时间：2022-10-19 09:43:28
【Abstract】In this paper， the joint strategy of the single cycle fresh product about inventory and promotion is considered， and the order promotion joint decision model is established. By the initial procurement， promotion starting time， discount sales promotion efforts， iterative method of best strategy is obtained and retailers get the maximum benefits. Through numerical simulation example， the paper analyzes the effects on the objective function and decisions which are exerted by the changes of parameters of deteriorating rate. The results show that the smaller deterioration rate， the later promotion starting time； The results of this paper have reference value for the storage and promotion of fresh products.
【Key words】Fresh products； Promotion； Price discount； Deterioration； Promotion starting time
0 Introduction
In recent years， the requirements of fresh products are increasing. So the inventory management of fresh products is more important. Meanwhile some scholars launched studies on the inventory and sales of fresh products. The preliminary research results are as follows： Wee[1] construct an inventory model under some conditions that product’s life is subjected to double parameter weibull distribution. Wee and yu[2] found out how quantity discount affected the inventory strategies of retailers. Monahan[3] studied quantity discount problem from the perspective of suppliers. Tersine[4] studied the temporary price discount and presented OTOS（one time only sale）， then Tersine[5] also proposed a generalized EOQ model which was given temporary price discounts；
Currently in the study of inventory model on price discount decision， the demand rate is mostly assumed to be price-related functions without considering the effects of freshness on demand. Therefore， this paper introduces the concept of freshness to portray the freshness of products and to research the impact of freshness inventory and sales strategies.
1 Problem description
The joint decision problem of fresh products on order and sale inventory and promotion can be viewed as a single-cycle inventory problem. Businesses arrange promotions（e.g.， price， etc.） at an appropriate time so that they can make the maximum profit after selling out at the end of cycle.
2 Model assumption and symbolic meaning
（1）We only consider one sales cycle（T）.
（2）Inventory is zero when the cycle of sale is finished.
（3）Fresh products have refreshing time tf （0
（4）The price of products is influenced by freshness； construct fresh degree function F（t）=f 1， here 0
（5）Products go bad at a freshness rate of ？兹（0
（6）Demand rate of fresh products is influenced by their price and freshness， so the demand rate of fresh products is assumed as D（t）=（a-bp）f t.
（7）In order to maximize profit， businesses carry out promotional activities in a period of time（t1（0≤t1≤T））.
（8）The objective function of this paper is the maximum profit which businesses can make in a sales cycle， the decision variables are organized as follows： duration of promotion t1（0≤t1≤T）， the coefficient of discount rate ？茁（0≤？茁≤1） and the initial purchase quantity.
（9）I（t）： The inventory level of fresh products at the time of.
（10）HR： The sales revenue in a sales cycle.
（11）HY： The inventory cost in a sales cycle.
（12）h： The inventory cost of per unit product in a cycle.
（13）HC： The variable costs that businesses cost in a sales cycle.
（14）p0： The purchasing price of per unit product.
（15）p： The selling price of per unit product.
（16）E： The gross profit which businesses obtain in a sale cycle.
（17）A： The fixed cost that businesses order once.
（18）C： The fixed cost that businesses promote once.
3 modeling
From the assumption， it can be seen that the function of demand rate is D1（t）=（a-bp）f 1 when 0≤t≤t1. Businesses start to carry out promotional activities from the moment of t1 and the coefficient of discount rate is ？茁， so the function of demand rate is D2（t）=（a-bp？茁）f 1 when t1≤t≤T. Fresh products will not go bad during quality guarantee period. Based on the actual situation， businesses generally carry out promotion after quality guarantee period（tf）， so t1 ranges from tf to T. The inventory function in this paper is a piecewise function and the change law of inventory is defined as follows；
The original value of t1 is given to t0 1 ， then we can obtain ？茁0 and E0； To make t1 1=t0 1+？着 （？着 is a sufficiently small）， it can obtain ？茁1 and E1. We do not stop doing iteration until t1 or ？茁 is not in the domain of definition. Comparing the results （t1， ？茁， E）， we can find out the optimal solution.
5 numerical simulation and analysis
Study the effect of parameters （？兹， tf ， f） on the decision
Case 1： study the influence of deterioration rate on decisions， therefore， in a given model parameter values are as follows：
a=120，b=10，T=10，tf=8，p=4，p0=2，h=0.05，f=0.95，A=20，C=10。
Experimental results are showed in the following form：
form 1 The impact of deterioration rate on decision
The results show that the smaller the deterioration rate is， the more late promotion began to and the smaller discounts will be. This is in line with the actual situation.
6 Conclusions
In this paper， the joint strategy of the single cycle fresh product about inventory and promotion is considered， and the order promotion joint decision model is established. The shortcomings of this paper are that it only considers the demand whose ty is certain， without considering the demand which is uncertain and random. The next step of research is to take these factors into consideration and study the stochastic inventory sales problems.
【References】
[1]Wee H M. Deteriorating inventory model quality discount， pricing and partial backordering[J].International Journal of Production Economics， 1999， 59：511-518.
[2]Wee H M. Yu J. A deteriorating inventory model with a temporary price discount[J].International Journal of Production Economics， 1997， 53：81-87.
[3]Monahan P. A quality pricing model to increase vendor profits[J].Management Science， 1984， 30（6）：1398-1400.
[4]Tersine R J， and Grasso E T. Forward Buying in Response to Announced Price increase[J].Journal of Purchasing and Materials Management， 1978， 14（2）： 20-22.
[5]Tersine Richard， Barman Samir. Economic Purchasing Strategies for Temporary Price Discount[J].European Journal of Operational Research.
[6]P. M. ghare and G.. E. Scharder， A model for exponentially decaying inventory， J. lnd. Eng[J].1963， 14：238-243.