Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration

This paper presents and analyzes a comprehensive model for the design of cellular manufacturing systems (CMS). A recurring theme in research is a piecemeal approach when formulating CMS models. In this paper, the proposed model, to the best of the authors’ knowledge, is the most comprehensive one to date with a more integrated approach to CMS design, where production planning and system reconfiguration decisions are incorporated. Such a CMS model has not been proposed before and it features the presence of alternate process routings, operation sequence, duplicate machines, machine capacity and lot splitting. The developed model is a mixed integer non-linear program. Linearization procedures are proposed to convert it into a linearized mixed integer programming formulation. Computational results are presented by solving some numerical examples, extracted from the existing literature, with the linearized formulation.     

Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customer due dates

We consider a two-stage make-to-order manufacturing system with random demands, processing times, and distributed customer due dates. The work to each stage is released based on a planned lead time. A general approach to minimize total inventory holding and customer order tardiness cost is presented to find the optimal manufacturing capacities and planned lead times for each manufacturing stage. Expressions are derived for work-in process inventories, finished-goods-inventory and expected backorders under the assumption of a series of M/M/1 queuing systems and exponentially distributed customer required lead times. We prove that the distribution of customer required lead time has no influence on the optimal planned lead times whenever capacity is predefined but it influences the optimal capacity to invest into. For the simultaneous optimization of capacity and planned lead times we present a numerical study that shows that only marginal cost decreases can be gained by setting a planned lead time for the upstream stage and that a considerable cost penalty is incurred if capacity and planned lead time optimization are performed sequentially.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

A two-level hedging point policy for controlling a manufacturing system with time-delay,demand uncertainty and extra capacity

This paper focuses on the production control of a manufacturing system with time-delay, demand uncertainty and extra capacity. Time-delay is a typical feature of networked manufacturing systems (NMS), because an NMS is composed of many manufacturing systems with transportation channels among them and the transportation of materials needs time. Besides this, for a manufacturing system in an NMS, the uncertainty of the demand from its downstream manufacturing system is considered; and it is assumed that there exist two-levels of demand rates, i.e., the normal one and the higher one, and that the time between the switching of demand rates are exponentially distributed. To avoid the backlog of demands, it is also assumed that extra production capacity can be used when the work-in-process (WIP) cannot buffer the high-level demands rate. For such a manufacturing system with time-delay, demand uncertainty and extra capacity, the mathematical model for its production control problem is established, with the objective of minimizing the mean costs for WIP inventory and occupation of extra production capacity. To solve the problem, a two-level hedging point policy is proposed. By analyzing the probability distribution of system states, optimal values of the two hedging levels are obtained. Finally, numerical experiments are done to verify the effectiveness of the control policy and the optimality of the hedging levels.     

Production and replacement policies for a deteriorating manufacturing system under random demand and quality

This work investigates the production planning of an unreliable deteriorating manufacturing system under uncertainties. The effect of the deterioration phenomenon on the machine is mainly observed in its availability and the quality of the parts produced, with the rates of failure and defectives increasing with the age of the machine. The option to replace the machine should be considered to mitigate the effect of deterioration in order to ensure long-term satisfaction of demand. The objective of this paper is to find the production rate and the replacement policy that minimize the total discounted cost, which includes inventory, backlog, production, repair and replacement costs, over an infinite planning horizon. We formulate the stochastic control problem in the framework of a semi-Markov decision process to consider the machine's history. The integration of random demand and quality behaviour led us to propose a new modeling approach by developing optimality conditions in terms of a second-order approximation of Hamilton–Jacobi–Bellman (HJB) equations. Numerical methods are used to obtain the optimal control policies. Finally, a numerical example and a sensitivity analysis are presented in order to illustrate and confirm the structure of the optimal solution obtained.     

Some open problems in the design and use of modern production systems

During the past two decades, manufacturing systems have moved towards automation, integration and modularity. These trends will certainly continue in the future due to the constraints of the market and to evolution of resources and worker requirements. As a consequence, the design and use of manufacturing systems are increasingly expensive. Numerous methods and tools have been developed to face up to this situation, but some complementary aids could be provided for designers and manufacturing engineers. The goal of this paper is to present important open problems whose solutions could certainly significantly improve the design and use of modern production systems.     

Optimal capacity for substitutable products under operational postponement

We consider a monopolist producing two substitutable products with one flexible (shared) capacity. The demand of each product is a linear function of the prices of both products, and is subject to an additive shock. We study the impact of two key drivers, namely the degree of substitution between the products and the level of operational postponement, on the optimal capacity and the resulting expected profit. We show that the relationship between the optimal capacity and the degree of product substitution is not impacted by the different postponement strategies the firm can utilize or by the different settings (forced clearance versus holdback) considered in the previous literature. On the other hand, how capacity is affected by postponement critically depends on how closely substitutable the products are. In particular, we show that the well-known result that operational postponement and capacity are strategic complements in a single-product setting (Van Mieghem and Dada, 1999) no longer holds in our setting, because the two substitutable products are now linked through consumer-driven substitution, which the firm can influence through pricing. In particular, capacity and operational postponement (in the form of quantity postponement) can be either strategic substitutes or strategic complements, and this depends on both the firm’s cost structure and the degree of substitution between the products. We also study the impact of forced clearance on the firm’s expected profit and find that clearance deteriorates the firm’s earnings more when the products it offers are highly differentiated.     

Optimal production and rationing policies of a make-to-stock production system with batch demand and backordering

In this paper, we consider the stock rationing problem of a single-item make-to-stock production/inventory system with multiple demand classes. Demand arrives as a Poisson process with a randomly distributed batch size. It is assumed that the batch demand can be partially satisfied. The facility can produce a batch up to a certain capacity at the same time. Production time follows an exponential distribution. We show that the optimal policy is characterized by multiple rationing levels.     

Technology selection and capacity investment under uncertainty

We analyze the problem of technology selection and capacity investment for electricity generation in a competitive environment under uncertainty. Adopting a Nash-Cournot competition model, we consider the marginal cost as the uncertain parameter, although the results can be easily generalized to other sources of uncertainty such as a load curve. In the model, firms make three different decisions: (i) the portfolio of technologies, (ii) each technology’s capacity and (iii) the technology’s production level for every scenario. The decisions related to the portfolio and capacity are ex-ante and the production level is ex-post to the realization of uncertainty. We discuss open and closed-loop models, with the aim to understand the relationship between different technologies’ cost structures and the portfolio of generation technologies adopted by firms in equilibrium. For a competitive setting, to the best of our knowledge, this paper is the first not only to explicitly discuss the relation between costs and generation portfolio but also to allow firms to choose a portfolio of technologies. We show that portfolio diversification arises even with risk-neutral firms and technologies with different cost expectations. We also investigate conditions on the probability and cost under which different equilibria of the game arise.     

Tool capacity planning for semiconductor fabrication facilities under demand uncertainty

This research is motivated by issues faced by a large manufacturer of semiconductor devices. Semiconductor manufacturing companies allocate millions of dollars every year for new types of machine tools for their facilities. Typically these are special purpose machine tools which are made to order. The rate of change in products and technology makes it difficult for manufacturers to have a good estimate of future tool requirements. Further, manufacturers experience a long lead time while procuring these tools. In this paper, we model the tool capacity planning problem under uncertainty in demand. The number of tools required in a facility is sufficiently large (nearly hundred or more tools) to make it nearly impossible to obtain efficient exact algorithms. We provide heuristics to find efficient tool procurement plans and test their quality using lower bounds on the formulation.     

Joint management of capacity and inventory in make-to-stock production systems with multi-class demand

We evaluate the benefits of coordinating capacity and inventory decisions in a make-to-stock production environment. We consider a firm that faces multi-class demand and has additional capacity options that are temporary and randomly available. We formulate the model as a Markov decision process (MDP) and prove that a solution to the optimal joint control problem exists. For several special cases we characterize the structure of the optimal policy. For the general case, however, we show that the optimal policy is state-dependent, and in many instances non-monotone and difficult to implement. Therefore, we consider three pragmatic heuristic policies and assess their performance. We show that the majority of the savings originate from the ability to dynamically adjust capacity, and that a simple heuristic that can adjust production capacity (based on workload fluctuation) but uses a static production/rationing policy can result in significant savings.     

Raw materials and production control with random supply and demand,an outside market and production capacity

We study a capacitated periodic inventory review problem in which the optimal control of both raw materials and finished product inventories simultaneously involves optimal decisions on materials purchasing from suppliers, buying or selling of materials in spot market, and production quantity in each period. We found that the dynamic program model of the problem is decomposable, and there is an independent relationship between the decisions on materials purchasing/selling and finished product production. Optimal policies are characterized and extensions are discussed.     

Hierarchical decision making in production and repair/replacement planning with imperfect repairs under uncertainties

In this paper, we analyse an optimal production, repair and replacement problem for a manufacturing system subject to random machine breakdowns. The system produces parts, and upon machine breakdown, either an imperfect repair is undertaken or the machine is replaced with a new identical one. The decision variables of the system are the production rate and the repair/replacement policy. The objective of the control problem is to find decision variables that minimize total incurred costs over an infinite planning horizon. Firstly, a hierarchical decision making approach, based on a semi-Markov decision model (SMDM), is used to determine the optimal repair and replacement policy. Secondly, the production rate is determined, given the obtained repair and replacement policy. Optimality conditions are given and numerical methods are used to solve them and to determine the control policy. We show that the number of parts to hold in inventory in order to hedge against breakdowns must be readjusted to a higher level as the number of breakdowns increases or as the machine ages. We go from the traditional policy with only one high threshold level to a policy with several threshold levels, which depend on the number of breakdowns. Numerical examples and sensitivity analyses are presented to illustrate the usefulness of the proposed approach.     

Minimax production planning in failure-prone manufacturing systems

In this paper, we consider a minimax production planning model of a flexible manufacturing system with machines that are subject to random breakdown and repair. The objective is to choose the rate of production that minimizes the related minimax cost of production and inventory/shortage. The value function is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Isaacs equation. Under certain conditions, it is shown that the value function is continuously differentiable. A verification theorem is given to provide a sufficient condition for optimal control. Finally, two examples are solved explicitly.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grants OGP0036444 and A4169.     

Hierarchical production control of a flexible manufacturing system

A hierarchical production control framework for a flexible manufacturing system is proposed. The machines in the system are subject to failures in a wide spectrum band. At first, failures are clustered near some discrete points on the failure spectrum in order to define the hierarchical model. Each level in the hierarchy corresponds to a discrete point on the failure spectrum. At each level, faster varying failures are modelled by their mean behaviour, and more slowly varying failures are treated as static. Then, a hierarchical controller of multiple time scale type is proposed. System control at each level is based on the work of Kimemia and Gershwin. Simulation results conclude the paper.     

Optimal production run time for a deteriorating production system under an extended inspection policy

A deteriorating production system is subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. In order to reduce the defective items, part inspection policy, under which production inspections are performed only at the end of the production run, and full inspection policy are both considered in the literature. Moreover, the former dominates the latter. Since the product produced towards the end of a production cycle are more likely to be defective, it can further economize the inspection costs that they are directly reworked without inspection. In this paper, we propose an extended product inspection policy for a deteriorating production system. Product inspections are performed in the middle of a production cycle, and after the inspection, all products produced until the end of the production run are fully reworked. Based on the model, we show that there exists a production run time and a corresponding unique inspection policy such that the expected total cost per item per cycle is minimized. Finally, numerical examples are provided to illustrate our extended inspection policy, and indicate that such product inspection model will reduce the quality-related cost than part inspection does.     

Stability and optimality of a multi-product production and storage system under demand uncertainty

This work develops a discrete event model for a multi-product multi-stage production and storage (P&S) problem subject to random demand. The intervention problem consists of three types of possible decisions made at the end of one stage, which depend on the observed demand (or lack of) for each item: (i) to proceed further with the production of the same product, (ii) to proceed with the production of another product or (iii) to halt the production. The intervention problem is formulated in terms of dynamic programming (DP) operators and each possible solution induces an homogeneous Markov chain that characterizes the dynamics. However, solving directly the DP problem is not a viable task in situations involving a moderately large number of products with many production stages, and the idea of the paper is to detach from strict optimality with monitored precision, and rely on stability. The notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied P&S problem. An approximate value iteration algorithm is proposed, which applies to the broader class of control problems described by homogeneous Markov chains that satisfy a structural condition pointed out in the paper. This procedure iterates in a finite subset of the state space, circumventing the computational burden of standard dynamic programming. To benchmark the approach, the proposed algorithm is applied to a simple two-product P&S system.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes

We study a pure assemble-to-order system subject to multiple demand classes where customer orders arrive according to a compound Poisson process. The finished product is assembled from m different components that are produced on m distinct production facilities in a make-to-stock fashion. We show that the optimal production policy of each component is a state-dependent base-stock policy and the optimal inventory allocation policy is a multi-level state-dependent rationing policy. Using numerical experimentation, we first study the system behavior as a function of order size variability and order size. We show that the optimal average cost rate is more sensitive to order size variability than to order size. We also compare the optimal policy to the first-come first-serve policy and show that there is great benefit to inventory rationing. We also propose two simple heuristics and show that these can effectively mimic the optimal policy which is generally much more difficult to determine and, especially, to implement.     

Fixed versus flexible production systems: A real options analysis

In this work, we address investment decisions in production systems by using real options. As is standard in literature, the stochastic variable is assumed to be normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. The methodology establishes a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case) and then, computes the project value. We have developed and implemented stochastic dynamic programming models both for fixed and flexible capacity systems. In the former case, we consider three standard options: the option to postpone investment, the option to abandon investment, and the option to temporarily shut-down production. For the latter case, we introduce the option of corrective action, in terms of production capacity, that the management can take during the project by considering the existence of one of the following: (i) a capacity expansion option; (ii) a capacity contraction option; or (iii) an option considering both expansion and contraction. The full flexible capacity model, where both the contraction and expansion options exist, leads, as expected, to a better project predicted value and thus, investment policy. However, we have also found that the capacity strategy obtained from the flexible capacity model, when applied to specific demand data series, often does not lead to a better investment decision. This might seem surprising, at first, but it can be explained by the inaccuracy of the binomial model. The binomial model tends to undervalue future decreases in the stochastic variable (demand), while at the same time tending to overvalue an increase in future demand values.