as f (q,α j ) = (β + β 1 q β ω q ω ) (1 α j )q q α j (9) 6kα j β k = (1 α j 1 k ω )ω(ω + 1)(2ω + 1), (1) β = 1 (β β ω ) (11) The states of the system can be estimate from the current measurements, y(k) while rejecting the unmeasure isturbance using a Kalman filter as follows: X(k k 1) = A X(k 1 k 1) + B 1 u(k 1) + B 2 δ(k 1) +B 3 z(k 1) + B (k 1) (12) X(k k) = X(k k 1) + K f (y(k) C X(k k 1)) (13) Here K f is the filter gain, an optimal value of which can be foun by solving an algebraic Riccati equation. We use the parametrization of filter gain (Lee an Yu, 1994) as follows, K f = [ F b F a ] T (14) Here F a = iag{( f a ) 1,,( f a ) ny }, F b = iag{( f b ) 1,,( f b ) ny }, ( f b ) j = (( f a ) j 2 )\(1 + α j α j ( f a ) j ), 1 j n y an ( f a ) j is a tuning parameter between an 1. While the unmeasure isturbances are rejecte using the state observer presente in (12)-(14), the spee of rejection is proportional to the tuning parameter ( f a ) j. As ( f a ) j approaches zero, the state estimator increasingly ignores the preiction error correction, an the control solution is mainly etermine by the eterministic moel, (12). On the other han, the state estimator tries to compensate for all preiction error as ( f a ) j approaches to 1, with a corresponing increase in the aggressiveness of the control action. In practice, the juicious selection of ( f a ) j requires making the proper traeoff between performance an robustness. 3. CASE STUDIES In this section, we present applications of MPC with 3-DoF algorithm on case stuies from two ifferent non-traitional areas escribe in the Introuction: aaptive behavioral interventions an supply chain management. 3.1 Aaptive Time-Varying Behavioral Interventions As a representative case stuy of a time-varying aaptive behavioral intervention we examine the hypothetical problem inspire by the Fast Track program (C.P.P. Res. Grp., 1992). Fast Track was a multi-year, multi-component program esigne to prevent conuct isorer in at-risk chilren. Youth showing conuct isorer are at increase risk for incarceration, injury, epression, substance abuse, an eath by homicie or suicie. In Fast Track, some intervention components were elivere universally to all participants, while other specialize components were elivere aaptively. In this paper we analyze a hypothetical aaptive intervention inspire by Fast Track for assigning home-base family counseling visits, which are provie to families on the basis of parental functioning. There are several possible levels of intensity, or oses, of family counseling. The iea is to vary the oses of family counseling epening on the nees of the family, in orer to avoi proviing an insufficient amount of counseling for very trouble families, or wasting counseling resources on families that may not nee them or be stigmatize by excessive counseling. The ecision about which ose of counseling to offer each family is base primarily on the family s level of functioning, assesse by a family functioning questionnaire complete by the parents. As escribe in Collins et al. (24), families with very poor functioning are given weekly counseling; families with poor functioning are given biweekly counseling; families with near threshol functioning are given monthly counseling; an families at or above threshol are given no counseling. Family functioning is reassesse at a review interval of three months, at which time the intervention osage may change. This goes on for three years. We consier the scenario in which the total number of home base family counseling visits is limite ue to resource constraints, an a monthly group meeting option is mae available to participant families once the maximum number of home-base family counseling visits has been reache. Following as in Rivera et al. (27), the open-loop ynamics of the intervention is moele by means of a flui analogy represente in Fig. 1. Parental function y 1 (k) is treate as flui in a tank, which is eplete by exogenous isturbances (k). The tank is replenishe by the intervention components (k) (home base counseling visits) or u 2 (k) (monthly group meeting), which are manipulate variables. The use of flui analogy enables eveloping a mathematical moel of the openloop ynamics of the intervention using the principle of conservation of mass. This moel can be escribe by following ifference equations which relates parental function y 1 (k) with the intervention components (k) an u 2 (k) as follows:

4 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy Counseling visits PF (%) 1 5 Weekly Bi Weekly Monthly No Visits Total visits Counseling visits PF (%) 1 5 Weekly Bi Weekly Monthly No Visits Total visits Group Meeting Yes Unlimite counseling visits Limite (48) counseling visits No Time (Month) Group Meeting Yes No Time (Month) Fig. 2. Aaptive behavioral intervention case stuy. Control performance for unlimite an limite (48) counseling visits, in the absence of the group meeting component. Step isturbance D(k) = 5, α r =, α =., f a = 1, Q y = 1, Q u =.5, Q u = Q = Q z =. y 1 (k + 1) = y 1 (k) + K 1 (k θ 1) + K 2 u 2 (k θ 2) (k) (15) K 1 =.15 an K 2 = 5 represent the intervention gain for counselor home visits an monthly group meeting, respectively, θ 1 = θ 1 1 = represents the time elay between the intervention component an its effect on parental function, θ 2 = θ 2 1 = represents the time elay between the intervention component u 2 an its effect on parental function. (k) is the unknown source of parental function epletion (i.e. unmeasure isturbance). The measure isturbance an hence feeforwar control is not consiere here in this application. Here it shoul be note that (k) has a restriction on the frequency of counselor visits such that these can be only possible either weekly, biweekly or monthly, or none at all. This problem requires imposing a restriction on the intervention (k) such that it takes only four values:, u weekly, u biweekly an u monthly. In orer to capture iscreteness in the intervention, four binary auxiliary variables, δ 1, δ 2, δ 3, δ 4 an three continuous auxiliary variables, z 1, z 2, z 3 are introuce. The etaile escription of logical conitions are not presente here for the brevity of the paper. Moreover, u 2 (k) has a restriction such that it can be available if an only if intervention component of home base counseling visits is exhauste (i.e. total 48 home visits complete). Thus, an u 2 can not be given simultaneously. In orer to implement this restriction one aitional binary variable δ 5 is introuce with the following aitional relationships, y 2 (k) = y 2 (k 1) + b 1 z 1 (k) + b 2 z 2 (k) + b 3 z 3 (k) (16) δ 5 (k) = 1 48 y 2 (k) & u 2 (k) = δ 5 (k) (17) Here y 2 refers total number of counselor home visits. Equation (17) make sure that intervention component corresponing to monthly group meeting is available only in a situation where home base counselor visit is not available. Thus, the problem has inherent iscreteness along with the continuous ynamics, which can be characterize by the hybri ynamical system an can be moel using the MLD framework. Control performance for unlimite number of counseling visits in absence of group meeting (i.e. nominal case) is ocumente in Fig. 2 using soli line. From the figure, it can be seen that the parental function achieves esire goal satisfactorily using 69 in-home counseling visits uring the perio of 3 years. While Fig. 3. Aaptive behavioral intervention case stuy. Control performance for limite (48) counseling visits, with a group meeting component available. Step isturbance D(k) = 5, α r = α =., f a = 1, Q y = 1, Q u =.5, Q u = Q = Q z =. ashe-otte line in Fig. 2 represent control performance for the case where total home base counseling visits are restricte to 48 without availability of the group meeting (i.e. K 2 = ). From the figure, it is observe that the osage constraints places a funamental limit on the effects of the intervention an it is unable to achieve esire parental function goal in absence of any other aitional intervention. However, as it is clearly seen from the figure, the controller oes the best that it can an uses available resources such that it can reach as close as possible to the the esire goal. A ecline in the parental function after 24 months is notice because of the epletion of the parental function by some unknown isturbances an at the same time unavailability of the intervention osage (i.e inhome counseling visits). Fig. 3 ocuments performance for the case with similar restriction on total number of visits. However, in this case, option for the monthly group meeting is available (i.e. K 2 = 5) on completion of 48 home base counseling visits. Here it can be seen that the ecision policy assigns intervention osages (in-home counseling visits) similar to the nominal case until total number of visits reach to maximum value of 48 an then it assigns group meeting in orer to reach an maintain the esire parental function goal. Thus, the propose MPC-base ecision policy is capable of enforcing constraints on intervention osages, as well as switching between two ifferent interventions as neee. 3.2 Supply Chain Management Case Stuy In this case stuy, we consier a supply chain management problem comprise of a prouction-inventory system with one inventory an two prouction noes. The prouction noes consist of one primary factory an a seconary auxiliary one, as shown in Figure 1. Throughput time θ 1 = θ an yiel K 1 for the primary factory are 4 ays an.9, respectively; for the auxiliary factory, the throughput time θ 2 = θ an yiel K 2 are 9 ays an.8, respectively. Here we consier that the operating cost for the auxiliary factory is greater than the primary one because of the longer throughput time an lower yiel. Therefore, this auxiliary prouction noe shoul be accesse if an only if the primary noe is running at its full capacity an unable to meet future market eman; likewise, prouction from the auxiliary noe must be iscontinue if future eman

5 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy cannot justify its operation. The iscrete ecision of startup or shutown of the auxiliary factory is a function of the continuous variables f (k) (eman forecast) an the work-in-progress () in the primary prouction noe. Consequently, the system can be categorize as a hybri system, where the inventory ynamics are governe by continuous variables (inventory, factory starts, eman an ) an a iscrete ecision (shutown/start-up of the auxiliary factory). The ynamics of this system can be escribe using first principles moel follows: y(k + 1) = y(k) + K 1 (k θ 1) + K 2 u 2 (k θ 2) (k) (18) (k + 1) = θ 1 i= (k i) (19) where (k) = f (k θ f ) + u (k) is the total customer eman comprising forecaste f an unforecaste u components, (k) [, 2] represents the starts for the primary prouction noe, u 2 (k) [, 2] is the starts for the auxiliary prouction noe, an [, 6] represents the work-in-progress in the primary prouction noe. In orer to ensure that the auxiliary factory is activate if an only if in the primary factory is at its maximum capacity, we embe the following logical conition u 2 (k θ 2 ) (k + 1) > Cap max = 6 into the ynamical moel. The implication ( ) can be converte into linear inequality constraints using Big-M constraints (Raman an Grossmann, 1991). This conversion can be accomplishe by introucing an auxiliary binary variable (δ) an an auxiliary continuous variable (z) followe by a MLD representation of (18)-(19) as in (1)-(3). The MLD moel of (18)-(19) an linear constraint from aforementione logical conition along with boun constraints on process variables are then use to formulate an MPC problem. The operational goal of this system is to meet the customer eman (k) relying on prouction from the auxiliary factory only when necessary, while maintaining the net stock inventory level at a preefine setpoint. This can be accomplishe by manipulating factory starts (k), u 2 (k) an feeforwar compensation of forecaste eman f (k) simultaneously imposing the above escribe logical conition. Here we consier a sampling interval of T = 1 ay, θ f = p = 3 ays. In practice, it is esirable to keep the factory starts as constant as possible (i.e., avoi factory thrash ) while maintaining inventory at esire levels in the face of uncertain customer eman (Wang an Rivera, 28). In orer to examine the performance of the propose multi-egree-of-freeom MPC formulation, we consier a piecewise stochastic customer eman signal an its forecast, which are shown in Figure 4. Figure 5 emonstrates the performance of the propose formulation that uses multiegree-of-freeom tuning parameters, α r =.9, α =, f a =.1, penalty weight parameters Q y = 1, Q u = iag{ }, Q u = Q = Q z =, preiction horizon p = 3 an control horizon m = 25. From the figure, it can be seen that the propose MPC algorithm is able to satisfactorily maintain inventory at its preefine target, while proucing little variation in the starts of the factories. Moreover, it is able to ecie on the start-up / shutown of the auxiliary factory in a esirable manner (i.e., by making minimal use of the auxiliary factory). This reuces operational cost while allowing the prouction system to meet customer eman without backorers. In orer to assess the effectiveness of the propose formulation, we compare its performance with the MPC formulation that relies on a constant plant-moel mismatch over the preiction horizon. This formulation uses the move suppression weight (Q u ) in lieu of f a to reuce the variation in the manipulate Time (ay) Fig. 4. Customer eman (k) (re ashe line) an eman forecast f (k) (soli black line), SCM case stuy. y, u u Time (ay) Fig. 5. Response of net stock (y), work-in-progress (W IP), an factory starts (,u 2 ) for the propose multipleegree-freeom formulation with tuning parameters: α r =.9, α =, f a =.1 an Q y = 1, Q u = iag{ }, Q u = Q = Q z = for the eman in Fig. 4. variables (i.e., starts) of the factories. Figure 6 presents the simulation results using Q u = iag{ } while keeping all other parameters as in the previous case. The responses show evience of very poor inventory control an very high variation in the starts of the factories as compare to the propose formulation. To reuce the variation in the starts of the factories an verify the performance against the propose formulation, we apply various values of the move suppression weight Q u. Table 1 ocuments the maximum (peak) value of the inventory (y max ) an the close-loop performance metrics J e an J u using the MPC formulation relying on a constant plant-moel mismatch over the preiction horizon for five values of Q u between to 2. The last row of Table 1 ocuments these values for the three-egree-of-freeom (3-DoF) MPC formulation. The performance metrics J e an J u are measures of cumulative error (e(k) = y(k) y r ) an variation in the rate-of-change of factory starts ( u(k) = u(k) u(k 1)), respectively, which are given as J = t/t s k=1 (k)t (k), where = e, u. From the table, it can be seen that the propose 3-DoF formulation outperforms the constant plant-moel mismatch base MPC formulation in terms of maximum peak in the inventory an J e for all values of Q u. On the other han, increasing the move suppression weight Q u lowers J u, with the last two cases (i.e. Q u = iag{1 1} an Q u = iag{2 2}) yieling lower values of J u than the 3-DoF MPC formulation. f

6 Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy y, u u Time (ay) Fig. 6. Response of net stock (y), Work-in-Progress (), an factory starts (,u 2 ) for the MPC formulation that relies on constant plant-moel mismatch an move suppression tuning, with Q u = iag{ } an Q y = 1, Q u = Q = Q z = for the eman profile in Fig. 4. y, u u Time (ay) Fig. 7. Response of net stock (y), Work-in-Progress (), an factory starts (,u 2 ) for the MPC formulation that relies on constant plant-moel mismatch an move suppression tuning with Q u = iag{2 2} an Q y = 1, Q u = Q = Q z = for the eman profile in Fig. 4. Table 1. J u, J e an y max using MPC relying on constant plant-moel mismatch for various Q u an a 3-DoF MPC formulation for f a =.1. Sl. No. Q u J u J e y max 1 iag{ } iag{1 1} iag{1 1} iag{1 1} iag{2 2} DoF Contrasting Fig. 5 with Fig. 7 shows that for the 3-DoF formulation, factory starts remain constant over a significant portion of the simulation, without leaing to the substantial maximum inventory peak an corresponing emans on warehouse space resulting from Q u = iag{2 2}. Thus, we observe that the 3-DoF-MPC algorithm can be useful for reucing overall operating costs an efficiently managing this class of hybri prouction-inventory systems. 4. SUMMARY Control applications of hybri systems are becoming increasingly important in many fiels, among them process control. In this work, the application of hybri moel preictive control (HMPC) to aaptive time-varying behavioral interventions an inventory management in supply chains, two problems that can be conceptualize using flui analogies, are presente. These systems are represente as mixe logical ynamical (MLD) moels, which can then be use to specify a hybri moel preictive control law relying on the three-egree-of-freeom (3-DoF) tuning formulation of Nanola an Rivera (21). The use of 3-DoF tuning enables iniviually ajusting the spee of isturbance rejection (measure an unmeasure) an setpoint tracking for each output; this has intuitive appeal for the user an facilitates achieving robust operation uner uncertainty. The effectiveness of the propose formulation is emonstrate in these applications uner iverse scenarios involving variations in constraints, isturbances, an tuning. REFERENCES Bempora, A. an Morari, M. (1999). Control of systems integrating logic, ynamics, an constraints. Automatica, 35(3), Camacho, E.F., Ramirez, D.R., Limon, D., Muñoz e la Peña, D., an Alamo, T. (21). Moel preictive control techniques for hybri systems. Ann. Rev. in Control, 34, Collins, L.M., Murphy, S.A., an Bierman, K.L. (24). A conceptual framework for aaptive preventive interventions. Prevention Science, 5(3), C.P.P. Res. Grp. (1992). A evelopmental an clinical moel for the prevention of conuct isorers: The Fast Track program. Development an Psychopathology, 4, Lee, J.H. an Yu, Z.H. (1994). Tuning of moel preictive controllers for robust performance. Comput. Chem. Eng., 18(1), Morari, M. an Zafiriou, E. (1989). Robust Process Control. Englewoo Cliffs, NJ: Prentice-Hall. Nanola, N.N. (29). A Multiple Moel Approach for Moeling, Ientification an Control of Nonlinear Hybri Systems. Ph.D. thesis, Inian Institute of Technology Bombay, Inia. Nanola, N.N. an Bhartiya, S. (28). A multiple moel approach for preictive control of nonlinear hybri systems. J. Process Control, 18(2), Nanola, N.N. an Rivera, D.E. (21). A novel moel preictive control formulation for hybri systems with application to aaptive behavioral interventions. In Amer. Cntrl. Conf., Baltimore, Marylan, USA. Raman, R. an Grossmann, I.E. (1991). Relation between milp moelling an logical inference for chemical process synthesis. Comput. Chem. Eng., 15(2), Rivera, D.E., Pew, M.D., an Collins, L.M. (27). Using engineering control principles to inform the esign of aaptive interventions a conceptual introuction. Drug an Alcohol Depenence, 88(2), S31 S4. Schwartz, J.D. an Rivera, D.E. (21). A process control approach to tactical inventory management in prouctioninventory systems. International Journal of Prouction Economics, 125(1), Wang, W. an Rivera, D.E. (28). Moel preictive control for tactical ecision-making in semiconuctor manufacturing supply chain management. IEEE Trans. Control Syst. Technol., 16(5),

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1 This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1 An Improved

More information

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market RATIO MATHEMATICA 25 (2013), 29 46 ISSN:1592-7415 Optimal Control Policy of a Prouction an Inventory System for multi-prouct in Segmente Market Kuleep Chauhary, Yogener Singh, P. C. Jha Department of Operational

More information

State of Louisiana Office of Information Technology. Change Management Plan

State of Louisiana Office of Information Technology. Change Management Plan State of Louisiana Office of Information Technology Change Management Plan Table of Contents Change Management Overview Change Management Plan Key Consierations Organizational Transition Stages Change

More information

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014 ISSN: 77-754 ISO 900:008 Certifie International Journal of Engineering an Innovative echnology (IJEI) Volume, Issue, June 04 Manufacturing process with isruption uner Quaratic Deman for Deteriorating Inventory

More information

DETERMINING OPTIMAL STOCK LEVEL IN MULTI-ECHELON SUPPLY CHAINS

DETERMINING OPTIMAL STOCK LEVEL IN MULTI-ECHELON SUPPLY CHAINS HUNGARIAN JOURNA OF INDUSTRIA CHEMISTRY VESZPRÉM Vol. 39(1) pp. 107-112 (2011) DETERMINING OPTIMA STOCK EVE IN MUTI-ECHEON SUPPY CHAINS A. KIRÁY 1, G. BEVÁRDI 2, J. ABONYI 1 1 University of Pannonia, Department

More information

Boiler Drum Level Control In Thermal Power Plant

Boiler Drum Level Control In Thermal Power Plant International Avance Research Journal in Science, Engineering an Technology National Conference on Emerging Trens in Engineering an Technology (NCETET 16) Loures Matha College of Science & Technology,

More information

Optimal Control Of Production Inventory Systems With Deteriorating Items And Dynamic Costs

Optimal Control Of Production Inventory Systems With Deteriorating Items And Dynamic Costs Applie Mathematics E-Notes, 8(2008), 194-202 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.eu.tw/ amen/ Optimal Control Of Prouction Inventory Systems With Deteriorating Items

More information

10.2 Systems of Linear Equations: Matrices

10.2 Systems of Linear Equations: Matrices SECTION 0.2 Systems of Linear Equations: Matrices 7 0.2 Systems of Linear Equations: Matrices OBJECTIVES Write the Augmente Matrix of a System of Linear Equations 2 Write the System from the Augmente Matrix

More information

An Introduction to Event-triggered and Self-triggered Control

An Introduction to Event-triggered and Self-triggered Control An Introuction to Event-triggere an Self-triggere Control W.P.M.H. Heemels K.H. Johansson P. Tabuaa Abstract Recent evelopments in computer an communication technologies have le to a new type of large-scale

More information

A Universal Sensor Control Architecture Considering Robot Dynamics

A Universal Sensor Control Architecture Considering Robot Dynamics International Conference on Multisensor Fusion an Integration for Intelligent Systems (MFI2001) Baen-Baen, Germany, August 2001 A Universal Sensor Control Architecture Consiering Robot Dynamics Frierich

More information

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT OPTIMAL INSURANCE COVERAGE UNDER BONUS-MALUS CONTRACTS BY JON HOLTAN if P&C Insurance Lt., Oslo, Norway ABSTRACT The paper analyses the questions: Shoul or shoul not an iniviual buy insurance? An if so,

More information

A Centralized Model Predictive Control Strategy for Dynamic Supply Chain Management

A Centralized Model Predictive Control Strategy for Dynamic Supply Chain Management Preprints of the 2013 IFAC Conference on Manufacturing Modelling, Management, and Control, Saint Petersburg State University and Saint Petersburg National Research University of Information Technologies,

More information

Stock Market Value Prediction Using Neural Networks

Stock Market Value Prediction Using Neural Networks Stock Market Value Preiction Using Neural Networks Mahi Pakaman Naeini IT & Computer Engineering Department Islamic Aza University Paran Branch e-mail: m.pakaman@ece.ut.ac.ir Hamireza Taremian Engineering

More information

Modelling and Resolving Software Dependencies

Modelling and Resolving Software Dependencies June 15, 2005 Abstract Many Linux istributions an other moern operating systems feature the explicit eclaration of (often complex) epenency relationships between the pieces of software

More information

Optimal Energy Commitments with Storage and Intermittent Supply

Optimal Energy Commitments with Storage and Intermittent Supply Submitte to Operations Research manuscript OPRE-2009-09-406 Optimal Energy Commitments with Storage an Intermittent Supply Jae Ho Kim Department of Electrical Engineering, Princeton University, Princeton,

More information

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data UCLA STAT 3 Introuction to Statistical Methos for the Life an Health Sciences Instructor: Ivo Dinov, Asst. Prof. of Statistics an Neurology Chapter 9 Paire Data Teaching Assistants: Jacquelina Dacosta

More information

! # % & ( ) +,,),. / 0 1 2 % ( 345 6, & 7 8 4 8 & & &&3 6

! # % & ( ) +,,),. / 0 1 2 % ( 345 6, & 7 8 4 8 & & &&3 6 ! # % & ( ) +,,),. / 0 1 2 % ( 345 6, & 7 8 4 8 & & &&3 6 9 Quality signposting : the role of online information prescription in proviing patient information Liz Brewster & Barbara Sen Information School,

More information

The one-year non-life insurance risk

The one-year non-life insurance risk The one-year non-life insurance risk Ohlsson, Esbjörn & Lauzeningks, Jan Abstract With few exceptions, the literature on non-life insurance reserve risk has been evote to the ultimo risk, the risk in the

More information

Unbalanced Power Flow Analysis in a Micro Grid

Unbalanced Power Flow Analysis in a Micro Grid International Journal of Emerging Technology an Avance Engineering Unbalance Power Flow Analysis in a Micro Gri Thai Hau Vo 1, Mingyu Liao 2, Tianhui Liu 3, Anushree 4, Jayashri Ravishankar 5, Toan Phung

More information

Chapter 9 AIRPORT SYSTEM PLANNING

Chapter 9 AIRPORT SYSTEM PLANNING Chapter 9 AIRPORT SYSTEM PLANNING. Photo creit Dorn McGrath, Jr Contents Page The Planning Process................................................... 189 Airport Master Planning..............................................

More information

Optimizing Multiple Stock Trading Rules using Genetic Algorithms

Optimizing Multiple Stock Trading Rules using Genetic Algorithms Optimizing Multiple Stock Traing Rules using Genetic Algorithms Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, 040-00 Lisboa, Portugal.

More information

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi

More information

Achieving quality audio testing for mobile phones

Achieving quality audio testing for mobile phones Test & Measurement Achieving quality auio testing for mobile phones The auio capabilities of a cellular hanset provie the funamental interface between the user an the raio transceiver. Just as RF testing

More information

Data Center Power System Reliability Beyond the 9 s: A Practical Approach

Data Center Power System Reliability Beyond the 9 s: A Practical Approach Data Center Power System Reliability Beyon the 9 s: A Practical Approach Bill Brown, P.E., Square D Critical Power Competency Center. Abstract Reliability has always been the focus of mission-critical

More information

Control-Relevant Demand Forecasting for Management of a Production-Inventory System

Control-Relevant Demand Forecasting for Management of a Production-Inventory System 28 American Control Conference Westin Seattle Hotel, Seattle, Washington, USA June -3, 28 FrA3. Control-Relevant Demand Forecasting for Management of a Production-Inventory System Jay D. Schwartz, Manuel

More information

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES 1 st Logistics International Conference Belgrae, Serbia 28-30 November 2013 INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES Goran N. Raoičić * University of Niš, Faculty of Mechanical

More information

Towards a Framework for Enterprise Architecture Frameworks Comparison and Selection

Towards a Framework for Enterprise Architecture Frameworks Comparison and Selection Towars a Framework for Enterprise Frameworks Comparison an Selection Saber Aballah Faculty of Computers an Information, Cairo University Saber_aballah@hotmail.com Abstract A number of Enterprise Frameworks

More information

Open World Face Recognition with Credibility and Confidence Measures

Open World Face Recognition with Credibility and Confidence Measures Open Worl Face Recognition with Creibility an Confience Measures Fayin Li an Harry Wechsler Department of Computer Science George Mason University Fairfax, VA 22030 {fli, wechsler}@cs.gmu.eu Abstract.

More information

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines EUROGRAPHICS 2000 / M. Gross an F.R.A. Hopgoo Volume 19, (2000), Number 3 (Guest Eitors) Unsteay Flow Visualization by Animating Evenly-Space Bruno Jobar an Wilfri Lefer Université u Littoral Côte Opale,

More information

Chapter 2 Review of Classical Action Principles

Chapter 2 Review of Classical Action Principles Chapter Review of Classical Action Principles This section grew out of lectures given by Schwinger at UCLA aroun 1974, which were substantially transforme into Chap. 8 of Classical Electroynamics (Schwinger

More information

Feedback linearization control of a two-link robot using a multi-crossover genetic algorithm

Feedback linearization control of a two-link robot using a multi-crossover genetic algorithm Available online at www.scienceirect.com Expert Systems with Applications 3 (009) 454 459 Short communication Feeback linearization control of a two-link robot using a multi-crossover genetic algorithm

More information

Option Pricing for Inventory Management and Control

Option Pricing for Inventory Management and Control Option Pricing for Inventory Management an Control Bryant Angelos, McKay Heasley, an Jeffrey Humpherys Abstract We explore the use of option contracts as a means of managing an controlling inventories

More information

Tracking Control of a Class of Hamiltonian Mechanical Systems with Disturbances

Tracking Control of a Class of Hamiltonian Mechanical Systems with Disturbances Proceeings of Australasian Conference on Robotics an Automation, -4 Dec 4, The University of Melbourne, Melbourne, Australia Tracking Control of a Class of Hamiltonian Mechanical Systems with Disturbances

More information

A hybrid approach to supply chain modeling and optimization

A hybrid approach to supply chain modeling and optimization Proceeings of the 2013 Feerate Conference on Computer Science an Information Systems pp. 1211 1218 A hybri approach to supply chain moeling an optimization Paweł Site Kielce University of Technology Al.

More information

Improving Direct Marketing Profitability with Neural Networks

Improving Direct Marketing Profitability with Neural Networks Volume 9 o.5, September 011 Improving Direct Marketing Profitability with eural etworks Zaiyong Tang Salem State University Salem, MA 01970 ABSTRACT Data mining in irect marketing aims at ientifying the

More information

Enterprise Resource Planning

Enterprise Resource Planning Enterprise Resource Planning MPC 6 th Eition Chapter 1a McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserve. Enterprise Resource Planning A comprehensive software approach

More information

Innovation Union means: More jobs, improved lives, better society

Innovation Union means: More jobs, improved lives, better society The project follows the Lisbon an Gothenburg Agenas, an supports the EU 2020 Strategy, in particular SMART Growth an the Innovation Union: Innovation Union means: More jobs, improve lives, better society

More information

If you have ever spoken with your grandparents about what their lives were like

If you have ever spoken with your grandparents about what their lives were like CHAPTER 7 Economic Growth I: Capital Accumulation an Population Growth The question of growth is nothing new but a new isguise for an age-ol issue, one which has always intrigue an preoccupie economics:

More information

Safety Stock or Excess Capacity: Trade-offs under Supply Risk

Safety Stock or Excess Capacity: Trade-offs under Supply Risk Safety Stock or Excess Capacity: Trae-offs uner Supply Risk Aahaar Chaturvei Victor Martínez-e-Albéniz IESE Business School, University of Navarra Av. Pearson, 08034 Barcelona, Spain achaturvei@iese.eu

More information

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 190 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page

More information

Sensitivity Analysis of Non-linear Performance with Probability Distortion

Sensitivity Analysis of Non-linear Performance with Probability Distortion Preprints of the 19th Worl Congress The International Feeration of Automatic Control Cape Town, South Africa. August 24-29, 214 Sensitivity Analysis of Non-linear Performance with Probability Distortion

More information

Professional Level Options Module, Paper P4(SGP)

Professional Level Options Module, Paper P4(SGP) Answers Professional Level Options Moule, Paper P4(SGP) Avance Financial Management (Singapore) December 2007 Answers Tutorial note: These moel answers are consierably longer an more etaile than woul be

More information

Firewall Design: Consistency, Completeness, and Compactness

Firewall Design: Consistency, Completeness, and Compactness C IS COS YS TE MS Firewall Design: Consistency, Completeness, an Compactness Mohame G. Goua an Xiang-Yang Alex Liu Department of Computer Sciences The University of Texas at Austin Austin, Texas 78712-1188,

More information

6.3 Microbial growth in a chemostat

6.3 Microbial growth in a chemostat 6.3 Microbial growth in a chemostat The chemostat is a wiely-use apparatus use in the stuy of microbial physiology an ecology. In such a chemostat also known as continuous-flow culture), microbes such

More information

Forecasting and Staffing Call Centers with Multiple Interdependent Uncertain Arrival Streams

Forecasting and Staffing Call Centers with Multiple Interdependent Uncertain Arrival Streams Forecasting an Staffing Call Centers with Multiple Interepenent Uncertain Arrival Streams Han Ye Department of Statistics an Operations Research, University of North Carolina, Chapel Hill, NC 27599, hanye@email.unc.eu

More information

Stochastic Modeling of MEMS Inertial Sensors

Stochastic Modeling of MEMS Inertial Sensors BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 10, No Sofia 010 Stochastic Moeling of MEMS Inertial Sensors Petko Petkov, Tsonyo Slavov Department of Automatics, Technical

More information

CHAPTER 5 : CALCULUS

CHAPTER 5 : CALCULUS Dr Roger Ni (Queen Mary, University of Lonon) - 5. CHAPTER 5 : CALCULUS Differentiation Introuction to Differentiation Calculus is a branch of mathematics which concerns itself with change. Irrespective

More information

View Synthesis by Image Mapping and Interpolation

View Synthesis by Image Mapping and Interpolation View Synthesis by Image Mapping an Interpolation Farris J. Halim Jesse S. Jin, School of Computer Science & Engineering, University of New South Wales Syney, NSW 05, Australia Basser epartment of Computer

More information

CALCULATION INSTRUCTIONS

CALCULATION INSTRUCTIONS Energy Saving Guarantee Contract ppenix 8 CLCULTION INSTRUCTIONS Calculation Instructions for the Determination of the Energy Costs aseline, the nnual mounts of Savings an the Remuneration 1 asics ll prices

More information

The Inefficiency of Marginal cost pricing on roads

The Inefficiency of Marginal cost pricing on roads The Inefficiency of Marginal cost pricing on roas Sofia Grahn-Voornevel Sweish National Roa an Transport Research Institute VTI CTS Working Paper 4:6 stract The economic principle of roa pricing is that

More information

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY Jörg Felhusen an Sivakumara K. Krishnamoorthy RWTH Aachen University, Chair an Insitute for Engineering

More information

Sustainability Through the Market: Making Markets Work for Everyone q

Sustainability Through the Market: Making Markets Work for Everyone q www.corporate-env-strategy.com Sustainability an the Market Sustainability Through the Market: Making Markets Work for Everyone q Peter White Sustainable evelopment is about ensuring a better quality of

More information

IPA Derivatives for Make-to-Stock Production-Inventory Systems With Lost Sales

IPA Derivatives for Make-to-Stock Production-Inventory Systems With Lost Sales IPA Derivatives for Make-to-Stock Prouction-Inventory Systems With Lost Sales Yao Zhao Benjamin Melame Rutgers University Rutgers Business School Newark an New Brunswick Department of MSIS 94 Rockafeller

More information

Lecture L25-3D Rigid Body Kinematics

Lecture L25-3D Rigid Body Kinematics J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L25-3D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general three-imensional

More information

Digital barrier option contract with exponential random time

Digital barrier option contract with exponential random time IMA Journal of Applie Mathematics Avance Access publishe June 9, IMA Journal of Applie Mathematics ) Page of 9 oi:.93/imamat/hxs3 Digital barrier option contract with exponential ranom time Doobae Jun

More information

Minimizing Makespan in Flow Shop Scheduling Using a Network Approach

Minimizing Makespan in Flow Shop Scheduling Using a Network Approach Minimizing Makespan in Flow Shop Scheuling Using a Network Approach Amin Sahraeian Department of Inustrial Engineering, Payame Noor University, Asaluyeh, Iran 1 Introuction Prouction systems can be ivie

More information

Simulation-based optimization of process control policies for inventory management in supply chains

Simulation-based optimization of process control policies for inventory management in supply chains Automatica 42 (26) 1311 132 www.elsevier.com/locate/automatica Simulation-based optimization of process control policies for inventory management in supply chains Jay D. Schwartz, Wenlin Wang, Daniel E.

More information

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND art I. robobabilystic Moels Computer Moelling an New echnologies 27 Vol. No. 2-3 ransport an elecommunication Institute omonosova iga V-9 atvia MOEING OF WO AEGIE IN INVENOY CONO YEM WIH ANOM EA IME AN

More information

Reading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14.

Reading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14. 7 Shocks Reaing: Ryen chs 3 & 4, Shu chs 5 & 6 For the enthusiasts, Shu chs 3 & 4 A goo article for further reaing: Shull & Draine, The physics of interstellar shock waves, in Interstellar processes; Proceeings

More information

A Data Placement Strategy in Scientific Cloud Workflows

A Data Placement Strategy in Scientific Cloud Workflows A Data Placement Strategy in Scientific Clou Workflows Dong Yuan, Yun Yang, Xiao Liu, Jinjun Chen Faculty of Information an Communication Technologies, Swinburne University of Technology Hawthorn, Melbourne,

More information

Liquid Pricing for Digital Infrastructure Services

Liquid Pricing for Digital Infrastructure Services iqui Pricing for Digital Infrastructure Services Subhajyoti Banyopahyay * an sing Kenneth Cheng Department of Decision an Information Sciences Warrington College of Business Aministration University of

More information

Product Differentiation for Software-as-a-Service Providers

Product Differentiation for Software-as-a-Service Providers University of Augsburg Prof. Dr. Hans Ulrich Buhl Research Center Finance & Information Management Department of Information Systems Engineering & Financial Management Discussion Paper WI-99 Prouct Differentiation

More information

Using research evidence in mental health: user-rating and focus group study of clinicians preferences for a new clinical question-answering service

Using research evidence in mental health: user-rating and focus group study of clinicians preferences for a new clinical question-answering service DOI: 10.1111/j.1471-1842.2008.00833.x Using research evience in mental health: user-rating an focus group stuy of clinicians preferences for a new clinical question-answering service Elizabeth A. Barley*,

More information

Web Appendices of Selling to Overcon dent Consumers

Web Appendices of Selling to Overcon dent Consumers Web Appenices of Selling to Overcon ent Consumers Michael D. Grubb A Option Pricing Intuition This appenix provies aitional intuition base on option pricing for the result in Proposition 2. Consier the

More information

Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014

Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014 Consumer Referrals Maria Arbatskaya an Hieo Konishi October 28, 2014 Abstract In many inustries, rms rewar their customers for making referrals. We analyze the optimal policy mix of price, avertising intensity,

More information

arxiv:1309.1857v3 [gr-qc] 7 Mar 2014

arxiv:1309.1857v3 [gr-qc] 7 Mar 2014 Generalize holographic equipartition for Friemann-Robertson-Walker universes Wen-Yuan Ai, Hua Chen, Xian-Ru Hu, an Jian-Bo Deng Institute of Theoretical Physics, LanZhou University, Lanzhou 730000, P.

More information

A LIQUIDITY-PROFITABILITY TRADE-OFF MODEL FOR WORKING CAPITAL MANAGEMENT MIHIR DASH 1 RANI HANUMAN

A LIQUIDITY-PROFITABILITY TRADE-OFF MODEL FOR WORKING CAPITAL MANAGEMENT MIHIR DASH 1 RANI HANUMAN A LIQUIDITY-PROFITABILITY TRADE-OFF MODEL FOR WORKING CAPITAL MANAGEMENT MIHIR DASH RANI HANUMAN ABSTRACT This paper proposes a goal programming moel for working capital management. Goal programming is

More information

Dynamic Network Security Deployment Under Partial Information

Dynamic Network Security Deployment Under Partial Information Dynamic Network Security Deployment Uner Partial nformation nvite Paper) George Theoorakopoulos EPFL Lausanne, Switzerlan Email: george.theoorakopoulos @ epfl.ch John S. Baras University of Marylan College

More information

A Case Study of Applying SOM in Market Segmentation of Automobile Insurance Customers

A Case Study of Applying SOM in Market Segmentation of Automobile Insurance Customers International Journal of Database Theory an Application, pp.25-36 http://x.oi.org/10.14257/ijta.2014.7.1.03 A Case Stuy of Applying SOM in Market Segmentation of Automobile Insurance Customers Vahi Golmah

More information

RUNESTONE, an International Student Collaboration Project

RUNESTONE, an International Student Collaboration Project RUNESTONE, an International Stuent Collaboration Project Mats Daniels 1, Marian Petre 2, Vicki Almstrum 3, Lars Asplun 1, Christina Björkman 1, Carl Erickson 4, Bruce Klein 4, an Mary Last 4 1 Department

More information

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law Detecting Possibly Frauulent or Error-Prone Survey Data Using Benfor s Law Davi Swanson, Moon Jung Cho, John Eltinge U.S. Bureau of Labor Statistics 2 Massachusetts Ave., NE, Room 3650, Washington, DC

More information

The influence of anti-viral drug therapy on the evolution of HIV-1 pathogens

The influence of anti-viral drug therapy on the evolution of HIV-1 pathogens DIMACS Series in Discrete Mathematics an Theoretical Computer Science Volume 7, 26 The influence of anti-viral rug therapy on the evolution of HIV- pathogens Zhilan Feng an Libin Rong Abstract. An age-structure

More information

Study on the Price Elasticity of Demand of Beijing Subway

Study on the Price Elasticity of Demand of Beijing Subway Journal of Traffic an Logistics Engineering, Vol, 1, No. 1 June 2013 Stuy on the Price Elasticity of Deman of Beijing Subway Yanan Miao an Liang Gao MOE Key Laboratory for Urban Transportation Complex

More information

Cost optimization of supply chain with multimodal transport

Cost optimization of supply chain with multimodal transport Proceeings of the Feerate Conference on Computer Science an Information Systems pp. 8 ISB 978-83-6080-5-4 Cost optimization of supply chain with multimoal transport Paweł Sitek Kielce University of Technology

More information

On Adaboost and Optimal Betting Strategies

On Adaboost and Optimal Betting Strategies On Aaboost an Optimal Betting Strategies Pasquale Malacaria 1 an Fabrizio Smerali 1 1 School of Electronic Engineering an Computer Science, Queen Mary University of Lonon, Lonon, UK Abstract We explore

More information

Stochastic Planning for Content Delivery: Unveiling the Benefits of Network Functions Virtualization

Stochastic Planning for Content Delivery: Unveiling the Benefits of Network Functions Virtualization Stochastic Planning for Content Delivery: Unveiling the Benefits of Network Functions Virtualization Michele Mangili, Fabio Martignon an Antonio Capone LRI, Université Paris-Su {michele.mangili, fabio.martignon}@lri.fr

More information

Cross-Over Analysis Using T-Tests

Cross-Over Analysis Using T-Tests Chapter 35 Cross-Over Analysis Using -ests Introuction his proceure analyzes ata from a two-treatment, two-perio (x) cross-over esign. he response is assume to be a continuous ranom variable that follows

More information

Formulations of Model Predictive Control. Dipartimento di Elettronica e Informazione

Formulations of Model Predictive Control. Dipartimento di Elettronica e Informazione Formulations of Model Predictive Control Riccardo Scattolini Riccardo Scattolini Dipartimento di Elettronica e Informazione Impulse and step response models 2 At the beginning of the 80, the early formulations

More information

Performance And Analysis Of Risk Assessment Methodologies In Information Security

Performance And Analysis Of Risk Assessment Methodologies In Information Security International Journal of Computer Trens an Technology (IJCTT) volume 4 Issue 10 October 2013 Performance An Analysis Of Risk Assessment ologies In Information Security K.V.D.Kiran #1, Saikrishna Mukkamala

More information

DECISION SUPPORT SYSTEM FOR MANAGING EDUCATIONAL CAPACITY UTILIZATION IN UNIVERSITIES

DECISION SUPPORT SYSTEM FOR MANAGING EDUCATIONAL CAPACITY UTILIZATION IN UNIVERSITIES DECISION SUPPORT SYSTEM OR MANAGING EDUCATIONAL CAPACITY UTILIZATION IN UNIVERSITIES Svetlana Vinnik 1, Marc H. Scholl 2 Abstract Decision-making in the fiel of acaemic planning involves extensive analysis

More information

Jitter effects on Analog to Digital and Digital to Analog Converters

Jitter effects on Analog to Digital and Digital to Analog Converters Jitter effects on Analog to Digital an Digital to Analog Converters Jitter effects copyright 1999, 2000 Troisi Design Limite Jitter One of the significant problems in igital auio is clock jitter an its

More information

Energy Cost Optimization for Geographically Distributed Heterogeneous Data Centers

Energy Cost Optimization for Geographically Distributed Heterogeneous Data Centers Energy Cost Optimization for Geographically Distribute Heterogeneous Data Centers Eric Jonari, Mark A. Oxley, Sueep Pasricha, Anthony A. Maciejewski, Howar Jay Siegel Abstract The proliferation of istribute

More information

Estimating the drilling rate in Ahvaz oil field

Estimating the drilling rate in Ahvaz oil field J Petrol Explor Pro Technol (2013) 3:169 173 DOI 10.1007/s13202-013-0060-3 ORIGINAL PAPER - PRODUCTION ENGINEERING Estimating the rilling rate in Ahvaz oil fiel Masou Cheraghi Seifaba Peyman Ehteshami

More information

The most common model to support workforce management of telephone call centers is

The most common model to support workforce management of telephone call centers is Designing a Call Center with Impatient Customers O. Garnett A. Manelbaum M. Reiman Davison Faculty of Inustrial Engineering an Management, Technion, Haifa 32000, Israel Davison Faculty of Inustrial Engineering

More information

Safety Management System. Initial Revision Date: Version Revision No. 02 MANUAL LIFTING

Safety Management System. Initial Revision Date: Version Revision No. 02 MANUAL LIFTING Revision Preparation: Safety Mgr Authority: Presient Issuing Dept: Safety Page: Page 1 of 11 Purpose is committe to proviing a safe an healthy working environment for all employees. Musculoskeletal isorers

More information

Web Appendices to Selling to Overcon dent Consumers

Web Appendices to Selling to Overcon dent Consumers Web Appenices to Selling to Overcon ent Consumers Michael D. Grubb MIT Sloan School of Management Cambrige, MA 02142 mgrubbmit.eu www.mit.eu/~mgrubb May 2, 2008 B Option Pricing Intuition This appenix

More information

Ch 10. Arithmetic Average Options and Asian Opitons

Ch 10. Arithmetic Average Options and Asian Opitons Ch 10. Arithmetic Average Options an Asian Opitons I. Asian Option an the Analytic Pricing Formula II. Binomial Tree Moel to Price Average Options III. Combination of Arithmetic Average an Reset Options

More information

A New Evaluation Measure for Information Retrieval Systems

A New Evaluation Measure for Information Retrieval Systems A New Evaluation Measure for Information Retrieval Systems Martin Mehlitz martin.mehlitz@ai-labor.e Christian Bauckhage Deutsche Telekom Laboratories christian.bauckhage@telekom.e Jérôme Kunegis jerome.kunegis@ai-labor.e

More information

Bellini: Ferrying Application Traffic Flows through Geo-distributed Datacenters in the Cloud

Bellini: Ferrying Application Traffic Flows through Geo-distributed Datacenters in the Cloud Bellini: Ferrying Application Traffic Flows through Geo-istribute Datacenters in the Clou Zimu Liu, Yuan Feng, an Baochun Li Department of Electrical an Computer Engineering, University of Toronto Department

More information

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Aalborg Universitet Heat-An-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Publishe in: International Journal of Heat an Mass Transfer

More information

GPRS performance estimation in GSM circuit switched services and GPRS shared resource systems *

GPRS performance estimation in GSM circuit switched services and GPRS shared resource systems * GPRS performance estimation in GSM circuit switche serices an GPRS share resource systems * Shaoji i an Sen-Gusta Häggman Helsinki Uniersity of Technology, Institute of Raio ommunications, ommunications

More information

A New Pricing Model for Competitive Telecommunications Services Using Congestion Discounts

A New Pricing Model for Competitive Telecommunications Services Using Congestion Discounts A New Pricing Moel for Competitive Telecommunications Services Using Congestion Discounts N. Keon an G. Ananalingam Department of Systems Engineering University of Pennsylvania Philaelphia, PA 19104-6315

More information

Different approaches for the equalization of automotive sound systems

Different approaches for the equalization of automotive sound systems Auio Engineering Society Convention Paper Presente at the 112th Convention 2002 May 10 13 Munich, Germany This convention paper has been reprouce from the author's avance manuscript, without eiting, corrections,

More information

CHAPTER 3 DIODES. NTUEE Electronics L. H. Lu 3 1

CHAPTER 3 DIODES. NTUEE Electronics L. H. Lu 3 1 CHAPER 3 OE Chapter Outline 3.1 he eal ioe 3.2 erminal Characteristics of Junction ioes 3.3 Moeling the ioe Forwar Characteristics 3.4 Operation in the Reerse Breakown Region Zener ioes 3.5 Rectifier Circuits

More information

Rural Development Tools: What Are They and Where Do You Use Them?

Rural Development Tools: What Are They and Where Do You Use Them? Faculty Paper Series Faculty Paper 00-09 June, 2000 Rural Development Tools: What Are They an Where Do You Use Them? By Dennis U. Fisher Professor an Extension Economist -fisher@tamu.eu Juith I. Stallmann

More information

Cost Efficient Datacenter Selection for Cloud Services

Cost Efficient Datacenter Selection for Cloud Services Cost Efficient Datacenter Selection for Clou Services Hong u, Baochun Li henryxu, bli@eecg.toronto.eu Department of Electrical an Computer Engineering University of Toronto Abstract Many clou services

More information

Compact Form of Expressions for Inductance Calculation of Meander Inductors

Compact Form of Expressions for Inductance Calculation of Meander Inductors SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 1, No. 3, November 2004, 57-68 Compact Form of Expressions for Inuctance Calculation of Meaner Inuctors Goran Stojanovic 1, Ljiljana Živanov 2, Mirjana Damjanovic

More information

Factoring Dickson polynomials over finite fields

Factoring Dickson polynomials over finite fields Factoring Dickson polynomials over finite fiels Manjul Bhargava Department of Mathematics, Princeton University. Princeton NJ 08544 manjul@math.princeton.eu Michael Zieve Department of Mathematics, University

More information

A joint control framework for supply chain planning

A joint control framework for supply chain planning 17 th European Symposium on Computer Aided Process Engineering ESCAPE17 V. Plesu and P.S. Agachi (Editors) 2007 Elsevier B.V. All rights reserved. 1 A joint control framework for supply chain planning

More information

Search Advertising Based Promotion Strategies for Online Retailers

Search Advertising Based Promotion Strategies for Online Retailers Search Avertising Base Promotion Strategies for Online Retailers Amit Mehra The Inian School of Business yeraba, Inia Amit Mehra@isb.eu ABSTRACT Web site aresses of small on line retailers are often unknown

More information