On a multi-product lot scheduling problem subject to an imperfect process with standby modules

Abstract

An Economic Lot Scheduling Problem is considered under the condition that the production process may shift from an in-control state to an out-of-control state due to the deterioration of the facility’s key module. We adopt the Common Cycle policy in two mathematical models depending on whether the key module is repairable or not. Several standby modules are available during a production run. For the model with non-repairable key modules, the active key module, once deteriorated, is disposed of and replaced by a new standby. For the model with repairable key modules, the active one is replaced by a standby as soon as it is deteriorated. The failing module will be restored in a repair shop and rejoin the standbys. The objective is to determine an optimal production cycle time and the economic number of standby modules in order to minimise the long-term average cost including set-up, inventory carrying, standby and defective costs. The convexity of the cost functions is revealed so that efficient algorithms can be developed accordingly to achieve optimal production-inventory policies. It is shown that these policies can be used to significantly improve the system performance.

Keywords:

• imperfect process
• standby modules
• inventory management
• non-linear programming

Acknowledgements

The authors are thankful for the partial support by Singapore Agency for Science, Technology and Research (A*STAR) SERC Grant 1122904020, as well as the valuable comments from the Associate Editor and anonymous reviewers.

Notes

1. Producing a defective item means the time and material are wasted. Usually, it takes more effort to rework the item.

2. The recent estimate of the annual cost rate to carry inventory ranges from 25 to 50% of the value of the inventory. Cf. Johnson, Leenders, and Flynn (2011).

3. According to Silver, Pyke, and Peterson (1998), the carrying charge ranges from 20 to 40%. According to Johnson, Leenders, and Flynn (2011), the carrying charge ranges from 25 to 50%. A manager may arbitrarily choose an adequate value for the carrying charge in order to control the inventory level. Here, we use the range of 20–40% in the experiment which should encompass most scenarios in practice.