Optimal due date quoting for a risk-averse decision-maker under CVaR

Abstract

This study investigates a due date quoting problem for a project with stochastic duration, taking the decision-maker’s risk attitude into consideration. The project profit is defined as the difference between the price and the cost that is comprised of production cost and earliness–tardiness penalties. In this situation, the due date determination has to be modelled as a stochastic optimisation due to stochastic duration. Conditional value at risk is thus employed as a performance measure to describe the decision-maker’s risk attitude. In fixed price contract, when the unit production cost is not smaller than the unit penalty on earliness, the optimal due date increases with the increase of the degree of a decision-maker’s risk aversion, the unit penalty on delay, and the decrease of the unit penalty on earliness. Besides, when the price is proportional to the due date and the slope is no bigger than the unit penalty on tardiness, the optimal due date is smaller than the result in fixed price. This is because high price for a short due date encourages a decision-maker to quote a small due date. Further, we compare the optimal due date in different parameter setting where the penalty coefficient of earliness is negative or zero, which means there is reward or no penalty on earliness, respectively. Finally, a case study is conducted to validate the effectiveness and efficiency of the proposed model.

Keywords:

• due date quoting
• CVaR
• stochastic duration
• just in time
• risk analysis
• decision support systems

Acknowledgments

The authors would like to thank the AE and reviewers for their constructive comments.

Notes

1. Let ,we have.

Besides,

Since , we get , therefore is decreasing in x_d.

2. Let , then we have .

Since , we obtain .

Therefore, we have .

Since ,we get , therefore is decreasing in .