Capacity and Inventory Planning for Make-to-Order Production Systems - The Impact of a Customer Required Lead Time Distribution

Research output: Types of ThesesDoctoral Thesis


This thesis presents different models for the simultaneous optimization problem of capacity investment and work release rule parameterization. The overall costs are minimized either including backorder costs or considering a service level constraint. The available literature is extended firstly with the integration of a distributed customer required lead time in addition to the actual demand distribution and secondly with the integration of an endogenous production lead time. Different models for a make-to-order production system with one or multiple serial processing stages and one or multiple machines at each stage are developed. Capacity investment is linked to the processing rates of the machines or to the number of the machines. The work release rule discussed implements either a planned lead time at each respective stage or a work-ahead-window for the whole production system. Results of the thesis are equations in integral form for service level, tardiness, and FGI lead time in such a production system. For special cases with M/M/1 and M/M/s queues explicit expressions for service level, tardiness, and FGI lead time are delivered which show that the work-ahead-window work release policy has a significant finished-goods-inventory reduction potential. Furthermore, explicit solutions of the optimization problems or optimality conditions concerning capacity investment and planned lead time or work-ahead-window setting are provided for different production system structures. It is proven that the distribution of customer required lead time has no impact on the optimal planned lead times for predefined capacity. However, the optimal capacity investment is strongly influenced by this distribution. Numerical studies are generated to provide some additional insights for the respective production system structures. These show, for example, that predefined machine sizes and uncertainty about customer order arrival rates considerably influence the optimal costs. Furthermore, a set of proof-based managerial and research insights is developed. It is found that a service level constraint model cannot be transformed to a backorder cost model by setting an appropriate constant backorder cost factor when capacity investment and work release rule are optimized. Additionally, the optimal capacity invested is proven to increase towards the customer end of the line in a serial production system, under certain conditions.
Original languageEnglish
Publication statusPublished - 2011


  • Operations Management
  • Capacity and Inventory Planning

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