The Effect Of Demand Uncertainty In Supply Chain Systems With Mixture Conditional Value-at-risk Constrain

With the rapid development of technology and globalization of economy, thecompetitive environment faced up by the enterprises has become more complicated, atthe same time the competition has become much more fierce. Modern commercialcompetition has transformed from the competition among individual enterprise intothe competition among the supply chains of these enterprises. Coordinating contractsto satisfy the uncertain market demand, making sure that the whole profits ofmembers among supply chain are equal to the optimal profits of centralized supplychain, which has already become an important measure of supply chain management.Meanwhile, uncertainties from market and supply make enterprises’ profits at risks,also each enterprise has its own attitude towards risk. Because of fear about riks, themajority of enterprises tend to be risk averse, however, there are some firms holdingthe view that the bigger risk is the much more profits will be. Only by having a clearunderstanding about the effects of risk preferences and demand uncertainty on systemdecision, will we be able to achieve the goal of business operations and improve theoperational efficiency. Therefore, it is necessary for us to adopt mixture ConditionalValue-at-Risk constrain to explore the effect of demand uncertainty on the inventoryand supply chain systems.In this paper, we analyze the newsvendor problem and supply chain coordinationissues when facing random demand and pricing dependent demand with mixtureConditional Value-at-Risk (CVaR) constrain by using stochastic dominance in appliedprobability. The mixture CVaR can be obtained by using weighted average of theminimization CVaR and the maximization CVaR, which includes three special cases:risk aversion, risk neutral and risk taking. We introduce the concept of―riskpreference coefficient‖. First, as to the classic newsvendor model and the newsvendormodel with emergency ordering, we give the optimal order quantities and optimalprofits of the newsvendors facing random demand, then study the effects of riskpreference and demand uncertainty in the two inventory systems: stochastic largerdemand leads to higher optimal order quantity and optimal profit; under the cutcriterion ordering, more variable demand leads to less optimal order quantity whenrisk preference coefficient is larger than a critical point, but more variable demandleads to larger optimal order quantity when risk preference coefficient is smaller thanthe critical point; optimal profits have stochastic monotonicity under secondstochastic dominance when risk preference coefficient is larger than or equal to one.Second, as to the pricing dependent newsvendor model, we give the optimal priceunder the sufficient conditions, the optimal order quantity and optimal profits on the assumption of general demand function. With the stochastic comparison method, weanalyze how the demand uncertainty (stochastic larger and variability) affect thesystem’s optimal price, optimal order quantity and optimal profit from additive andmultiply demand models. Third, for the supply chain composed of a risk-neutralsupplier and a retailer with mixture CVaR constrain, we show that optimal orderquantity and profit of retailer will decrease while risk preference coefficient increasesunder wholesale price contract, revenue sharing contract and buy back contract;wholesale price contract can coordinate the supply chain system when the riskpreference coefficient is less than one corresponding to risk-taking case; supply chainsystem can also be coordinated by buy back contract and revenue sharing contract forany risk preference coefficient that is larger than, equal to or less than one. We provethat under revenue sharing contract, stochastic larger demand leads to higher optimalprofit of retailer; more variable demand leads to less profit of retailer when riskpreference coefficient is larger than or equal to one, that is in accordance withintuition. Similar results can be obtained for supply chain model with buy backcontract. Several numerical examples are provided to illustrate the obtained results.