Inner And Outer Loop Optimization In Semiconductor Manufacturing Supply Chain Management

Transcription

1 CMS manuscript No. (will be inserted by the editor) Inner And Outer Loop Optimization In Semiconductor Manufacturing Supply Chain Management Wenlin Wang Daniel E. Rivera Hans D. Mittelmann Received: date / Revised version: date Abstract Supply Chain Management (SCM) in semiconductor manufacturing differs from many other SCM applications in that it has to simultaneously consider both long and short time scale stochasticity and nonlinearity. We present a two-level hierarchical structure for SCM motivated by these considerations. A Linear Programming (LP)-based Strategic Planning module forms the outer loop which makes long timescale decisions on the starts of factories. A Model Predictive Control (MPC) based Tactical Execution module forms the inner loop which generates short timescale decisions on the starts of factories by considering the stochasticity and nonlinearity on both supply and demand sides. Two representative case studies are examined under diverse realistic conditions with this integrated framework. It is demonstrated that given conditions of stochasticity, nonlinearity, and forecast error this hierarchical decision structure can be tuned to manage representative semiconductor manufacturing supply chains in a manner appealing to operations. Keywords semiconductor manufacturing, supply chain management, model predictive control, linear programming, strategic planning, tactical execution, hierarchical decision-making 1 Introduction Supply chain management (SCM) and other similar terms, such as network sourcing, supply pipeline management, value chain management, and value stream management have become subjects of increasing interest in recent years, to academics, consultants and business management [1 3]. The reasons why supply chain management is important are money and opportunity. In the US about 10% of gross domestic product, or almost $1 trillion, is spent on supply chain activities. Advances in Information Technology (IT) and expanding IT infrastructure are introducing new possibilities to improve service and efficiencies, and given the amount of money at stake, the opportunities are high [4]. Given the global supply-demand network that operates around the clock each day of the year, the resulting decision problem can be described as a continuous nonlinear stochastic combinatorial financial optimization This work was supported by grants from the Intel Research Council and the National Science Foundation (CMMI ). W. Wang Department of Chemical and Materials Engineering, Arizona State University, Tempe AZ USA wenlin.wang@freescale.com Present address: Computer Integrated Manufacturing Group, Freescale Semiconductor Inc., Chandler, AZ D.E. Rivera Department of Chemical Engineering, Arizona State University, Tempe AZ USA daniel.rivera@asu.edu H.D. Mittelmann Department of Mathematics and Statistics, Arizona State University, Tempe AZ USA mittelmann@asu.edu

2 2 [5]. Considering the scale of international supply-demand networks, the difference between an optimal and a non-optimal solution can be worth many hundreds of millions of dollars per year. For example, in the case of Intel Corporation with roughly 30B$ in annual revenue from its network, a 3 1/3% improvement in operations as a result of improved SCM results in an additional 1 B$ per annum [5]. SCM in semiconductor manufacturing differs from other areas in long throughput time, high stochasticity and nonlinearity in manufacturing processes. There are many approaches to building strategic plans to effectively operate complex supply chains [6]. The most sophisticated utilize some form of mathematical optimization, often Linear Programming (LP) [7, 8]. Considering the capacities, constraints, throughput times, and customer demand, the resulting plan specifies the material release from warehouse into factories and transport links over multiple future weeks and months. These strategic planning systems are very useful, however as deterministic algorithms it is very difficult to include the unavoidable stochasticity of supply and demand in semiconductor manufacturing into LP-based optimizers. Recent progress in multi-echelon inventory theory can act as adjuncts to the LP optimizers used for strategic plan construction [9, 10]. Given target service levels, estimates of future supply and demand uncertainty, and historical forecast bias and error, these inventory algorithms compute safety stock positions and targets to be used as inputs to the LP optimizers. This safety stock is intended to buffer the expected variability in both supply and demand while executing the LP-generated multiperiod plan. In common supply chain practice, such planning-with-safety-stock hybrids can be utilized on a weekly basis [5]. Unfortunately, the stochastic processes driving the supply and demand variability operate in very short time scale. To respond to the stochastic processes properly to get reduced levels of safety stock with lower supply chain costs and improved levels of delivery performance generating higher revenue, some decisions must be made on much shorter timescales. In this paper, we focus on simultaneously managing both long and short timescale stochasticity and nonlinearity in semiconductor manufacturing supply chains through a novel optimal decision structure. Our emphasis is specifically on the interplay between the strategic planning and tactical execution modules, and assume for the sake of simplicity that inventory targets are provided exogenously to these modules. In addition to using LP to generate strategic decisions, an advanced process control technique, Model Predictive Control (MPC) is used to generate decisions on daily bases so that short timescale stochasticity and nonlinearity can be properly addressed. The integrated hierarchical structure made of LP and MPC can give a better solution than LP-only based methods in that it can make the optimal decisions on factory starts depending on the properties of the manufacturing and demand variability and nonlinearity. The approach described in this paper relies on splitting the decision problem into a strategic planning function and a tactical execution function, as shown in Figure 1. The former can be thought of as an outer loop controller that considers business goals and trends over weeks, months and quarters into the future, the latter as a companion inner loop controller that manages day to day operations providing the network with responsiveness and agility. MPC, an advanced process control technique widely used in industry to handle multivariable systems with constraints, is a powerful tactical execution tool with the flexibility to handle the short-time scale stochasticity and some specific features in manufacturing processes. In this paper, we will present the formulation of a two-level hierarchical structure with an outer loop using LP and an inner loop using MPC. The objective function and constraints are derived to maximize the profits and meet the manufacturing requirements. We use a basic problem with backlog as an example and show simulation results demonstrating how to effectively integrate LPs with MPC controllers. The insights provided from these simulations are the scalability and capability of LP and MPC. LPs can deal with large scale problems, while QP-based MPC is more computationally demanding, with large number of decision variables and potentially requiring distributed real-time calculations. Inventory planning is a key component in this architecture which provides the inventory target levels for the tactical and strategic planning modules. The interaction between all three modules represents an open problem in the literature; however, as noted previously we will assume in this work that the inventory targets are provided exogenously. Additional information and insights on the formulation of inventory planning module for the semiconductor manufacturing problem can be found in [13].

3 3 The paper is organized as follows. In Sections 2 and 3, the MPC-based tactical inner loop and LP based strategic outer loop formulations are presented, respectively. Section 4 and 5 describe the simulation results involving stationary demand with and without forecast error. Section 6 concludes the paper with some observations and future directions. Fig. 1 Proposed two-level hierarchical decision architecture. 2 Model Predictive Control Based Tactical Inner Loop Formulation Model Predictive Control (MPC) stands for a family of methods that select control actions based on on-line optimization of an objective function. MPC has gained wide acceptance in the chemical and other process industries as the basis for advanced multivariable control schemes [11, 12]. In MPC, a system model and current and historical measurements of the process are used to predict the system behavior at future time instants. A control-relevant objective function is then optimized to calculate a sequence of future control moves that must satisfy system constraints. The first predicted control move is implemented and at the next sampling time the calculations are repeated using updated system states; this is referred to as a Moving or Receding Horizon strategy. MPC represents a general framework for control system implementation that accomplishes both feedback and feedforward control action on a dynamical system. The appeal of MPC over traditional approaches to feedback and feedforward control design include 1) the ability to handle large multivariable problems, 2) the explicit handling of constraints on system input and output variables, and 3) its relative ease-of-use. MPC applied to supply chain management relies on dynamical models of material flow to predict inventory changes among the various nodes of the supply chain. These model predictions are used to adjust current and future order quantities requested from upstream nodes such that inventory will reach the targets necessary to satisfy demand in a timely manner. Applications of MPC to multi-echelon production-inventory problems and supply chains have been reported in the literature [14 18]. The unique characteristics of semiconductor manufacturing supply chains merit the development of a novel MPC algorithm for this purpose [20]. The objective function of the MPC controller is as follows:

4 4 where the individual terms of J correspond to: min J (1) u(k k)... u(k+m 1 k) Keep Inventories at Inventory Planning Setpoints { }} { p J = Q e(l)(ŷ(k + l k) r(k + l)) 2 2 l=1 Penalize Changes in Starts { }} { m + Q u (l)( u(k + l 1 k)) 2 2 (2) l=1 Maintain Starts at Strategic Planning Targets { }} { m + Q u(l)(u(k + l 1 k) u target (k + l 1 k)) 2 2 l=1 Here p is the prediction horizon and m is the control horizon. ŷ(k) is the vector of the predicted inventory levels at time k, while r(k) is the corresponding reference vector for inventory targets. u, u and u target are vector-valued quantities representing the starts, the rate-of-change of starts and the starts targets, respectively. Q u, Q u, Q e are penalty weights on the control signal, move size and control error, respectively; the selection of these weights enables the user to trade-off the ability of the algorithm to satisfy inventory setpoint targets, adjust starts variability, and maintain starts close to strategic planning targets that may be supplied by an outer loop module (per Figure 1). To properly interact with the strategic outer loop, the tuning parameter Q u has to be selected based on the customer demands and manufacturing stochasticity. The integrating nature of the dynamics must be considered when formulating control algorithms, as well as the presence of some unique constraints. The problem benefits from a flexible controller formulation that enables independent tuning of measured disturbance rejection (meeting forecasted demand), unmeasured disturbance rejection (satisfying unforecasted demand) and inventory setpoint tracking. A multi-degree-of-freedom MPC controller algorithm is designed to satisfy these requirements. The three filters used to address different disturbances are as follows: Inventory Targets Tracking: A Type I filter is specified here: f r j (z) = (1 α I j )z z α Ij, j = 1,, n r. (3) n r is the number of inventory targets and α Ij is the tuning parameter corresponding to the j th inventory target. z refers to the Z-transform [19]. Measured Disturbance Rejection: A Type II filter to address disturbances with integrating dynamics has the following form: f d j (z) = [(1 α II j ) α II j ] 1 5 α II j z α II j z 2 1 α IIj z 1, j = 1,, n d. (4) Here n d corresponds to the number of measured disturbances (customer demand for each product) in the system. Unmeasured disturbance rejection: A Type II filter is used in the optimal state estimator: X(k k 1) = ΦX(k 1 k 1) + Γ u u(k 1), (5) X(k k) = X(k k 1) + K f (y(k) ΞX(k k 1)), (6)

5 5 where K f is the filter gain matrix, defined as K f = 0 F b, (7) F a and F a = diag{(f a) 1,..., (f a) ny }, (8) F b = diag{(f b ) 1,..., (f b ) ny }, (9) (f b ) i = (f a) 2 i 1 + α i α i (f a) i for 1 i n y. (10) (f a) i corresponds to the adjustable filter gain parameter for each output channel and ranges between 0 and 1. n y is the number of outputs. The details of the derivation of this novel MPC controller can be found in [20,21]. 3 Linear Programming Based Strategic Outer Loop Formulation There are many ways to formulate the strategic planner, such as Dynamic Programming (DP) and Linear Programming (LP). In this section, we will consider an LP formulation which generates weekly starts targets to each factory. These weekly starts targets consider a one or two quarter demand forecast and serve as references to the inner loop MPC daily decision on starts. MPC generates daily starts by considering the short-time scale stochasticity, a shorter (one or two months) demand forecast and the targets provided by the outer loop. There may be some conflicts between the LP and MPC solutions to the starts depending on the actual customer demand, demand forecast, and factory capacity. The objective of strategic planning is to maximize profit while achieving robustness. The constraints consider inventory target tracking, capacity limits and backlog generation. Let p be the prediction horizon and t be the time index. The objective function of the strategic LP is as follows: max p Shipment t ASP t=1 30 i=10 t=1 p (Ovr i,t + Und i,t ) InvCost i 30 p BackOvr t Backcost t=1 f=10 t=1 p Starts f,t Movesup f (11) The constraints are t (t,t T P T ] Starts f,t Cap f, (12) Inv i,t = Inv i,t 1 + Starts f,t T P T Y ield f Starts f,t, (13) InvT ar i,t = Inv i,t Ovr i,t + Und i,t, (14) p Backlog t = (Demand t Shipment t ), (15) t=1 0 = Backlog t BackOvr t. (16)

6 6 Here the input variables are: ASP : Average sale price, InvCost i : Inventory holding cost for i, InvT ar i,t : Inventory target for i at t, BackCost : Backorder cost, Movesup f : Starts change penalty for f, Cap f : Factory capacity for f, Y ield f : Factory yield for f, Demand : Customer demand forecast. The decision variables are The indices are: Shipment t : Shipment for customer demand at t, Ovr i,t : Slack variable for possitive deviation from inventory target for i at t, Und i,t : Slack variable for negative deviation from inventory target for i at t, BackOvr t : Amount of backorders at t, Starts f,t : Change of starts for f at t. t : Time unit in days, f : Factory positions, i : Inventory positions, p : Prediction horizon. As one can observe here, the goal of the LP is to maximize the net profit by subtracting the inventory holding cost and backorder cost from the total revenues. However, the objective function does not have a rigorous dollar significance because of the term of starts change penalty. The reason for requiring this term is because the fab starts or inlet flow should be as smooth as possible. A large penalty must be enforced to achieve robustness or smooth inlet flow for fab, which is not as easy to define in dollar terms as inventory holding or backorder costs. Although we need to solve the optimization with the objective function as shown in (11), only the first three terms describe the net profit, while the fourth term is used for the sake of robustness. The constraints enforced in the LP include factory capacity and inventory target tracking. The inequality constraint in (12) is used to force the Work-In-Progress of each factory to be within the capacity limits. Work-In-Progress is calculated based on the average throughput time. Equation (13) represents the material balance for each inventory position. Equation (14) calculates the deviations from the targets, which are penalized in the objective function. Equation (15) and (16) are equations for the backorders forecast, which are also penalized in the objective function. Compared with MPC, the LP problem solved in the strategic module has a very similar formulation. Both are trying to generate starts to track the inventory targets and meet customer demand. The difference between them is the time scale. MPC considers daily demand, inventory targets and stochasticity, while LP considers everything in weeks. One significant distinction is that MPC has a sophisticated state estimator which helps to deal with the unmeasured disturbances, while the LP does not have a corresponding filter built into it. LP and MPC have different forecast horizons, which is usually a few quarters for the LP, and a few months for the MPC. These are the reasons why the LP serves as a strategic planner and MPC serves as a tactical controller. Both LP and QP problems are solved via LOQO which is an interior point method-based software package for smooth constrained optimization problems [22]. It can solve large scale problems with reasonable speed and accuracy. Since the LP described in Equations (11) - (16) is used as a strategic planner or controller, it will generate weekly starts. These weekly starts are not passed directly to the factories, but serve as the

7 7 targets for daily starts generated by MPC, evenly divided over 7 days. Next we will show how LP interacts with MPC using a basic three node problem described in Figure 2 as an example. We will examine two scenarios, which are stationary demand without forecast error and stationary demand with forecast error. All the scenarios are implemented as discrete time simulations in Matlab. 4 Scenario 1: Stationary Demand Without Forecast Error In this section, a fluid representation of a three-node semiconductor manufacturing supply chain (consisting of one fab/test1 (F/T1), one assembly/test2 (A/T2), and one finish node) and its corresponding inventory locations is shown in Figure 2. We will use this basic problem as an example to study the interaction between the strategic outer loop (LP) and the tactical inner loop (MPC). The simulation structure is shown in Figure 3. The parameters used for MPC are the same as shown in Table 1. Since the LP runs every week instead of every day, the parameters are changed accordingly. The parameters for LP are described in Table 2. In the MPC controller, the filter gain f a in Equation 9 is 0.15 for the disturbance state and the output weight Q e is 1 for all inventories. Move suppression Q u = 0 is used in the simulation. Fig. 2 Basic three-node supply chain problem. As discussed in Section 3, using an LP as a strategic controller generates weekly starts, which is simply the summation of 7 days starts for each factory. Also as shown in Section 2, MPC has the ability to

8 8 Fig. 3 Inner/outer loop simulation structure. Factory nodes M10 M20 M30 M40 load Min TPT (days) [0%,70%] Ave TPT (days) Max TPT (days) Distribution Unif Unif Unif load Min TPT (days) (70%,90%] Ave TPT (days) Max TPT (days) load Min TPT (days) (90%,100%] Ave TPT (days) Max TPT (days) Yield Min % Ave % Max % Distribution Unif Unif Unif Capacity Max Items 4.5E Inventory nodes I10 I20 I30 UCL(Items) 1.2E4 6E3 3E3 TAR(Items) LCL(Items) Max(Items) 2E4 1E4 1E4 Table 1 Manufacturing and inventory nodes data for basic problem with backlog: TPT refers to throughput time; Unif to uniform distribution; UCL to Upper Control Limits, TAR to Target, LCL to Lower Control Limits. track the targets on the manipulated variables. The third term in MPC objective function as shown in Equation (3) is for manipulated variables /starts targets tracking. By changing the weights Q u, we can decide how close the daily starts should be to the weekly starts targets. Adjusting these weights leads to the case studies as shown in Table 3. The simulation results for each of the case studies are presented and discussed in this section.

9 9 Factory M10 M20 M30 M40 TPT(Weeks) Yield 95% 98.5% 99% 100% Capacity 4.5E Inventory I10 I20 I30 Initial value Target Holding cost Average selling price $100/unit Backlog cost $5/unit Move suppression 5 Table 2 Parameters for strategic outer loop LP controller. Experiment description Parameter: Q u Case 1 Inner loop only [ ] Case 2 Outer loop only [ ] Case 3 Inner/outer loop interaction [ ] Case 4 Outer loop for Fab, inner loop for A/T and F/P [ ] Table 3 Inner/outer loop simulation case studies. 4.1 Case 1: Inner Loop Only When Q u is zero for each starts variables, only MPC solutions will be applied to each factory. At first, the filter gain, f a is set to be 0.15 for each disturbance state. The responses are shown in Figure 4. The starts are aggressive since the filter gain allows large error correction. If f a is reduced to 0.01, the responses are much smoother as depicted in Figure Case 2: Outer Loop Only When the weights Q u are large, daily starts generated from MPC will be the same as or very close to the targets provided by LP. So in this case, the results of using the combined inner/outer controller will be the same as using LP controller only. The simulation structure in Figure 3 can be simplified to describe this case as shown in Figure 6. The results are shown in Figure 7. Here Q u is 100 for each starts tracking. Compared to the results from MPC control only in previous chapter, LP control gives smoother starts for factories in terms of day to day change. The reason is that the weekly decision is based on the summation of 7 days demand forecast and the averaged demand forecast has smaller variance than daily demand forecast and daily starts are held constant for one week. Figure 8 shows the comparison between the LP starts and MPC starts. One finds that these are almost the same, since the weight Q u is large and MPC should track LP solution very closely. 4.3 Case 3: Inner/Outer Loop Interaction In this case, Q u is 10 which is an intermediate value compared to 100 and 0. So one should see that MPC solutions will track, but not exactly match, the LP solutions. The results are shown in Figure 9. The factory starts are more aggressive than those in the previous case, because the MPC algorithm tries to compensate the short time stochasticity by manipulating the daily starts. Figure 10 shows both MPC and LP solutions. One finds that MPC is trying to track the LP weekly targets and make its own daily decisions at the same time. The responses in this case are smoother than MPC control only, but more aggressive than LP control only. This shows the effects of interaction between the strategic planning and the tactical planning. MPC focuses on the daily stochasticity while LP considers the long time scale stochasticity. Since in this simulation demand is stationary, no forecast error exists and capacity is not a bottleneck, MPC only increases the variability on the responses while not improving the other performance at all. The frequency of running the MPC is faster than that of the LP, which

10 10 I I I30 Backorders Shipment&Demand Fig. 4 Inner loop only simulation results in Scenario 1 (Case 1): Q u = [0 0 0], f a = [ ]. introduces high frequency noise into the system. The aggressive responses can be smoothed by imposing large move suppression on starts or small filter gain on disturbance states. 4.4 Case 4: Partial LP and Partial MPC In semiconductor manufacturing, operating restrictions in the fab dictate that the starts in the fab should be as stationary as possible, while in the Assembly/Test (A/T) and Finish/Pack (F/P) nodes the starts can change aggressively to meet the customer demand as much as needed. This motivates the partial LP and partial MPC structure as shown in Figure 11 revised from Figure 3. The weights Q u are set to be [ ] for, and to achieve this structure. So LP solutions will be fed directly to the fab only and MPC will manipulate the starts of A/T and F/P. The results for this partial LP and partial MPC simulation are shown in Figure 12. One can find that fab starts are directly manipulated by LP, while A/T and F/P starts are manipulated by MPC only. The fab starts are smoother than the A/T and F/P starts. Figure 13 shows this three starts comparison between LP and MPC. 4.5 Observations From the simulation results examined in this section, one can observe that LP and MPC provide similar performance under these ideal conditions. Table 4 shows the variance comparison for starts in each

11 11 I I I30 Backorders Shipment&Demand Fig. 5 Inner loop only simulation results in Scenario 1 (Case 1): Q u = [0 0 0], f a = [ ]. Fig. 6 Outer loop only simulation structure. case. LP generates the starts based on the averaged demand forecast which is smoother than the daily demand forecast. The daily starts will not change during a week. MPC-only operation introduces high frequency noise into the starts signals when executing daily, compared to LP that executes weekly. The aggressive responses generated by MPC can be smoothed by tuning, which ultimately gives the best performance in this case. In this scenario, each case is shown to meet customer demand and track the inventory targets; the only difference lies in the variance of the responses. However, in the presence of forecast error, LP and MPC will perform differently; this will be studied in the next section.

12 12 I I I30 Backorders Shipment&Demand Fig. 7 Outer loop only simulation results in Scenario 1 (Case 2): Q u = [ ]. Variance Variance Variance Case 1(f a = 0.15) Case 1(f a = 0.01) Case Case Case Table 4 Inner/outer loop simulation case studies. 5 Scenario 2: Stationary Demand with Forecast Error In Scenario 1, the demand forecast did not have any bias error to the actual demand on average. In this section, a systematic 100 unit error is introduced in the demand forecast; that is, on average, the forecast will be 100 units more than the actual demand. We will consider three cases, LP only, MPC only and LP/MPC interaction, to compare the performance of both strategic and tactical planning. The simulation setup is still the same as described in Figure Outer Loop Operation Only First, only strategic planning is used in the presence of forecast error by choosing a large weight of Q u = 100. Figure 14 shows the responses and Figure 15 is the comparison of LP and MPC solution. One can find here that although no backlog is observed, there are large offsets for all three inventory positions. The LP formulation cannot detect these offsets and manipulate the starts to bring the

13 Fig. 8 LP and MPC solution comparison in Scenario 1 (Case 2): LP (solid line), MPC (dash line), Q u = [ ]. inventory levels back to targets. 5.2 Inner Loop Only Now we use only MPC for daily starts generation. The weight Q u is set to be 0, which signifies that LP decisions will not influence the simulation at all. The results are shown in Figure 16. In order to detect the forecast error and compensate the overshoot on inventory levels, the filter gain f a is set 0.15 in the MPC controller. Although the inventories still have some overshoot at the beginning, these come back to the targets later on without any offsets. Figure 17 shows both LP and MPC solutions. It is clear to see that MPC detects the offsets on inventories and decreases the starts, while LP cannot detect them and still keeps the starts at a higher level. In this case, the starts of all factories are more aggressive than for LP only control. However, there are no offsets observed on all inventories. 5.3 Inner/Outer Loop Interaction If the weight Q u is set to 10 for each start variable, the simulation begins to show some of the interaction between the LP and MPC. The results are shown in Figure 18 and Figure 19. When MPC starts to contribute, better performance is observed for all of the three inventories. Compared to LP only control, the offset is reduced but not eliminated.

14 14 I I I30 Backorders Shipment&Demand Fig. 9 Outer/inner loop interaction simulation results in Scenario 1 (Case 3): Q u = [ ]. 5.4 Partial LP and Partial MPC If Q u is set to be [10 0 0], LP decisions will influence for Fab/Test (F/T) starts, while the MPC controller will manipulate the starts for A/T and F/P. The filter gain f a is still The results are shown in Figure 20 and 21. In this case, the forecast error is considered to generate the fab starts, and the target from LP is also considered at the same time. MPC controller manipulates the lower level factory starts. It is clear to see that all of the inventories can track the targets at steady state. Compared to MPC only control in the previous simulation, I10 has a larger overshoot, while both I20 and I30 have a smaller overshoot than in MPC only control. Also the variances on starts, and in this case are smaller than those in MPC only control. 5.5 Observations When forecast error is present, the LP cannot detect it because it lacks a state error update in its formulation. Although the LP results in smoother responses for starts, it can not provide offset free control in this situation. MPC relies on a sophisticated filter for state estimation, which helps to detect the error between the forecast and actual demand. In order to update the states with the error information, the filter gain f a cannot be too small, which introduces large day to day variation on starts. However MPC can give better performance in terms of offset free inventory control. When LP decisions influence the daily starts in the fab, the overall performance is improved since the starts variance is small while offset-free control is ensured.

15 Fig. 10 LP and MPC solution comparison in Scenario 1 (Case 3): LP (solid line), MPC (dash line), Q u = [ ]. 6 Conclusions A two level hierarchical structure for semiconductor manufacturing SCM composed of two planning modules is presented in this paper. A strategic planning module (LP) is used to generate weekly starts targets by considering future demand forecasts, capacity limits, and inventory targets. These weekly targets are passed to the tactical planning module (MPC) which performs daily decision-making. Strategic planning is used to deal with long time scale stochasticity, while tactical planning is used for short time scale stochasticity. Two scenarios were studied in this paper, stationary demand with and without forecast error. Additional scenarios and case studies can be found in [21] including step changes on inventory targets and step changes on customer demand. All these simulation results showed that strategic planning alone gives the satisfactory performance in terms of small day-to-day changes on starts and offset free target tracking when there is no forecast error, while tactical planning outperforms strategic planning when there is some forecast error, and can give smooth responses with proper tuning. A partial LP - MPC structure (accomplished through the choice of tuning) can result in a suitable tradeoff of starts variability and performance meaningful for semiconductor manufacturing SCM. In order to extend these results to practice, scalability needs to be considered. LP based strategic planning can handle large scale problems with many decision variables and run very fast, while QPbased MPC runs slowly when the number of decision variables is large. Multiple distributed MPC controllers may be considered in practice to handle the large scale problems. Additional aspects need to be studied to better understand the interaction between strategic and tactical planning, such as the role of capacity limits and choice of forecast horizons. Optimally selecting weights to determine how

16 16 Fig. 11 Partial LP and partial MPC simulation structure. closely the tactical planning algorithm should track the strategic planning targets will depend on the demand forecast, the actual demand signal and capacity limits. Novel optimization techniques may be used to find the optimal tuning parameters for LP/MPC interaction. References 1. Christopher, M. (1992) Logistics and Supply Chain ManagementPitman Publishing, London 2. Hines, P. (1995), Network sourcing: a hybrid approach, International Journal of Purchasing and Materials Management, Volume 31, Number 2, Lamming, R.C. (1996), Squaring lean supply with supply chain management: lean production and work organization, International Journal of Operations and Production Management, Volume 16, Number 2, Syracuse University, (2006) Martin J. Whiteman School of Management, 5. Kempf, K. G. (2004) Control-Oriented Approaches to Supply Chain Management in Semiconductor Manufacturing, Proceedings of American Control Conference, 5: D. Simchi-Levi and P. Kaminsky and E. Simchi-Levi (2000), Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies, McGraw Hill, New York 7. W. J. Hopp and M. L. Spearman (1996), Factory Physics: Foundations of Manufacturing Management, McGraw Hill, New York 8. Chopra, S. and Meindl, P. (2001) Supply Chain Management: Strategy, Planning, and Operation, Prentice- Hall, Upper Saddle River, New Jersey 9. R. Kapuscinski and S. Tayur (1999) Optimal Policies and Simulation-Based Optimization for Capacitated Production Inventory Systems, Quantitative Models for Supply Chain Management, Kluwer Academic, Boston S. C. Graves and S. P. Willems (2000) Optimizing Strategic Safety Stock Placement in Supply Chains, Manufacturing and Service Operations Management, Volume 2, Number 1, C. E. García and D. M. Prett and M. Morari (1989) Model Predictive Control: Theory and Practice - A Survey, Automatica, Volume 25, Number 3, E. F. Camacho and C. Bordons (1999), Model Predictive Control, Springer-Verlag, London 13. K. G. Kempf (2004) Control-oriented approaches to supply chain management in semiconductor manufacturing, American Control Conferences, Boston, MA. Volume 5, pp

17 17 I I I30 Backorders Shipment&Demand Fig. 12 Partial LP and partial MPC simulation results in Scenario 1 (Case 4): Q u = [ ]. 14. S. Tzafestas and G. Kapsiotis and E. Kyriannakis (1997) Model-based predictive control for generalized production planning problems, Computers in Industry, 34: S. Bose and J.F. Pekny (2000) A Model Predictive Control framework for planning and scheduling problems: a case study of consumer goods supply chain, Computers and Chemical Engineering, 24: E. Perea and E. Ydstie and I. Grossmann (2003) A model predictive control strategy for supply chain optimization, Computers and Chemical Engineering, 27: M. W. Braun and D. E. Rivera and W. M. Carlyle and K. G. Kempf (2003) Application of Model Predictive Control to Robust Management of Multi-Echelon Demand Networks, Simulation: Transactions of the Society for Modeling and Simulation International, Volume 79, Number 3, P. Seferlis and N. F. Giannelos (2004) A two-layered optimisation-based control strategy for multi-echelon supply chain networks, Computers and Chemical Engineering, 28: Åström, K. J. and B. Wittenmark, Computer Controlled Systems: Theory and Design (Prentice-Hall, Englewood Cliffs, NJ 1984). 20. W. Wang and D. E. Rivera (2008) Model Predictive Control for Tactical Decision-Making in Semiconductor Manufacturing Supply Chain Management, IEEE Transactions on Control Systems Technology, Vol. 16, No. 5, W. Wang (2007) Model Predictive Control strategies for Supply Chain Management in Semiconductor Manufacturing, Ph.D dissertation, Dept. of Chemical Engineering, Arizona State University 22. H. D. Mittelmann (1999) Benchmarking Interior Point LP/QP Solvers, Opt. Meth. Software 12:

18 Fig. 13 LP and MPC solution comparison in Scenario 1 (Case 4): LP (solid line), MPC (dash line), Q u = [ ].

19 19 I I I Backorders Shipment&Demand 920 Fig. 14 LP control simulation results in Scenario 2: Q u = [ ].

20 Fig. 15 LP and MPC solution comparison in Scenario 2: LP (solid line), MPC (dash line), Q u = [ ].

21 I I I Backorders Shipment&Demand Fig. 16 MPC-only control simulation results in Scenario 2: Q u = [0 0 0].

22 Fig. 17 LP and MPC solution comparison in Scenario 2: LP (solid line), MPC (dash line), Q u = [0 0 0].

23 23 I I I Backorders Shipment&Demand Fig. 18 LP/MPC interaction control simulation results in Scenario 2: Q u = [ ].

24 Fig. 19 LP and MPC solution comparison in Scenario 2: LP (solid line), MPC (dash line), Q u = [ ].

25 I I I30 Backorders Shipment&Demand Fig. 20 Partial LP and partial MPC control simulation results in Scenario 2: Q u = [10 0 0].

26 Fig. 21 LP and MPC solution comparison in Scenario 2: LP (solid line), MPC (dash line), Q u = [10 0 0].