Research On Robust Optimization Model And Strategy Of A Single Period Inventory Based On CVaR Under The Limited Demand Information

Enterprises face more and more uncertainty with intensifying of market competition and change of operation environment.Those uncertainties make operator have more difficulty in forcasting market demand.Especially for short life cycle products and it is difficult to get accurate demand distribution in real word.Therefore,enterprises should take a robust strategy to deal with uncertain disturbances.However most robust strategies dosen't take the risk problem caused by demand uncertainty into consider.Empirical investigations show that the strategy in actual operation is not aways coincident with traditional operation strategy based on expected profit or cost because of the different preferences of decision maker about performance risk resulting from uncertainty.Based on the above,the robust optimization model of a single period inventory based on conditional value-at-risk(CVaR)is established for risk-aversion inventory managers under the limited demand information by using maximum entropy approach and ψ-divergence and likelihood estimation.Main research content is as follows:Firstly,considering only demand interval,mean and variance information are known,and the decision-maker's risk aversion attitude,the single period inventory model based on conditional value-at-risk is developed.A maximum entropy approach is used to estimate the demand distribution for both of the two demand uncertainties.On this basis,the robust order and performances of a risk-aversion decision-maker based on CVaR are deduced.Specially,the effectiveness of the robust order based on maximum entropy is analyzed when getting the true demand distribution.Secondly,the robust optimization model of a single-period inventory based on conditional value-at-risk(CVaR)is established for risk-aversion inventory managers under the discrete stochastic demand with uncertain probability.Using ψ-divergence,the confidence region of uncertain demand probability with a certain confidence level is constructed based on statistical theory when only knowing discrete demand scenarios.The robust optimization model of a single period inventory is transformed into a tractable one by Lagrange dual theory.Specially,an inventory strategy based on data-driven is proposed in the setting of only demand scenarios are known.Thirdly,the robust mean-risk model of an inventory based on conditional value-at-risk(CVaR)is established for risk-aversion retailer.Two robust counterpart models with Pareto efficient but more conservative solutions and non-Pareto but less conservative solutions respectively are presented under discrete demand distributional uncertainty.Using the statistical theory,the uncertain set of demand probability distribution is constructed with a certain confidence level based on likelihood estimation when only knowing historical demand samples.Two robust counterpart models are transformed into tractable concave optimization problems by Lagrange dual theory,and a proof is given to show the equivalence of transformed models with original ones.And a Pareto frontier between retailer's expectation profit and its conational value-at-risk is also proposed.Finally,some numerical examples are executed to analyze the robustness of model,the results show that:(1)The order strategy derived from the estimated distribution by maximum entropy will lead to a certain performance loss,however the loss ratio is very limited,which indicates that the ordering strategy based on maximum entropy has good robustness.(2)The robust inventory strategy based onψ-divergence and likelihood estimation are robust to restrain the effects of uncertain demand probability on the inventory performance.(3)Comparing with the results derived by data-driven,the robust inventory strategy based on ψ-divergence can ensure inventory managers to get a more ideal performance which indicates that the mining for statistical information implicit in demand data can effectively improve the inventory managers' operation performance.(4)The more the historical demand samples,the closer the retailer's operational performance under robust inventory strategy based on likelihood estimation to its optimal level.Furthermore,the optimal inventory strategies for the above two robust counterpart models are qualitatively consistent,although they are different in conservation.Furthermore,the more risk-aversion,the less quantity and operation performance of managers.