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Analysis and Modeling of Manufacturing Systems is a set of papers on some of the newest research and applications of mathematical and computational techniques to manufacturing systems and supply chains. These papers deal with fundamental questions (how to predict factory performance: how to operate production systems) and explicitly treat the stochastic nature of failures, operation times, demand, and other important events.

Analysis and Modeling of Manufacturing Systems will be of interest to readers with a strong background in operations research, including researchers and mathematically sophisticated practitioners.



Chapter 1. Capacitated Two-Echelon Inventory Models for Repairable Item Systems

In this paper, we consider two-echelon maintenance systems with repair facilities both at a number of local service centers (called bases) and at a central location. Each repair facility may be considered to be a job shop and is modeled as a (limited capacity) open queuing network, while any transport from the central facility to the bases (and vice versa) is modeled as an ample server. At all bases as well as at the central repair facility, ready-for-use spare parts are kept in stock. Once an item in the field fails, it is returned to one of the bases and replaced by a ready-for-use item from the spare parts stock, if available. The returned failed item is either repaired at the base or shipped to and repaired at the central facility. In the case of local repair, the item is added to the local spare parts stock as a ready-for-use item after repair. If a repair at the central facility is needed, the base orders an item from the central spare parts stock to replenish its local stock, while the failed item is added to the central stock after repair. Orders are satisfied on a first-come-first-serve basis while any requirement that cannot be satisfied immediately either at the bases or at the central facility is backlogged.
We assume that failed items are returned to the bases according to a Poisson process, and that each repair shop (at the bases as well as at the central facility) can be modeled as a Jackson network. Under these conditions, we propose a special near-product-form solution that provides an excellent approximation for the steady-state distribution of a slightly aggregated system, that permits us to calculate all relevant performance measures (such as fill rates and stockout probabilities) at the bases as well as at the central facility, as a function of target inventory levels at each location. Errors of these performance measures are generally less than one percent, when compared with simulation results. Finally, we show how these approximations can be used to determine optimal inventory levels at both the central and local facilities.
Zeynep Muge Avsar, W. Henk Zijm

Chapter 2. Distribution Resource Planning Systems: A Critique and Enhancement

Distribution Resource Planning (DRP) is a general framework for planning and managing inventory in distribution networks. The DRP framework can be applied to complex distribution networks with thousands of unique stock-keeping units and hundreds of stocking locations. It allows for non-stationary (e.g. seasonal) demand patterns and a wide variety of user-specified inventory control rules including all standard inventory policies such as (S, s) and fixed order quantity rules. A number of software implementations of DRP are commercially available and are widely used in industry. In this paper, we describe the logic underlying DRP and point out some of its limitations. The inner workings of DRP are not always familiar to the research/academic community. On the other hand, practitioners may be unaware of some of the shortfalls and limitations of the system. Our objective here is to bridge this gap. In particular, we show how the performance evaluation capability of DRP can be substantially enhanced by some simple analytical formulas, derived as approximations from base-stock and (S, s) control schemes.
Gerald E. Feigin, Kaan Katircioglu, David D. Yao

Chapter 3. Process Adjustment for Assemblies

Should Components, or Assemblies, Be Made to Specifications?
After the design and construction of manufacturing tools, adjustment is often necessary to reduce mean deviation from target of product dimensions. We formulate a stochastic dynamic program to find the optimal adjustment policy when the adjustment outcome is uncertain. The optimal policy minimizes the sum of adjustment cost during pre-production and quality cost during production. The formulation is developed for a single process and for two processes producing components for assembly. In the single process case, sufficient conditions are given for the optimal policy to have an upper and lower control limit form. In the two process case, we compare separate and combined policies and give an example where appreciable savings can be realized from a combined policy.
David W. Glenn, Stephen M. Pollock

Chapter 4. Exact Analysis of a Continuous Material Merge System with Limited Buffer Capacity and Three Stations

We develop a Markov process model of a flow line consisting of three unreliable machines and one buffer of limited capacity. Two machines upstream of the buffer perform the same operation and feed the same buffer in such a way that one machine has priority over the other when the buffer is full. The third machine removes material from the buffer. Processing times are deterministic and machine-specific. Exponentially distributed times to failure and to repair are also machine-specific. We develop an exact procedure to compute the average production rate and inventory level. The procedure is intended to be used as a building block of decomposition methods for the analysis of flow lines with non-linear flow of material that may, for example, be due to rework loops in flow lines with quality inspections.
Stefan Helber, Nicole Mehrtens

Chapter 5. Optimal Scheduling for Piecewise Deterministic Multi-Armed Bandit Problem

We derive explicit expressions for the priority indices (Gittins’ indices), associated with a class of multi-armed Bandit processes. The underlying dynamic governing the arms belong to piecewise deterministic random evolutions. We then use this class of model to discuss a simple version of the scheduling problem of a flexible manufacturing resource, with limited capacity, operating in a random environment.
Max-Olivier Hongler, Fabrice Dusonchet

Chapter 6. Production Planning for Short Life-Cycle Products in Consideration of Clearance Sale

A method that reduces economical risks in product planning for short life-products is proposed in this paper. In this method, it is assumed that production is decided before sales and at the end of the selling period, the products are sold at clearance prices and the optimum production level is calculated using the knowledge of experts. The effectiveness and convenience of the method is described with a numerical example.
H. Ishikura

Chapter 7. Analysis of Automated Flow Line Systems with Repair Crew Interference

The interrelations between production and maintenance are mostly neglected during the design phase of automated production systems. Thus, the relevant performance measures of a planned production system like throughput time, production rate, work in process etc. are often estimated inaccurately. The paper presents an analytical approach for performance evaluation of an automated flow line system (AFLS) which takes into account the dependency between the production and the repair system. The suggested model and solution approach are particularly helpful in the initial design phase as well as during a redesign process in order to evaluate alternative configurations of the planned production and repair system.
Heinrich Kuhn

Chapter 8. Performance Evaluation of Production Lines with Random Processing Times, Multiple Failure Modes and Finite Buffer Capacity — Part I: The Building Block

The paper presents an exact analytical method for the performance evaluation of two-machine lines with random processing times, multiple failure modes and finite buffer capacity. Unlike previous works on this subject, machines can fail in different modes, each one characterized by exponentially distributed time to failure and time to repair. The steady state probabilities of the Markov chain of the system is obtained in a compact form with a computational effort that depends only on the number of failure modes considered and not on the capacity of the buffer. Finally, the improvements provided by the proposed method over existing techniques are discussed and quantified. The method has been derived to be used as a building block within the development of a new set of decomposition equations for the analysis of larger systems, such long transfer lines and assembly/disassembly systems.
R. Levantesi, A. Matta, T. Tolio

Chapter 9. Performance Evaluation of Production Lines with Random Processing Times, Multiple Failure Modes and Finite Buffer Capacity — Part II: The Decomposition

The paper presents a decomposition method for the performance evaluation of production lines with exponential processing times, multiple failure modes and finite buffer capacity. The key feature of the proposed method is the capability to model machines subject to different types of failures, each one characterized by exponentially distributed time to failure and time to repair. This feature, being the method based on the approximation of the behavior of a K-machine transfer line by the behavior of K-1 two-machine lines, or building blocks, makes it possible to consider in each building block in which the original line is decomposed real failure and virtual failure modes. While real failures are directly connected with the reliability of the machines of the original line, virtual failures are introduced to model the interruption of flow that take place in the system as a result of machine disruption propagation. Simulation and numerical experiments are carried out to show the performance of the new method in comparison with existing ones. The method can be extended to the analysis of larger open systems, such as assembly/disassembly networks, and systems with loops.
R. Levantesi, A. Matta, T. Tolio

Chapter 10. Due-Time Performance of Production Systems with Markovian Machines

Customer demand satisfaction in serial production lines with Markovian machines and Finished Goods Buffers (FGB) is analyzed. The level of demand satisfaction is measured by the probability to ship to the customer a required number of parts during a fixed interval of time. This performance measure, referred to as Due-Time Performance (DTP), is analyzed using a simplification procedure termed stationarization. As a result, an iteration-based method for DTP calculation is obtained and utilized for analysis of various properties of DTP. In particular, it is shown that when the demand is relatively low (∼ 95% of the production capacity), FGB of 2–4 shipments is sufficient to ensure high DTP (∼ 0.98). When the demand is high (∼ 99%), FGB of 6–9 shipments is required. Further increase of FGB leads to highly diminishing return. Also, it is shown that a ramp, rather than an inverted bowl, of machine efficiency allocation leads to optimization of DTP.
Jingshan Li, Semyon M. Meerkov

Chapter 11. Analysis of Two-Valve Fluid-Flow Systems with General Repair Times

A two-valve fluid-flow system with finite storage in between is considered. Valves are subject to failures with exponential up times and phase type repair times. We have developed a continuous time Markov Chain approach to study the steady-state behavior of the valves and the material in the storage. The Markov chain has both continuous and discrete states. We have constructed a system of linear equations for the boundary states and a set of differential equations for the interior states, that are solved using the eigenvalue method. We have also investigated the impact of down time variability on the system performance metrics.
Ünsal Özdoğru, Tayfur Altiok

Chapter 12. Stochastic Lead Time Models for Supply Chain Networks

In this paper, we investigate use of stochastic network modeling techniques for analyzing supply chain networks. Supply chains are interconnections of several companies such as suppliers, manufacturers, distributors and retailers with the aim of producing and selling customer desired products. Computing the supply chain lead time, or the order-to-delivery time is an important exercise. In this paper, we present stochastic network models for computing the average lead times of make-to-order supply chains. In particular, we illustrate the use of static probabilistic and generalized queueing networks for computing the lead times.
N. R. Srinivasa Raghavan, N. Viswanadham

Chapter 13. Modeling and Performance Evaluation of Base-Stock Controlled Assembly Systems

In this work, we are interested in base-stock controlled assembly systems. We consider production systems, realizing an assembly operation between components. In a previous work, we defined precisely how the base-stock mechanism can be applied in the case of assembly systems, then we proposed a queueing network model for base-stock controlled assembly systems and we established some properties for this model. In this paper, we propose an analytical technique for performance evaluation of base-stock controlled assembly systems, based on a decomposition method. This analytical method provides steady-state performance measures, like the probability of immediately satisfying a demand, the average number of backordered demands, the average number of finished products, etc. It can be applied for systems assembling any number of components and containing any number of stages in series after the assembly operation.
N. Sbiti, M. Di Mascolo, T. Bennani, M. Amghar

Chapter 14. Designing Manufacturing Cells Using a Tabu Search Approach

We present a Tabu Search scheme for the solution of the NP-hard part of the manufacturing cells formation problem, on a simplified yet concise model which adequately fits to practice. The design can then be finalized using simple methods to incorporate additional parameters. This scheme integrates in a systematic way proper short and long-term memory structures and an overall search strategy for their use. At the code development stage, special care was taken to enhance the explorative capability of the algorithm by correlating hash information with the values of the search parameters. The resulting algorithm is robust and produces more than promising results for problems with up to 30 machines, with negligible computational effort. In the absence of known optimal solutions for larger dimensions and therefore of a testing benchmark, fine-tuning may be required. This could be achieved by incorporating dynamic parameters in the place of the static ones.
K. Spiliopoulos, S. Sofianopoulou

Chapter 15. State-Space Modeling and Analysis of Pull-Controlled Production Systems

A methodology that automatically generates the state space models of pull-controlled production systems is presented. The state space model generated by the algorithm is then used to evaluate the performance of these systems. In addition to long run measures such as the production rate, WIP levels, average backlog, fill rate, etc., the exact distribution of the number of parts produced in a short period of time, the distribution of the time to produce a given number of parts, and the distribution of the cycle time are also derived. This methodology can be applied to a wide range of discrete material flow production systems that can be modelled as Markov chains. The deterministic processing time model is considered to explain the methodology in detail. The state space models of unreliable automated production lines controlled by the kanban, constant WIP, Control Point Policy, Base Stock, and hybrids of these policies are generated and analysed.
Bariş Tan

Chapter 16. Using Fluid Solutions in Dynamic Scheduling

We review some recent work on fluid approximation of queueing network control problems and present new results. The relationship between the optimal control of a queueing network and the optimal control of the associated fluid model is investigated. A general theory, a number of examples, and a few numerical results are presented. The fluid model replaces stochastic counting processes by their mean rates. Surprisingly, although the fluid model is deterministic and transient, it often contains valuable information about the original problem. We show that, under some technical assumptions, the asymptotic slope (normal vector in higher dimensions) of the switching surfaces for large queue lengths can be found from the fluid model. The implications of the fluid policy for designing manufacturing scheduling and control policies are discussed. Unlike the queueing network control problem, which is usually an intractable dynamic program, very efficient algorithms exist to solve the fluid problem from a given initial buffer state. Fluid solutions are presented for a number of examples, some of them new.
Michael H. Veatch


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