Throughput, flow times, and service level in an unreliable assembly system

Department of Industrial Engineering and Engineering Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
European Journal of Operational Research (Impact Factor: 1.84). 12/2001; 135(3):602-615. DOI: 10.1016/S0377-2217(01)00028-5

ABSTRACT This paper considers an unreliable assembly network where different types of components are processed by two separate work centers before being merged at an assembly station. The operation complexity of the system is a result of finite inter-station buffers, uncertain service times, and random breakdowns that lead to blocking at the work centers and starvation at the assembly station. The objective of this study is to gain an understanding of the behavior of such systems so that we can find a way to maximize the system throughput while maintaining the required customer service level. By constructing appropriate Markov processes, we obtain the probability distribution of the production flow time and derive formulas for throughput, the loss probability of type-2 workpieces, and the mean flow time. We present expressions for average work-in-process (WIP) and study their monotone properties. Using the distribution of the flow time, a customer service level can be defined and computed. We then formulate a system optimization model that can be used to maximize the throughput while maintaining an acceptable service level.

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    • "The throughput of a balanced three station assembly system was studied by Baker and Powell (1995). Moreover, an unreliable assembly system with finite buffer was modeled by Liu and Yuan (2001), in which different types of elements are performed by two separate service stations before coming to an assembly station with random breakdown. Yuan and Liu (2005) also studied the same problem. "
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    ABSTRACT: In this paper, we model multi-class multi-stage assembly systems with finite capacity as queueing networks. It is assumed that different classes (types) of products are produced by the production system and products’ orders for different classes are received according to independent Poisson processes. Each service station of the queueing network specifies a manufacturing or assembly operation, in that processing times for different types of products are independent and exponentially distributed random variables with service rates, which are controllable, and the queueing discipline is First Come First Served (FCFS). Different types of products may be different in their routing sequences of manufacturing and assembly operations. For modeling multi-class multi-stage assembly systems, we first consider every class separately and convert the queueing network of each class into an appropriate stochastic network. Then, by using the concept of continuous-time Markov processes, a system of differential equations is created to obtain the distribution function of manufacturing lead time for any type of product, which is actually the time between receiving the order and the delivery of finished product. Furthermore, we develop a multi-objective model with three conflicting objectives to optimally control the service rates, and use goal attainment method to solve a discrete-time approximation of the original multi-objective continuous-time problem.
    Computers & Industrial Engineering 12/2013; 66(4):808–817. DOI:10.1016/j.cie.2013.10.004 · 1.69 Impact Factor
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    • "predicted the throughput of balanced three station assembly systems. Liu and Yuan (2001) investigated an unreliable assembly system with finite buffer, in which different types of components were executed by two separate work centres before merging into an assembly station with random breakdown. It was further extended by Yuan and Liu (2005). "
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    ABSTRACT: In this paper, we attempt to present a constant due-date assignment policy in a multi-server multi-stage assembly system. This system is modelled as a queuing network, where new product orders are entered into the system according to a Poisson process. It is assumed that only one type of product is produced by the production system and multi-servers can be settled in each service station. Each operation of every work is operated at a devoted service station with only one of the servers located at a node of the network based on first come, first served (FCFS) discipline, while the processing times are independent random variables with exponential distributions. It is also assumed that the transport times between each pair of service stations are independent random variables with generalised Erlang distributions. Each product's end result has a penalty cost that is some linear function of its due date and its actual lead time. The due date is calculated by adding a constant to the time that the order enters into the system. Indeed, this constant value is decided at the beginning of the time horizon and is the constant lead time that a product might expect between the time of placing the order and the time of delivery. For computing the due date, we first convert the queuing network into a stochastic network with exponentially distributed arc lengths. Then, by constructing an appropriate finite-state continuous-time Markov model, a system of differential equations is created to find the manufacturing lead-time distribution for any particular product, analytically. Finally, the constant due date for delivery time is obtained by using a linear function of its due date and minimising the expected aggregate cost per product.
    International Journal of Systems Science 07/2013; DOI:10.1080/00207721.2013.815826 · 1.58 Impact Factor
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    • "The literature reviewed in this part, shows that a number of methods for service level and tardiness calculation already exist and that these are mostly based on the current queuing system state (Hopp/Roof-Sturgis 2000, Liu/Yuan 2001 and Duenyas/Hopp 1995). The distribution of the customer required leadtime to define the service level and tardiness of an MTO production system is not yet used in queuing models. "
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    ABSTRACT: In this paper an analytical model to calculate service level, FGI and tardiness for a make-to-order (MTO) production system based on the production leadtime, utilisation and WIP is presented. The distribution of customer required leadtime is linked to the already available equations for an M/M/1 production system from queuing theory. Explicit equations for service level, FGI, FGI leadtime and tardiness are presented for an M/M/1 production system within an MTO environment. For a G/G/1 production system an approximation based extension is provided – discussing the influence of variation in the inter-arrival and processing time distribution in this framework. Moreover, the integration of a work ahead window (WAW) work release policy is discussed. Based on a numerical study, a high potential to decrease FGI (up to 97% FGI reduction) when applying such a WAW strategy is found and it is shown that the higher the targeted service level is, the higher the FGI reduction potential. The paper contributes to a better understanding of the relationship between customer required leadtime distribution and the M/M/1 production system. By applying this model a decision maker can base his capacity investment decisions on the service level and expected tardiness for certain levels of FGI and WIP and can additionally define the optimal WAW policy.
    International Journal of Production Research 04/2011; 49(7):1827-1850. DOI:10.1080/00207541003660176 · 1.32 Impact Factor
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