Dynamic newsvendor model for Optimistic and Pessimistic policy-based profit forecasting

Abstract

The aim of this study is to propose and implement a dynamic multi-period newsvendor model for a perishable product by incorporating forecasts for profit maximization within optimistic, neutral and pessimistic scenarios learned through partial knowledge of demand. The proposed model is an attempt to simulate the inventory management process under varying levels of risk in order to evaluate risk management strategies.

Note: As this is a working paper, the full-length paper is not shared here.

Results

Profit levels: Profit forecasts when the manager collects simulates the environment using (1) Monte Carlo, (2) Pessimistic, (3) Optimistic, and (4) Hybrid inventory management policies:

• Poisson distribution of demand:

  • Manager is a far-sighted optimist: The algorithm predicts profits across all transition states as an optimistic far sighted prediction.

  • Manager is a near-sighted pessimist: The algorithm predicts no profits, or very small profits across various transition states as a pessimistic prediction policy.

It can be concluded that Poisson distribution has an optimistic bias, as the algorithm trained on various MCMC rounds never predicts losses even with pessimistic settings.

• Weibull distribution of demand:

  • Manager is a far-sighted optimist: The algorithm predicts low profits under Weibull distribution, even though the manager is an optimist.

  • Manager is a near-sighted pessimist: The algorithm predicts losses across almost all transition states as a pessimistic prediction policy.

It can be concluded that Weibull distribution does not has a pessimistic bias, as the algorithm trained on various MCMC rounds never predicts high profits even with optimistic settings.

Monte Carlo trained Neural Network: Performance of NN trained on Monte Carlo simulation:

• Poisson distribution:

  • Farsighted optimist:

  • Nearsighted pessimist:

• Weibull distribution:

  • Farsighted optimist:

  • Nearsighted pessimist:

The Neural Network overfits the training data in the case of k=1000 and performs better for most transition states for k=100. The mean squared error, and the Wasserstein metric support the observation.

Hybrid Monte Carlo trained Neural Network: Performance of NN trained on Hybrid Monte Carlo simulation:

• Poisson distribution:

  • Farsighted optimist:

  • Nearsighted pessimist:

• Weibull distribution:

  • Farsighted optimist:

  • Nearsighted pessimist:

The Neural Network is able to learn the optimistic and pessimistic prediction setting, which is demonstrated through the plot above. The hybrid algorithm is able to provide the Inventory Manager with the required predictive flexibility.

Conclusion

The dynamic, manager friendly inventory management system provides the decision maker with flexibility to choose risk levels, and management policy methods (far/near sighted, or optimist/pessimist) than a simple risk-neutral Monte Carlo method. In cases when the demand is unknown, or partially known, well known demand-distribution curves like Poisson or Weibull distribution can be used to approximate them, and train the AI which helps take the best possible approach to manage inventory such that the profit attains highest-possible levels.