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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    ABSTRACT: This book is strongly based on the Ph.D. thesis of the author submitted in 2013. It presents seven chapters on 138 pages and includes the results from four earlier research papers of the author. After a short introduction in Chapter 1, a brief literature review is given in Chapter 2. In three sections, a review on the literature covering the relationship between the logical key performance indicators utilization (Section 2.1), work release rules (Section 2.2) and on capacity investment (Section 2.3) are given. Chapter 3 deals with the single-stage service level and tardiness model. After some introductory comments, a model is developed which gives a deeper understanding of the relationship between production lead time, utilization and work-in-progress in a single-stage production system and the service level as well as the tardiness of such a system (Section 3.2). Moreover, an extension of this model is presented which allows the reduction of finished-goods-inventory. In a separate section, a numerical study by means of three examples is provided (Section 3.3). Chapter 4 deals with simultaneous capacity and planned lead time optimization. First the general optimization problem is presented and analyzed (Section 4.2). Then the special case of a single-stage production system with an upfront buffer and a planned lead time is investigated (Section 4.3). Furthermore, a two-stage production system with exponentially distributed processing times and interarrival times as well as exponentially distributed costumer required lead times is analyzed. A numerical study completes this chapter. Chapter 5 deals with an optimal composition of the number and size of the machines. After some introductory comments, the general multi-stage model is presented and structural properties of an optimal solution are given (Section 5.2). Then expressions for the work-in-progress, the finished-goods-inventory and the backorder costs for the two-stage M|M|s production system are presented (Section 5.3). Finally, a numerical study is provided, where the influence of the machine size on the optimal cost, the influence of the machine number on the optimal cost, the performance of the heuristic is analyzed and the influence of uncertain input rates is discussed. Chapter 6 discusses the problem of capacity investment and a work-ahead-window setting in a service level constraint model. Again after some short introductory remarks for this chapter, the single-stage M|M|1 model discussed in Chapter 4 is extended to satisfy the service level constraint instead of including the backorder costs, and a numerical example is presented (Section 6.2). Then a service level constraint, single-stage, multi-item capacity investment model considering inventory costs is developed for a normally distributed demand applying an earliest due date rule (Section 6.3). Finally, the service level equation for a two-stage M|M|s production system applying a work-ahead-window work release rule with exponentially distributed customer required lead time together with as numerical example are presented (Section 6.4). In particular, it turned out that the general findings from Chapter 5 do not change when the backorder costs are replaced by a service level constraint. The proofs of the major results are presented in the appendices to the particular chapters. Finally, some conclusions are presented in Chapter 7.
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    ABSTRACT: This article models a single-stage hybrid production system, which can be regarded as a Make To Order (MTO) production system with safety stocks or a Make To Stock (MTS) production system with advance demand information. In an environment with multiple products and variable customer due dates, optimality conditions for safety stocks (base stocks) and safety lead times (work-ahead window) that minimize inventory and backorder costs are derived. For a simplified M/M/1 system with exponentially distributed customer required lead time, an explicit comparison between MTO and MTS is conducted. A pure MTO policy gets relatively more favorable to a pure MTS policy if inventory holding costs increase, backorder costs decrease, the mean customer required lead time increases, or the processing rate increases. In a numerical study, the influence of variance, the behavior of optimal parameters, and the cost reduction potential of this hybrid policy are shown.
    IIE Transactions 03/2014; 46(3). DOI:10.1080/0740817X.2013.803638 · 1.06 Impact Factor
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    2013 15th IEEE International Conference on Communication Technology (ICCT); 11/2013