This paper investigates optimal choices for the etailer with inventory rationing, hybrid channel strategies, and service level constraint under multiperiod environment. Based on different operational conditions, five mathematical models are proposed for the etailer who faces two types of fuzzy demand and a framework is designed to illustrate the etailer’s operation in different models. This paper presents the advantages of inventory rationing and hybrid channel strategies and analyzes the influences of channel differences variability on optimal choices for the etailer, where the channel differences include margin difference of priority and margin difference of channel. Through computer simulation, the optimal choices for the etailer under different multiperiod environments are obtained, and the influences of margin difference of priority and margin difference of channel on the etailer’s optimal choices are also examined. Experiment results show that the pureplay drop shipping model and the hybrid channel with inventory rationing model are the optimal choices for the etailer; these findings have valuable guiding significance for the etailer to make optimal tactical decisions under multiperiod environment.
China’s ECommerce Report (2014) shows that the total amount of Chinese ecommerce transactions is up to
The rapid development of ecommerce requests more on the efulfillment, which is the critical operation of distributing the goods to the customers, so the etailer tries to improve service level of efulfillment, and adopts drop shipping as an efulfillment option. With the popular of drop shipping in ecommerce, the etailer can choose two different basic operational models, which include the pureplay drop shipping etailer model and the traditional etailer model [
In addition, if different demand types bring the same profit to the etailer, then the etailer will treat all types of demand equally. When the etailer gets different margins from different demand types, the etailer has the power to fulfill the demand type with higher margin first compared to the others. Furthermore, when the etailer obtains different margins from different demand types with different efulfillment options, the etailer should use the efulfillment option with more profit to satisfy the demand type with higher margin first. In this situation, the etailer with limited drop shipping ability faces a problem: how to allocate stock for different demand types to get more profit. There are many cases of adoption on inventory rationing strategy with multiple types of demand [
The motivation of this research comes from the etailer who sells products on the internet under multiperiod environment. The etailer gets different margins from the same units of demand by different efulfillment options, whereas they obtain different margins from different types of demand with the same efulfillment option. In order to get more profit under multiperiod environment with inventory rationing, hybrid channel strategies, and service level constraint, the etailer wants to know which model is optimal under certain multiperiod environment, and how channel differences are influent on the optimal choices in ecommerce. Through computer simulation, this paper analyzes these problems and gets the optimal choices for the etailer within different mathematical models. The advantages of inventory rationing and hybrid channel strategies are also evaluated in this study.
The contributions of this research are as follows.
The remainder of this paper is organized as follows. Section
It is valuable to classify demand according to certain difference and treat different types of demand with different efulfillment options for the etailer. As a basis for classification, there are some different measurements which include shortage cost, lead time, service level and others.
The types of demand were characterized firstly by different shortage cost. Veinott [
There were also some other researches where the types of demand differed by lead time, service level, and so forth; Cattani and Souza [
Drop shipping had been used by mailorder firms in the 1980s and became one of the primary ways for the etailer to fulfill demand on the internet; there was a survey that indicated that 30% of pure play etailer relied heavily on drop shipping in the efulfillment [
Lots of previous researches focus on the operational aspects of the etailer or the retailer, such as pricing, stocking decision, and inventory rationing. This study evaluates the inventory rationing and hybrid channel strategies from other different perspectives. The goal of this research is principally to explore the optimal choices of the etailer with inventory rationing, hybrid channel strategies, and service level constraint under multiperiod environment, and this paper makes several contributions to understand the characteristics of inventory rationing and hybrid channel strategies. One unit of the operational period of five mathematical models is illustrated for the etailer and the reason why more and more etailers adopting inventory rationing and hybrid channel strategies are found in the comparisons between the models with inventory rationing and hybrid channel strategies and other models without them. Furthermore, the mixture influences of channel differences on the etailer’ optimal choices are also considered in the experiment. These results will help the etailer to make the optimal decisions under multiperiod environment.
Comparing with other etailer models on the internet, this paper focuses on the situations about the etailer who uses both inhouse inventory and drop shipping to fulfill two different classes of fuzzy demand and the etailer wants to choose the optimal mathematical model to get more profit under multiperiod environment. On the one hand, the etailer earns more margins with inhouse inventory than drop shipping from satisfying the same unit of demand; then the etailer should prepare enough stock in order to maximize profit. On the other hand, there are two classes of demand: the priority demand and the common demand. The etailer gets more profit from selling the same unit of commodity to the priority demand than the common demand. With limited stock in inventory system, the priority demand should be fulfilled first compared the common demand. In other words, the priority demand has priority compared to the common demand in the efulfillment.
According to inventory rationing and hybrid channel strategies, the etailer uses inhouse inventory to fulfill two classes of demand when stock in the inventory is sufficient. If onhand stock of inhouse inventory reaches or becomes less than the threshold level, the etailer fulfills the priority demand by inhouse inventory and adopts drop shipping to satisfy all the common demand. Finally, if inventory system has no stock, drop shipping will be used to fulfill both the priority demand and the common demand. These are the efulfillment rules of the etailer with inventory rationing and hybrid channel strategies in the efulfillment.
The inventory system of the etailer used in this paper is a
The operational process of the pureplay drop shipping etailer is as follows; first, two types of demand surf the internet and place orders to the etailer; second, the etailer gets the demand information from two types of demand and forwards it to the supplier; third, the supplier distributes the products to two types of demand based on the demand information obtained from the etailer. With service level constraint of the supplier’s drop shipping, a few of demand will not be satisfied and seems as lost sale, which will cause additional penalty cost to the etailer. Equation (
Then, the etailer’s profit function is got in (
Supply chain of the pureplay drop shipping etailer.
The traditional etailer runs an inhouse inventory and replenishes products from the supplier. The etailer fulfills the priority demand first because of getting more margins from it than that from the common demand. If onhand stock cannot fulfill all the priority demand, the remaining and all the common demand will be lost sale. The common demand will be satisfied when on hand stock is not empty after fulfilling the priority demand. If on hand stock is fewer than the quantity of the priority demand, some of the priority demand will be lost sale and cause penalty cost to the etailer. The traditional etailer model is shown in Figure
Supply chain of the traditional etailer.
Two types of demand satisfied by inventory system are shown in (
The difference between model III and model II is the adoption of inventory rationing strategy, which can be found in the comparison between Figures
Supply chain of the traditional etailer with inventory rationing.
Equation (
Because the pureplay drop shipping etailer completely relies on the supplier to fulfill customers, the failure in the drop shipping service causes bad impact directly on the etailer, but not the supplier, so the etailer runs an inventory system to improve the efulfillment performance. In other words, the traditional etailer owns an inhouse inventory and completely depends on it to satisfy customers; what should the etailer do when stock out happens? One solution is drop shipping. The etailer who uses both inhouse inventory and drop shipping in the efulfillment is denoted as the hybrid channel etailer. Figure
Supply chain of the hybrid channel etailer.
Two types of demand satisfied by inventory system in model IV are similar to model II, and (
In this model, the etailer adopts the threshold policy in inventory system based on model IV, and the etailer’s inventory operational process is similar to model III. The difference between this model and model IV is the computation of the common demand which is satisfied by the etailer’s inhouse inventory. And the difference between this model and model III is the arrangement of the demand which cannot be fulfilled by inhouse inventory. The supply chain of model V shows is as shown in Figure
Supply chain of the hybrid channel etailer with inventory rationing.
The priority demand fulfilled by the etailer’s inventory system is obtained same as (
According to five mathematical models, a framework is designed to illustrate their operational processes in every unit of time
The operational processes of five different etailer models in time
In this section, the inventory rationing and hybrid channel strategies with service level constraint is evaluated based on five mathematical models in Section
The experiment platform consists of a Dell D630 (RAM: 3 G, CPU: Intel Core 2 Duo T7250 2.0 GHz, HDD: 120 G) and Matlab (v. R2008a).
The values of parameters.
Notations  Values  Notations  Values  Notations  Values 


















0.1–0.9 





5000 

80% 



0 

60% 



1200 
When priority preference is rising, the average profits of both model II and model III are increasing. Because the etailer can get more margins from the priority demand, more profit will be earned by the etailer when priority preference increases. With the priority preference raises from 0.1 to 0.9, the average profit of model II increases from
Average profits of model II and model III.
Figure
Average profits of model II and model IV.
Average profits of model III and model V.
In this section, the optimal choices of the etailer with channel differences variability are analyzed, which include the variability of margin difference of priority and margin difference of channel. For simplicity, MDP and MDC are used to represent them, separately. And experiment results show that the variability of MDP and MDC is very important for the etailer to make tactical decision under multiperiod environment.
Given three different MDC levels, the influences of MDP on the optimal choices of the etailer are analyzed. Figure
Impact of MDP on the etailer’s average profits with MDC = 1.0.
Impact of MDP on the etailer’s average profits with MDC = 1.4.
In addition, the average profit differences between model V and model IV are relatively small in Figures
Average profits of the etailer with MDC = 1.4.
MDP 






1.0 





1.3 





1.6 





1.9 





2.2 





2.5 





2.8 





3.1 





3.4 





3.7 





4.0 





Impact of MDP on the etailer’s average profits with MDC = 1.8.
Similar to the analysis of MDP in Section
Average profits of the etailer with MDP = 1.6.
MDC 






1.0 





1.2 





1.4 





1.6 





1.8 





2.0 





2.2 





2.4 





2.6 





2.8 





3.0 





Impact of MDC on the etailer’s average profits with MDP = 1.0.
Impact of MDC on the etailer’s average profits with MDP = 1.6.
Impact of MDC on the etailer’s average profits with MDP = 2.2.
Based on inventory rationing and hybrid channel strategies, this paper analyzes five mathematical models for the etailer under multiperiod environment with service level constraint, fuzzy demand, and fuzzy lead time through computer simulation. A general framework is designed to illustrate the operational processes of different etailer models; the advantages of inventory rationing and hybrid channel strategies are evaluated when the etailer aims to maximize average profit with two types of demand, and the optimal choices of the etailer are obtained within different mathematical models. The mixture influences of margin differences of priority and channel on the optimal choices for the etailer are also considered. The results show that inventory rationing and hybrid channel strategies can bring more margins to the etailer, and the additional margins become more with the rising of margin difference of channel. The pureplay drop shipping model and the hybrid channel with inventory rationing model are the optimal choices for the etailer. In addition, this research has some extensions; when the cost of running an inventory system becomes higher, or the margins obtained from inhouse inventory are decreasing, and so forth, the optimal choices of the etailer will become uncertain under these scenarios; these problems should be concerned and studied in the future.
Total demand, a triangular fuzzy number
The class
Unit margin of using inhouse inventory to fulfill class
Unit margin of using drop shipping to fulfill class
Lead time, a triangular fuzzy number
The optimal threshold value
Stock reorder point
Order lot size
Inventory position of inhouse inventory at time
On hand stock of inhouse inventory at time
Units on order of inhouse inventory at time
Class
Class
Lost sale of class
Inventory holding cost per unit per time
Inventory ordering cost per replenishment
Service level of the supplier’s drop shipping for class
Penalty cost per unit of class
Profit function of the etailer in model
Flag of placing an order at time
Flag of arriving an order at time
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the Research Fund for the Doctoral Program of Higher Education of China (no. 20100032110034), the Research Fund of Humanities and Social Sciences of the Ministry of Education of China (no. 12YJAZH052), and Langfang Science and Technology Support Program (no. 2015011065).