Lijun Ma

Coordination of Supply Chains with Bidirectional Option Contracts

In this paper we develop a supply contract for a two-echelon manufacturer–retailer supply chain with a bidirectional option, which may be exercised as either a call option or a put option. Under the bidirectional option contract, we derive closed-form expressions for the retailer’s optimal order strategies, including the initial order strategy and the option purchasing strategy, with a general demand distribution. We also analytically examine the feedback effects of the bidirectional option on the retailer’s initial order strategy. In addition, taking a chain-wide perspective, we explore how the bidirectional option contract should be set to attain supply chain coordination.

The informational aspect of the group-buying mechanism

This paper studies the group-buying mechanism from a dynamic perspective. We consider a seller that offers a product in the form of group buying (priced low but uncertain) and spot purchasing (priced high but guaranteed). In the case of group buying, the information associated with the number of participating customers is updated in the middle of the sale. Customers are assumed to be strategic with a time-dependent utility. In addition to choosing between spot purchasing and group buying, customers could choose to delay their decisions until the information update. We characterize the customer behavior within a rational expectations framework. We then consider the effect of information and demand dynamics. Our results show that whereas an improvement in information quality has a positive effect on customer surplus and the group-buying success rate, the effect of inter-temporal demand correlation is mixed. We also discuss the seller’s profit maximization problem and derive the condition to be satisfied at the optimal group size.

Loss-Averse Newsvendor Problem with Supply Risk

Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor’s loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker’s optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.

Empty container management and coordination in intermodal transport

In this paper, we study the empty container inventory sharing and coordination problem in intermodal transport. We focus on dry ports in intermodal transport to raise the coordination issue in empty container management. We consider an intermodal transport system composed of one railway transport firm at a dry port and one liner firm at a seaport. First, we characterize the optimal delivery policy between the dry port and seaport in the centralized model. We investigate how the optimal policy changes with the initial inventories of empty containers at the dry port and seaport. Next, we design a bilateral buy-back contract to coordinate the decentralized system. We derive the Nash equilibrium of the inventory sharing game between the rail firm and liner firm under the decentralized model as well as the equilibrium delivery quantity with a given bilateral buy-back contract. Moreover, we coordinate the decentralized system by choosing appropriate contract parameters and show how the system’s profit can be distributed between the two firms under coordination.

Inventory rationing and markdown strategy in the presence of lead-time sensitive customers

Appropriate customer segmentation, together with tailor-made strategies which dynamically change prices for customers, helps firms allocate resources more effectively. We incorporate markdown tools into the inventory-rationing model with customers segmented by lead-time sensitivity. We characterize the threshold-type optimal commitment policies and propose an efficient algorithm to compute the thresholds.

Examples from Industry

In this chapter, we provide a number of industry examples of how firms implement the strategy of flexible delivery times. The first example is Toyota China’s dealerships. Dealerships use a price- and delivery-time-based segmentation strategy to ameliorate the supply-demand imbalance due to inaccurate demand forecast and a rigid production schedule. We also discuss examples such as multiple shipping options offered by online retailers and the priority queue system as commonly seen in the service industry. In all of these examples, firms segment customers based on their price and delivery-time sensitivities, and the critical question is how firms should implement the strategy optimally in a dynamically changing context. This question is elucidated by the theoretical discussion in the following chapters.

Inventory Models with Delivery-Time Upgrade

In this chapter, we extend the unitary inventory commitment policy discussed in Chap. 3 to a more general upgrade policy, which allows the seller to choose the delivery time of all backlogged long lead-time orders. We characterize the optimal inventory upgrade and replenishment policies. In our analysis, we resort to the technique of anti-multimodularity to derive the structural properties of the value function. We further calibrate the model parameters using the empirical data collected from Toyota China dealerships and calculate the optimal policies and several performance metrics accordingly. The numerical results show that the upgrade mechanism can improve both profit and inventory usage .

Inventory Models with Two Delivery-Time Options

In this chapter, we consider a multi-period inventory model in which a seller provides alternative delivery lead-time choices to customers: a short lead time and a long lead time . In addition to the cyclic inventory replenishment decision, the seller makes the inventory commitment decision, i.e., whether to use a unit of on-hand inventory to satisfy a long lead-time customer immediately. We first characterize the optimal inventory commitment and replenishment policies in a non-capacitated setting. The optimal inventory commitment policy is subject to a commitment level, and the optimal replenishment policy is of a base-stock type. We then consider an extended model with a supply-capacity constraint , in which the commitment policy further includes rejections of short and long lead-time orders. We show that the optimal inventory commitment policy for short lead-time customers is characterized by a switching commitment level and that the optimal inventory commitment policy for long lead-time customers is characterized by three switching commitment levels. We then compare the performance of the optimal dynamic commitment policy with that of a static rationing policy through numerical studies.

Inventory Management with Alternative Delivery Times: The Case of Group Buying

In this chapter, we apply the method of modeling and analysis used in previous chapters to a discussion of the inventory control problem of group buying . The seller offers two purchasing options to its customers: a regular option and a group-buying option . The outcome of the group buying is uncertain and affects the inventory allocation at the end of the selling season. The seller thus can choose to ration the demand from regular customers to reduce possible penalty. We derive the optimal inventory rationing policy and demonstrate that it remains robust in several extensions.