Journal of Global Optimization

, Volume 8, Issue 4, pp 349–378 | Cite as

Transient and steady-state analysis of a manufacturing system with setup changes

  • Sherman X. Bai
  • Mohsen Elhafsi


This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.

Key words

Dynamic setups setup and production flow control optimal control 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Sherman X. Bai
    • 1
  • Mohsen Elhafsi
    • 1
  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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