USING REAL-TIME INFORMATION IN PRODUCTION PLANNING AND OPERATIONAL CONTROL

Transcription

1 9 th International Conferene on Prodution Researh USING REAL-TIME INFORMATION IN PRODUCTION PLANNING AND OPERATIONAL CONTROL Ronald G. Askin, Detlef Pabst, Mihael Pew, Young Jun Son 2 Department of Industrial Engineering, Arizona State University, Tempe, AZ 85287, USA Department of Systems& Industrial Eingineering, University of Arizona, Tuson, AZ 8572, USA 2 Abstrat Many prodution planning and ontrol systems in use today were designed under a paradigm of a stati, deterministi world with hierarhial ontrol systems and regular periodi updates. These systems were oneived in a time of lower ompetition, more stable markets, and limited information and ommuniation apability. The modern manufaturing world is haraterized by muh different onditions. We present a oneputal overview of a prodution planning system that maintains the hierarhial struture but is networked aross federates and integrates real-time status and sensor information to guide planning and ontrol in a dynami fashion. Information indiating deviations from expeted status initiates the replanning ativity. Beginning with linear programming for aggregate planning, duality theory is used to measure the validity of existing plans. Distributed models are integrated to ontinuously monitor and update model parameters. Several examples are provided to illustrate how the dynami data-driven planning and ontrol framework an signifiantly improve manufaturing performane. Keywords: Prodution Planning, Real-time Control, Hierarhial Control INTRODUCTION. Bakground and Motivation Modern prodution planning and ontrol integrates many interating large-sale dynami systems. For many supply networks, the omplete system is too omplex for detailed omputational and mathematial analysis. The behavior of suh system networks depends on their linkages and the external environment. Sientifi redutionism, the dissetion and analysis of the individual omponents, is inapable of fully defining behavior. In this paper we fous on hierarhial prodution planning and ontrol in disrete manufaturing system networks. Modern disrete manufaturing systems operate under omputer ontrol and may enompass thousands of proess tools, simultaneous prodution lots, and workers. The system typially spans multiple organizations through the supply hain but must meet stringent ustomer expetations to remain ompetitive. Logistial supply networks, whih soure and deliver globally, may engage many interdependent orporate partners, with hundreds of loations, dozens of transportation partners, thousands of in-transit shipments, and expetations for quik response and minimal in-transit inventory. These appliations are typially haraterized by hierarhial ontrol and horizontally, interdependent omponents (federates). The dynami environment requires the whole or sub system(s) to respond adaptively to hanges. Dynamis is a key element for omputing and ommuniations in a modern manufaturing system. For example, automated guided vehiles (AGV) urrently deployed in modern manufaturing systems are equipped with an on-board miroproessor that helps vehiles ommuniate with eah other, and with a entral materialhandling (dispathing) omputer. These vehiles transport raw materials, sub-assemblies, and tooling devies from various loading loations to various unloading loations throughout the faility. As prodution for the existing orders is omplete and new orders with different produt mix arrive, the map of the travel requirement evolves during its operations. At a higher level, GPS systems on truks an trak the arrival of materials. With the minimal inventory stoks and safety lead times required to be ompetitive and responsive to ustomer demands, the status of stok in transit ould signifiantly impat the job order release strategy and priorities for the faility. In a typial hierarhial system (Albus et al. []; Jones and MLean [2]; Joshi et al. [3]; Senehi et al. [4]; Cho and Wysk [5]; Askin and Goldberg [6], Cho et al. [7]), sensors at the base level provide data for planning ontrol ations and for verifying ommand exeution. In this dynamially hanging environment, distributed omputing solutions must view the manufaturing system as a dynami entity and oordinate deisions at multiple sale levels. This requires ontinual and timely updating of its sensor, ommuniations and ontrol systems. Moreover, the models that support the simulation, ontrol and management funtions must also respond to observed hanges. Suh dynami environments present new hallenges for distributed omputing and deision making in networked sensor and multi-sale deision systems, and provide the impetus for this researh. Prodution planning and ontrol systems are naturally hierarhial forming a tree struture with eah level enompassing a different time sale and setting goals/onstraints for the lower levels. A typial five level system (see Figure ) would involve ) Strategi Planning with a planning horizon measured in years to selet operating failities (loation and apaity), produt lines, and prodution tehnologies; 2) Aggregate Planning setting monthly levels for workfore, inventory, and prodution by produt family; 3) Disaggregation setting weekly prodution goals for produts as desribed in a master prodution shedule; 4) Prodution Sheduling defining order releases and job priorities daily; and 5) Shop Floor Control to handle details of job status, labor reporting, material handling, and tooling. As we desend eah level of the hierarhy, prodution goals and resoure availabilities are provided from above and detailed plans are onstruted for eah organizational unit. For example, the strategi plan will inform eah faility what resoures are available to meet the antiipated produt type demands for whih it is responsible. Eah faility will then

2 Partners in supply network Market Foreasts Finanial Plans Corporate Strategy Tehnology Foreast Strategi Planning Failities; Produt Families; Tehnologies Aggregate Planning Master Sheduling (per faility) Prodution Level; Workfore; Inventories Master Sheduling (per faility) Produt Engineering Operational model Manufaturing Engineering Prodution Sheduling (per workenter) Shop Floor Control MPS/Assembly Shedule Prodution Sheduling (per workenter) Job Priorities; Mahine Shedules; Order Releases Math Programs Heuristis Deision Rules AMHS model Real-world Figure 2: Diret and offline data appliation and integration Materials Job Status Report; Labor Report; MH Exeution; Operations Produts Figure : Prodution planning and ontrol hierarhy ompute an aggregate plan for the next several months using best estimates of time-phased demand. The aggregate plan will separate out the produt types into multiple families and resoures into more speifi resoure types, keying on potential bottleneks and expensive proesses. Prodution sheduling time phases dependent orders through finite apaity proessors. While strategies for oordinating between levels have been proposed over the past thirty years (Hax and Meal [8]; Bitran et al. [9]; Graves [0]), researh has been limited in this area and tended to assume stati, rigid strutures with signifiant setup osts leading to infrequent and often fixed interval setups. Askin and Goldberg [6] disuss ontinuous disaggregation with multiple setups per produt per period. Replanning frequenies (Wu et al. []) and dynami dispathing prie-direted models (Roundy et al. [2]) have been onsidered for disruption management, but models for ontinuously monitored replanning and oordination in integrated hierarhies faing dynami events are needed. In a dynami environment, performane of a distributed omputing system depends on its ability to observe hanges, and make deisions to adapt to those hanges without generating unintended disruption ripples. From an abstrat point of view, suh systems may be oneptualized as onsisting of a large number of automatons that sense the environment, ommuniate with eah other, and as a group, perform tasks that meet desired performane goals. To ahieve overall produtivity goals, omputerized vehiles and sensors in a manufaturing system monitor their surroundings, and ommuniate data among themselves. Some of the sensors provide spatial and topographial data (e.g. loation, distanes, speeds et.), whereas others provide environmental data (e.g. temperature, humidity affeting produt quality) and mahining proess data (e.g. vibration, pressure, fore, and temperature). As operations proeed, suh data reflets the environmental hanges, whih in turn should ause the overall system to adapt its model and prodution plans/shedules to suh hanges. By ombining data from eah automaton, the manufaturing system must determine a sequene of ations suffiient to produe produts to meet quality requirements in the most produtive way. The overall sheme envisioned is a multi-sale federation of models that support planning and ontrol deisions as shown in Figure 2. Planning and ontrol models are updated both diretly from real-world sensed data and from simulations. While the real world may yield parameters suh as urrent osts or inventory status, the simulation or analytial model, in synhronization with other federates representing the other entities in the prodution and supply network, will be used to ompute more omplex model parameters suh as lead times and effetive resoure availabilities. In addition the supporting models will be used off-line to test the performane of various proposed deision rules/algorithms and guide the seletion of model onstrution and seletion at eah replanning instane. Replanning will our when a defined threshold of disordane between atual observation and model form used to onstrut the ative plan is reahed. This researh an be viewed as exploiting the value of data aquisition and information sharing at multiple sales. The value of information sharing at the upper levels of the planning hierarhy has previously been studied in several ontexts for prodution systems. For planning oordination, Lee et al. [3] desribe the types of information that an shared and why eah may be useful. Gavirneni [4] and Gavirneni et al. [5] show for a two stage supply hain that information sharing is valuable when apaity is high, and demand variane, setup and shortage osts are low. The bullwhip effet (Lee et al. [6]) is known to be strongly affeted by information sharing, lead times, and foreasting methods. Coordination in global supply hains is disussed in Lee and Billington [7]. In this paper we examine the value of using real-time data on the status of a prodution system to drive the prodution planning and operational ontrol deisions in a dynami, stohasti environment. We assume an environment where produts are produed to foreasted demand with onsideration of prodution apaities and ost. Traditional hierarhial prodution planning onstruts aggregate prodution plans on a fixed rolling horizon basis whih are then broken down into a master prodution shedule defining subperiod prodution levels of end items. This is followed by use of dependent demand based materials requirements planning (MRP) explosion using fixed lead times to shedule order releases. While in MRP the order releases may be updated on an on-going net hange basis, this normally applies only to transation updates. Parameters suh as lead times and the produtivity estimates used in apaity planning and for shop order releases are treated as fixed. Total prodution

3 9 th International Conferene on Prodution Researh effort is oordinated to math the prodution plan. Moreover, there is no diret linkage upward to determine when the aggregate plan has beome invalid or when the master prodution shedule is likely to be invalid due to urrent shop performane. It should be noted that while for the sake of disussion in this paper we assume an MRP environment, pull ontrol systems also require seletion of parameters suh as lead times in order to set kanban levels and thus suffer from similar onerns (Monden [8]). We propose a new bi-diretional real-time planning and ontrol strategy that inorporates dynami, real-time data to dynamially determine replanning frequenies and projeted shop outomes. In the dynami system, weekly prodution levels are traked and adjusted based on atual demand. The monthly plan is maintained in priniple as long as atual demand and shop performane remain within the limits allowed for optimality ranges for the urrently ative plan. However, duality information is used to update the weekly plan (as a fration of the monthly plan) based on the hange to the right hand side demand value. One a range is exeeded, the model is rerun and the plan updated for determining future order releases. On a more fundamental level, state dependent lead times are ontinuously traked and used to ditate the timing of order releases. Two approahes are explored using real-time shop data. In the first, urrent loadings and planned progressions of work-in-proess are used to projet flow through the faility using antiipated availability fators. In the seond, utilization data is used along with a queueing model to predit lead times. The potential improvement from using real-time data with eah approah is demonstrated for a small test faility. In the following setion we elaborate on the model framework. Setion 3 provides examples to demonstrate the importane and performane of the framework. 2 MODELING INNOVATIONS Planning is typially performed using a stati view with possibly a deterministi estimate of future events. Thus plans have a limited range for whih they are appropriate. With dynami, ontinuous sensing, we an maintain an aurate world view at the detailed level and ompare that to planning assumptions. For aggregate planning we propose to use linear programming. Linear programming has a well-developed theory for sensitivity analysis and optimality ranging (Winston [9]). By monitoring we an quantify the distane drifted towards range limits aross the aggregation of variables and parameters. Foreasting models an be used to trak parameters and used to predit points in time at whih the limits will be exeeded. By likewise traking shop status with sensors, future events an be predited. Thus we an estimate the duration of impat of speifi ations suh as the release of a job to the system or the sheduling of a job on a mahine. The foreast ould then be used to predit whether the ation would remain optimal throughout the time period of its diret impat. This information an be inorporated into the operational level to determine if ations are likely to be optimal in a dynami environment and not simply from the urrent stati view. Likewise, these preditions an imply when replanning is likely to be neessary and an initiate replanning to aommodate the use of models too sophistiated for real-time implementation. 2. Aggregate Planning To visualize the dynamially ontrolled hierarhial system to be developed, onsider the following situation. A linear programming model provides monthly aggregate plans for produt family prodution that is subsequently broken down into weekly prodution goals by end item through a master prodution shedule (MPS). Instead of fixed lead times being used for order releases, system dynami stok levels and prodution rates are maintained in the planning data base for eah workenter through dynamially data-streamed performane data. These levels are ontinuously updated based on atual shop events as reported by mahine and labor reporting sensors. Atual instantaneous and smoothed throughput rates (performane) for workenters are monitored and ompared to resoure produtivity parameters used in the linear program. When resoure effetiveness, availabilities, or servie ommitments range outside the allowable limits for the LP solution, the model is rerun. If the ost of the existing solution under the urrent parameter values differs from the new optimal by more than a threshold value set for shedule disruption, then the new solution is adopted and filtered down to the MPS level subjet to urrent operations and inventory status. Consider the following generi linear programming model for multiprodut, multiperiod aggregate prodution planning. The firm produes produts based on sales foreasts and apaity onstraints. Final produts i =,,n are assembled from manufatured omponents j =,, J. We use the notation: a ji = number of units of omponent j needed per unit of produt i; L U Dit, D it = minimum and maximum sales limits respetively for produt i in period t; h i = holding ost per unit of i per period; p = selling prie of item i; i r ik, r jk = amount of resoure k required per unit of item i and omponent j respetively; R kt = regular time level of resoure k available in period t; w k = overtime ost per hour for resoure k; M = prodution limit of j in t based on material availability. Deision Variables: Iit ( I ) = end of period t inventory for produt i (omponent j); S it = planned sales of produt i in period t; O kt = planned overtime hours at resoure k in period t; X it ( X ) = planned prodution of produt i (omponent j) in period t; T n n J K Maximize p S h I h I w O subjet to: L U it it it [] i it i it j k kt t= i= i= j= k= D S D i =,..., n; t =,..., T [2] Iit = Ii, t + Xit Sit i =,..., n; t =,..., T [3] n I = I j, t + X aji Xit ; j =,..., J; t =,..., T i= [4]

4 n J ik it jk kt kt i= j= r X + r X R + O ; k =,..., K; t =,..., T [5] X M ; j =,..., J; t =,..., T [6] All Vars 0 Equation [] maximizes profit equal to revenue minus inventory holding ost and overtime wages. Demand limits are speified in Equation [2]. Demand limits may onverge, but we allow for the possibility of fixed minimum ommitments and sales opportunities. Inventory balane onstraints for produts and omponents are stated in Equations [3] and [4] respetively. Equations [5] and [6] restrit prodution based on available resoures. A solution to the model defines planned prodution levels, inventory levels, and overtime for the planning horizon. Purhasing may rely on these values to obtain raw materials and supervisors plan shift shedules aordingly. Numerous parameters are likely to hange during the planning horizon. Suppose for instane the market hanges and demand for produt i is redued and the prie is lowered. Should the model be rerun immediately or wait until the next regular interval? Consider first the prie. Duality theory provides an answer. By priing out the updated redued ost of the olumns for the X it variables it is easy to determine if the solution is still optimal or additional pivoting is required to update the basis. Regarding the hange in maximum demand, feasibility is tested and the dual simplex applied if neessary. A major failure of a mahine enter would translate to a hange in R kt for one or more periods. Again, feasibility of the urrent solution basis is easily heked and the dual simplex applied to update the solution if neessary. Yield problems are likewise readily managed. Suppose it beomes apparent during the period that the prodution of ' good units of omponent i will only be X i instead of the originally planned X it. The restrition is added and the model updated. Note that in our framework, during the period inventory values are automatially updated as workenters report job ompletions and resoure availabilities are also updated based on onsumption or the passage of time. 2.2 Order Release Exeution A key deision is order release and a primary determinant of this deision is lead time. This is true whether authorization is through an MRP (Material Requirements Planning), CONWIP (Constant Work in Proess) with order prioritization, Kanban with ontrolled setting of ard levels, or some hybrid system. Working bakwards from assembly/test/shipping shedules as defined in the MPS, orders are sheduled for release and priorities are set for dispathing at workenters. Estimated lead times are maintained using urrent loads, performane (queue learane) rates and job priorities. Virtual queues that inlude work destined for a workenter are used in this estimation. Queueing models an be used for eah workenter and job priority ombination to estimate throughput time. For instane, for a servie time S p and arrival rates λ p for an order of priority p, expeted time in the workenter an be estimated by (see Askin and Standridge [20]) 2 λp ES ( ) p ET ( p) = ES ( p) + 2[ ρp ][ ρp] [7] where ρ p is urrent workenter utilization from jobs with priority p or higher. Alternatively, flow rate models based on numerial integration of stok levels an be used. The parameter values in these models an be ontinuously updated using data streamed on atual servie time distribution and arrival rates. Varianes an likewise be estimated to provide the desired level of safety lead time. Downtime distributions will also be maintained based on lass (seriousness) of ause and inorporated into the model. When any of the required resoures is down, the orresponding queue learane rate drops to zero. A generalized version maintains an effetiveness parameter for modeling slowed performane. As with the aggregate planning stage, when learane rates differ signifiantly from those assumed in the onstrution of the MPS, a new MPS will be omputed to provide a realisti plan. Note that for an M/M/ queue, the queue length is geometrially distributed with parameter ρ. Thus, throughput time in the system is the sum of a geometrially distributed number of exponential random variables (the exponential being derived from the servie times). Release times an be based either on a detailed projetion of in-proess jobs through the workenters to estimate ompletion times for eah job (effetively onstruting a Gantt hart with possible allowanes for future random ourrenes), or release times ould be based on queueing approximations using the urrent shop loadings. Our approah admits both alternatives along with weighted ombinations. 3 MODEL EVALUATION To illustrate the proposed planning and ontrol strategy we ompare the performane of a traditional fixed lead time, periodi replanning strategy to a real-time, data-driven, progression foreasting approah. The test faility is a small shop with two fabriation workenters that feed omponents to an assembly area. The faility produes three finished produts from five basi omponents. The Bill of Materials and operation times are shown in Tables and 2. The faility operates 0 hours per day. Demands are Poisson distributed with means for items, 2, and 3 of 0, 0, and 4 respetively per day. Eah week is five days, and eah month is four weeks. Table. Bill of Material Struture Requirements (units per unit) Produt A B C D E Table 2. Operational Times (Workenter; Days per Unit) Item Operation Operation 2 A (WC; 0.02) B (WC; 0.0) C (WC; 0.02) (WC2; 0.02) D (WC2; 0.0) E (WC2; 0.0) Assembly; Assembly; Assembly; 0.04

5 9 th International Conferene on Prodution Researh Eah workenter breaksdown on oasion aording to an exponential failure and repair rate. Mean times to failure and repair in hours are (0, 0.5); (5, 0.2) and (40, 2) respetively. 3. Aggregate Planning The traditional system works as follows. Prior to the start of the month a linear programming model is run to determine the planned prodution quantities of eah produt during the next month. The planning horizon for the LP is three months. Months orrespond to four weeks and the master prodution shedule is set to produe one fourth of the month s prodution for eah produt, eah week. Using average utilizations and arrival rates and the assumption of exponential queueing performane, jobs are sheduled to be released to ensure 99% hane of on-time ompletion. The system is evaluated based on ost and servie level using a simulation model. Inventory osts are omputed based on end of day inventory levels for eah item. Holding osts are harged at a rate of per day times the inventory value. Item values are $50/hr times standard unit prodution times. In the dynami system, weekly prodution levels are adjusted based on atual demand. The monthly plan is maintained as long as atual demand and shop performane remain within the limits allowed for optimality ranges on the LP parameters. One a range is exeeded, the model is rerun and the plan updated for determining future order releases. State dependent lead times are ontinuously traked and used to ditate the timing of order releases. To test the dynami data-driven approah, two simple senarios were tested overing a hange in demand produt mix and a hange in resoure availability. In addition to the data desribed above, workenters were osted at $50/hour for regular time and $60/hour for overtime. A penalty for late shipments was set at 0 times the daily inventory holding ost rate. Results reported below are based on averages over 00 repliations with eah repliation being three months. A linear programming model was used for planning prodution levels. Atual shop performane and osts were omputed with a disrete event simulation model that traked part flows, inventory levels, and daily osts. In the first senario, the produt mix hanged at the start of week five. Instead of daily demand averaging 0, 0, 4 units respetively for the produts, mean demands beame 5, 0, 6. Traking demands, the dynami system was able to update the optimal LP plan and issue new prodution goals. The result was fewer bakorders, lower inventory osts, and lower overtime osts. Average profit for the three month horizon inreased 0% from $3,84. with the stati system to $34,227 for the dynami system. In the seond senario, workenter one slows up to 70% of its previous prodution rate at the end of the fifth week. In this ase the dynami model deteted the resoure onstraint and was able to realloate apaity to omponents to minimize profit impliations. The dynami system inreased average profit by 3.3% from $30,365 to $3, Order Releases We an model the throughput time in the system as an open queueing network (see Askin and Standridge [20]). For this M/G/ system at eah work station, the variane of throughput time at a workstation is given by λes ( ) λ ES ( ) VT ( ) = VS ( ) ( ρ) 4( ρ) 2 [8] where S is the servie time, λ the arrival rate and ρ the utilization. Using the data above, the performane statistis for the three workstations an be omputed as shown in Table 3. To avoid shortages we release parts with a three standard deviation slak in the ase of the traditional approah. Equivalently we ould view this as maintaining a safety stok suffiient to over the planned maximum lead time demand. For this instane we assume the arrival proess at the assembly station is approximately exponential. A more aurate model ould be used by inorporating the linear interation equations desribed in Buzaott and Shanthikumar [2] for diretly modeling the onnetion of assembly to the fabriation workstations. Table 3. System Performane Charateristis WS WS 2 Assembly E(S) E(S 2 ) E E λ ρ V(S) 0.226E E E-4 V(T) E(T) The flowtime varianes for the omponents are found by aggregating over their flow paths for workstations and/or 2. For produts and 2, omponent C plus assembly defines the ritial path with high probability sine C visits both workstations. For produt 3, omponent A plus assembly defines the ritial path upper bound sine workstation has higher mean and variane than workstation 2. Thus the standard deviation of the longest path in the bill of materials for produts, 2, and 3 are estimated as (0.5642, , ) days respetively. Using a 3 standard deviation safety lead time to avoid shortages, this means all produts would have to be released with a planned ompletion date of approximately.7 days prior to foreasted demand. Using this release rule and the inventory holding ost parameters given above, we an ompute the exess WIP ost inurred due to use of a stati lead time. If h i is the holding ost rate per day, D i is the daily demand rate and T is the exess inventory storage time in days, the exess daily WIP ost for our system is Exess Daily WIP Cost = ED ( ) h T 3 i= H i i i 0 0 = ( )*$.20*0.94 day + ( )*$.20*0.94day day day 4 + ( ) *$.22 *0.96 day = $4.6. day This serves as an upper bound on savings from WIP inventory alone if we an use state-dependent information to release parts just-in-time. The example is small and thus the atual savings bound appears small in absolute terms but note that this is daily ost and represents 55% of the total WIP ost. Note that in either system we may arry safety stok to guard against high demand periods. While it may seem that the first model aounts for demand variation by virtue of the safety lead time, it is preisely when demand is high that lead times will inrease. Thus, these are very highly orrelated and the safety stok would still be neessary. Sine this is true in both systems, we exlude this ost from the omparison. H i [9]

6 4 SUMMARY AND CONCLUSIONS We have seen that traditional prodution planning and inventory ontrol systems build in signifiant slak due to variability and are sluggish in the fae of dynami events. This is due at least in part to the lak of real-time information. In a test senario, use of real-time data-driven traking and replanning improved profit by 0% for a hange in produt mix and 3% for a hange in available apaity. Also for the sample problem the safety time slak required when using stati flow time estimates aounted for over 50% of the work-in-proess inventory ost. By using real-time information on shop status to ontrol produt releases, the potential exists to greatly redue ost and improve servie. Future researh will further define the opportunities for information to improve performane and redue ost and to more ompletely determine the atual potential savings. 5 ACKNOWLEDGMENTS This material is based upon work supported by the National Siene Foundation under Grant No REFERENCES [] Albus, J. A. Barbera, N. Nagel, Theory and pratie of hierarhial ontrol, in Proeedings of the 23rd IEEE Computer Soiety International Conferene, Washington D.C., 98, [2] Jones, A., and C. R. Mlean, A proposed hierarhial ontrol model for automated manufaturing systems, Journal of Manufaturing Systems, vol. 5(), 5-26, 986. [3] Joshi, S., R. Wysk and A. Jones, A saleable arhiteture for CIM shop floor ontrol, in Proeedings of Cimon '90, A. Jones Ed., National Institute of Standards and Tehnology, 990, [4] Senehi, M., E. Barkmeyer, M. Lue, S. Ray, E. Wallae, and S. Wallae, Manufaturing systems integration initial arhiteture doument, National Institute of Standards and Tehnology, NIST Iterageny Report NISTIR 4682, Gaithersburg, MD, 99. [5] Cho, H., and R. A. Wysk, Intelligent workstation ontroller for omputer-integrated manufaturing: problems and models, Journal of Manufaturing Systems, vol. 4(4), , 995. [6] Askin, R. G. and J. B. Goldberg, Design and Analysis of Lean Prodution Systems, John Wiley & Sons, 2002, New York. [7] Cho, H., Son, Y., and Jones, A., Design and Coneptual Development of Shop Floor Controllers through the Manipulation of Proess Plans, International Journal of Computer Integrated Manufaturing, 2006, 9(4), [8] Hax, A. C. and H. C. Meal, (975), Hierarhial Integration of Prodution Planning and Sheduling, M. Geisler (ed.) TIMS Studies in Management Siene, Logistis, North-Holland, Elsevier, NY. [9] Bitran, G. R., E. A. Haas, and A.C. Hax, Hierarhial Prodution Planning: A Single State System, Operations Researh, 29(4), 98, Askin, R. G. and C. Standridge, Modeling and Analysis of Manufaturing Systems, John Wiley & Sons, 993, New York. [0] Graves, S. C., Using Lagrangian Tehniques to Solve Hierarhial Prodution Planning Problems, Management Siene, 28, 982, [] Wu, S. D., E. Byeon, and R. H. Storer, A Graph Theoreti Deomposition of the Job Shop Sheduling Problem to Ahieve Sheduling Robustness, Operations Researh, 47(), 999, [2] Roundy, R., W. Maxwell, Y. Herer, S. Tayur, and A. Getzler, A Prie Direted Approah to Real Time Sheduling of Prodution Operations, IIE Transations, 23, 99, [3] Lee, H. L., P. Padmanabhan, and S. Whang, Information Distortion in a Supply Chain : The Bullwhip Effet, Management Siene, 43, 997, [4] Gavirneni, S., Information Flows in Capaitated Supply Chains with Fixed Ordering Costs, Management Siene, 2002, 48, [5] Gavirneni, S., R. Kapusinski, and S. Tayur, Value of Information in Capaitated Supply Chains, Management Siene, 45, 999, [6] Lee, H. L. K. C. So, and C. S. Tang, The Value of Information Sharingi in a Two-Level Supply Chain, Management Siene, 46, 2000, [7] Lee, H. L. and C. Billington, The Evolution of Supply Chain Management Models and Pratie at Hewlett- Pakard, Interfaes, 25, 995, [8] Monden, Y., Toyota Prodution System, Engineering and Management Press, 998. [9] Winston, W. L., Operations Researh : Appliations and Algorithms, Brooks/Cole, Belmont, CA, [20] Askin, R. and C. Standridge, Modeling and Analysis of Manufaturing Systems, John Wiley & Sons, New York, 993. [2] Buzaott, J. and J. Shanthikumar, Models for Understanding Flexible Manufaturing Systems, IIE Transations, 2, 980,