Joint Ordering And Pricing Policy Of Fresh Products Under Lost Sales

Fresh products,which are as perishable products deteriorating rapidly,are offen wasted seriously in stock.Both the inventory inaccuracy caused by quantity decay and the freshness deterioration caused by quality decay result in the loss of the revenue.There are some challenges that retailers face during the retail process: severe quantity loss,exact description of demand model,different freshness levels of products existing in stock at the same time.Therefore,this paper studies the joint ordering and pricing policy for the quantity decay or the quality decay respectively to reduce the negative effects of product deterioration and uncertain demand.The main contents of this paper are as follows:1.For quantity decay,we study two robust replenishment policy in order to maximize the profit:probability-distribution-based policy and the expectation-based policy.The former first gives a recursive algorithm to estimate the probability distribution of real inventory level,and then proposes a policy based on the estimated inventory probability.The latter simplifies the problem by expectation of random variables in the mathematical model,gives a method to calculate the optimal replenishment quantity by the “zero-inventory” property,and proves the unimodal property of the objective function.The relevant theoretical analysis and numerical experiments show that:(1)the policy considering the impact of the future periods(probability-distribution-based policy,pexpectation-based policy)performs better than the policy only considering the current period;and(2)the policy considering invisible inventory loss performs better than the policy ignoring that.2.Further,considering the influence of price on demand,joint ordering and pricing problem is studied to maximize the average profit over infinite horizon.Besides,the sensitivity of the optimal policy on the price-demand parameters is analyzed.The research is divided into three parts:(1)For a deterministic price-demand function,the optimal joint ordering and pricing policy is studied,in which,the retailer decides the price in every period,namely,the price for the fresh product is not fixed.Theoretical analysis shows that the optimal pricing policy presents a trend of setting a lower price at first in order to avoid the inventory holding cost caused by a high inventory level.(2)From the sensitivity analysis of price-demand parameters,it can be found that the influence of price-demand parameters on the optimal order quantity and the optimal price is different: The optimal price is robust to the market capacity(i.e.,the maximum demand),while the optimal order policy is very sensitive to the change of the price-demand parameter;comparing to the optimal pricing policy,the optimal ordering policy is more sensitive to the price-demand parameters.(3)In order to solve the problem that the estimated price-demand parameter deviates from the real value,a heuristic parameter regulating method based on historical sales data is proposed.3.For the quality decay of fresh products,if the retailer orders new products when there are some remaining products in the shelf,there will be multiple freshness levels in the shelf at the same time.The multiple freshness levels of a products makes both the description of demand and the decision of the policy difficult because the random selection behavior of customers.In order to solve this problem,we adopt an two-shelf rule for fresh products.By the two-shelf rule,the products of different freshness level can be separated.In this part,we study the single deterministic problem of joint ordering of new items and pricing of old items and propose a joint ordering and markdown policy,when the demand of the product depends on its price and freshness and unsatisfied demand is lost.The main research contents are divided into two parts:(1)a single-period model is formulated,in which the present shelf ages of items in the two shelves are considered and the Karush-KuhnTucker condition is used to obtain the optimal solution of the joint ordering and markdown problem.(2)In order to evaluate the performance of the two-shelf policy in comparison with traditional oneshelf policy,the obtained optimal solution of the single-period model is applied to the multi-period problem in the form of a myopic policy.The results show that the proposed two-shelf policy for fresh products performs better than the traditional one-shelf policy.4.For the stochastic competitive demand over infinite horizon,we study the optimal ordering and markdown problem of the two-shelf model with lost sales.In this problem,the retailer decides the order quantity of the new items and the discount price of the old items at the same time in order to maximize the discounted profit of over infinite horizon.Stochastic dynamic programming is used to obtain the optimal ordering and markdown policy at the steady state.The results of numerical experiments provide some management implications for retailers:(1)For the case that neither the new products nor the old products have totally decayed,the order point depends on the inventory level of new products and the inventory level of old products together.However,the optimal order quantity is mainly affected by the inventory level of new products.In addition,when the old products are close to the shelf life,the ordering area has a trend of seperation(2)For the case that only the old products are completely decayed,both the optimal order quantity and the optimal discounted price decrease in the inventory level of new products.