Study On The Online Purchase Problem For Raw Material With Price And Yield Uncertainty

Raw material procurement of manufacturing industry plays an important role where the profit of a firm highly depends on the inventory cost.Therefore,efforts discovering potentials for the optimization of purchasing processes are essential to vitalize supply chain performance.Traditional purchasing inventory methods erither only considered price uncertainty or only considered yield uncertainty,assuming price/yield following some certain random distribution or stochastic process.However,companies often face both price and yield uncertainty.In the highly globalized world,the uncertainty of price and yield is increasing,price is too unpredictable to describie its probability distribution and it is difficult to ascertain the specific distribution of yield.In view of the above background,this paper study the problem based on the online theory and online purchasing inventory models are establised.All the policis proposed in this paper do not need to know the specific distribution of yield,and have good performance guarantees for arbitrary price sequence.Which only dependent on the lower and upper bounds of future price,and the first-order moment and second-order moment/variance of yiled.Thus,our policy delivers robustness to changing yield and price.The main research contents and conclusions are as follows:(1)This paper considers the online purchasing problem with yield dependent on lot size and arbitrary price.Yield is proportional to batch size.The corresponding model is established by competitive analysis method,and the corresponding purchasing policy under different cases is obtained.The theoretical competitive ratio of the policy is proved and the concise decision-making path is summarized.Finally,numerical examples are given to illustrate the effectiveness of the proposed policy.(2)Considering that in practice,there is no proportional relationship between yield and batch size in many cases,this paper studies the online purchasing problem with yield independent on lot size and arbitrary price.The corresponding purchasing policy is put forward,and the theoretical competitive ratio of the policy is proved.Finally,the detailed decision-making steps and flow chart are given.In theory,the polciy in this case depends directly on the variance of yield rather than the second-order moment,and the analysis process and decision-making path are more complex than those in batch-related case.Finally,numerical examples are given to illustrate the good performance of the policy.(3)Based on the existing analysis,the model in(1)is improved.An online purchasing model of raw materials considering inventory holding cost is established.The online inventory policy and decision path are given,and the competitive ratio of the policy is proved theoretically.Finally,numerical examples are given to further analyze the policy.