Stochastic programming based capacity planning for semiconductor wafer fab with uncertain demand and capacity

Capacity planning is a challenging problem in semiconductor manufacturing industry due to high uncertainties both in market and manufacturing systems, short product life cycle, and expensive capital invest. To tackle this problem, this paper proposes a scenario-based stochastic programming model which considers demand and capacity uncertainties via scenarios, where the overall equipment efficiency is employed to describe the uncertain capacity for the first time. Based on the decentralized structure of tool procurement, production, stockout, and inventory decision-making processes, recourse approximation strategies are presented with varying degree of information share. The computational experiments show that the resulting tool set is robust enough to cope with the changes in capacity with the expected profits being maximized for different scenarios, and the scheme can generate pretty good solutions in reasonable computational time.     

Production capacity planning and control in multi-stage manufacturing

This paper develops a mathematical model for determining the optimum lot-sizes for a set of products and the capacity required to produce them in a multi-stage production system. The purpose of the modelling is to support capacity planning at the production function level and the basic criterion considered for the optimisation is the minimisation of the total system cost (TSC) per unit time. The TSC consists of (i) set-up cost, (ii) cost due to the quenching of batches, and (iii) hiring cost of the machines. An example is presented to explain the model.     

Managing manufacturing risks by using capacity options

In this study, we investigate the strategy of increasing production capacity temporarily through contingent contractual agreements with short-cycle manufacturers to manage the risks associated with demand volatility. We view all these agreements as capacity options. More specifically, we consider a manufacturing company that produces a replenishment product that is sold at a retailer. The demand for the product switches randomly between a high level and a low level. The production system has enough capacity to meet the demand in the long run. However, when the demand is high, it does not have enough capacity to meet the instantaneous demand and thus has to produce to stock in advance. Alternatively, a contractual agreement with a short-cycle manufacturer can be made. This option gives the right to receive additional production capacity when needed. There is a fixed cost to purchase this option for a period of time and, if the option is exercised, there is an additional per unit exercise price which corresponds to the cost of the goods produced at the short-cycle manufacturer. We formulate the problem as a stochastic optimal control problem and analyse it analytically. By comparing the costs between two cases where the contract with the short-cycle manufacturer is used or not, the value of this option is evaluated. Furthermore, the effect of demand variability on this contract is investigated.     

A stochastic production planning problem in hybrid manufacturing and remanufacturing systems with resource capacity planning

DIRECT is derivative-free global-search algorithm has been found to perform robustly across a wide variety of low-dimensional test problems. The reason DIRECT’s robustness is its lack of algorithmic parameters that need be “tuned” to make the algorithm perform well. In particular, there is no parameter that determines the relative emphasis on global versus local search. Unfortunately, the same algorithmic features that enable DIRECT to perform so robustly have a negative side effect. In particular, DIRECT is usually quick to get close to the global minimum, but very slow to refine the solution to high accuracy. This is what we call DIRECT’s “eventually inefficient behavior.” In this paper, we outline two root causes for this undesirable behavior and propose modifications to eliminate it. The paper builds upon our previously published “MrDIRECT” algorithm, which we can now show only addressed the first root cause of the “eventually inefficient behavior.” The key contribution of the current paper is a further enhancement that allows MrDIRECT to address the second root cause as well. To demonstrate the effectiveness of the enhanced MrDIRECT, we have identified a set of test functions that highlight different situations in which DIRECT has convergence issues. Extensive numerical work with this test suite demonstrates that the enhanced version of MrDIRECT does indeed improve the convergence rate of DIRECT.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

Stochastic capacity expansion with multiple sources of capacity

In this paper, we consider the multi-period single resource stochastic capacity expansion problem with three sources of capacity: permanent, contract, and spot market. The problem is modeled as a multi-stage stochastic integer program. We show that the problem has the totally unimodular property and develop polynomial-time primal and dual algorithms to solve the problem.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

Stochastic integral in the case of infinite expected first exit time

We develop a method of analysis of a multidimensional semi-Markov process of diffusion type in the case of infinite expectation of the first exit time from a small neighborhood of the initial point. A generalization of Dynkin’s formula for this case is obtained. Itô’s formula for a stochastic integral over a multidimensional semi-Markov process of diffusion type is derived. Bibliography: 4 titles.     

A Lagrangean relaxation based approach for the capacity allocation problem in flexible manufacturing systems

This study considers the operation assignment and capacity allocation problem in flexible manufacturing systems. A set of operations is selected to be processed and assigned to the machines together with their required tools. The purchase or usage of the required tools incurs a cost. The machines have scarce time and tool magazine capacities. The objective is to maximize the total weight of the assigned operations minus the total tooling costs. We use Lagrangean relaxation approach to obtain upper and lower bounds on the optimal objective function values. The computational experiments show that our approach provides near optimal bounds in reasonable solution times.     

Analysis of expected queueing delays for decision making in production planning

Concepts such as Time Based Competition and criticism of traditional cost accounting's role as a basis for decision making in production planning have emphasized the need for operational measures as indicators of manufacturing performance. One such measure is the expected queueing delay at a production facility. In this paper a typical bottleneck work center is considered where semi-manufactured products are processed in batches. The expected queueing delay depends on the batch sizes used at the work center. Emphasis is placed on the derivation of analytical expressions of (bounds on) the minimal expected queueing delay that can be achieved by an optimal batching decision. The analytical expressions can be applied easily to support managerial decisions on reduction of setup time and on expansion of capacity.     

Capacity planning in networks of queues with manufacturing applications

This paper addresses capacity planning in systems that can be modeled as a network of queues. More specifically, we present an optimization model and solution methods for the minimum cost selection of capacity at each node in the network such that a set of system performance constraints is satisfied. Capacity is controlled through the mean service rate at each node. To illustrate the approach and how queueing theory can be used to measure system performance, we discuss a manufacturing model that includes upper limits on product throughput times and work-in-process in the system. Methods for solving capacity planning problems with continuous and discrete capacity options are discussed. We focus primarily on the discrete case with a concave cost function, allowing fixed charges and costs exhibiting economies of scale with respect to capacity to be handled.     

A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.     

Integral resource capacity planning for inpatient care services based on bed census predictions by hour

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.     

Optimal solution of cellular manufacturing system design: Benders' decomposition approach

In this paper, a mathematical model for cellular manufacturing system (CMS) design which incorporates three critical aspects - resource utilization, alternate routings, and practical constraints, is presented. The model is shown to be NP-complete. A linear, mixed-integer version of the model which not only has fewer integer variables compared to most other models in the literature, but one that also permits us to solve it optimally using Benders' decomposition approach is presented. Some results that allow us to solve the problem efficiently as well as computational results with Benders' decomposition algorithm and a modified version are presented.     

On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management

A new scheme for dealing with uncertainty in scenario trees is presented for dynamic mixed 0–1 optimization problems with strategic and operational stochastic parameters. Let us generically name this type of problems as capacity expansion planning (CEP) in a given system, e.g., supply chain, production, rapid transit network, energy generation and transmission network, etc. The strategic scenario tree is usually a multistage one, and the replicas of the strategic nodes root structures in the form of either a special scenario graph or a two-stage scenario tree, depending on the type of operational activity in the system. Those operational scenario structures impact in the constraints of the model and, thus, in the decomposition methodology for solving usually large-scale problems. This work presents the modeling framework for some of the risk neutral and risk averse measures to consider for CEP problem solving. Two types of risk averse measures are considered. The first one is a time-inconsistent mixture of the chance-constrained and second-order stochastic dominance (SSD) functionals of the value of a given set of functions up to the strategic nodes in selected stages along the time horizon, The second type is a strategic node-based time-consistent SSD functional for the set of operational scenarios in the strategic nodes at selected stages. A specialization of the nested stochastic decomposition methodology for that problem solving is outlined. Its advantages and drawbacks as well as the framework for some schemes to, at least, partially avoid those drawbacks are also presented.     

Optimization of capacity expansion planning for gas transportation networks

This paper presents techniques for solving the problem of minimizing investment costs on an existing gas transportation network. The goal of this program is to find, first, the optimal location of pipeline segments to be reinforced and, second, the optimal sizes (among a discrete commercial list of diameters) under the constraint of satisfaction of demands with high enough pressure for all users.     

Price-based planning and scheduling of multiproduct orders in symbiotic manufacturing networks

This paper addresses the problem of planning and scheduling operations when processing a multiproduct order in a Symbiotic Manufacturing Network (SMN). The order is characterized for each of its products, by linear routings of operations which can be performed in parallel by different contracting firms of the network. We first present a characterization of the decision process for planning and scheduling operations in SMN. Next, we propose a bidding scheme expressing pricetime trade-off and a multi-commodity network model that can be used to plan and schedule many types of order-based customized production. Finally, an illustrative example is detailed to permit full comprehension of the approach.