Xiaobo Zhao

Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies

We consider a multi-retailer system operated on an infinite horizon, in which each retailer faces stochastic demand following a Poisson process and adopts a continuous-review (r, Q) policy for replenishing inventory to satisfy customer demand. The system involves decisions of pricing and inventory management with the goal of maximizing profit, which equals the sales revenue minus the purchase and inventory costs. Taking Cournot competition into account, models are formulated to optimize simultaneously the expected sales volumes and (r, Q) policies of all retailers. An efficient approach is proposed to calculate the approximate inventory cost. Based on this approach, solution methods for centralized and decentralized scenarios are developed. A great number of numerical computations are provided to evaluate the efficiency of the solution methods, and their performance in the two scenarios. Moreover, system performance under sequential decisions (first pricing and then inventory management) is also investigated.

Inventory Management for Dual Sales Channels with Inventory-Level-Dependent Demand

This paper studies the inventory management problem of dual channels operated by one vendor. Demands of dual channels are inventory-level-dependent. We propose a multi-period stochastic dynamic programming model which shows that under mild conditions, the myopic inventory policy is optimal for the infinite horizon problem. To investigate the importance of capturing demand dependency on inventory levels, we consider a heuristic where the vendor ignores demand dependency on inventory levels, and compare the optimal inventory levels with those recommended by the heuristic. Through numerical examples, we show that the vendor may order less for dual channels than those recommended by the heuristic, and the difference between the inventory levels in the two cases can be so large that the demand dependency on inventory levels cannot be neglected. In the end, we numerically examine the impact of different ways to treat unmet demand and obtain some managerial insights.

Computing (r, Q) policy for an inventory system with limited sharable resource

This paper deals with inventory systems with limited resource for a single item or multiple items under continuous review (r, Q) policies. For the single-item system with a stochastic demand and limited resource, it is shown that an existing algorithm can be applied to find an optimal (r, Q) policy that minimizes the expected system costs. For the multi-item system with stochastic demands and limited resource commonly shared among all items, an optimization problem is formulated for finding optimal (r, Q) policies for all items, which minimize the expected system costs. Bounds on the parameters (i.e., r and Q) of the optimal policies and bounds on the minimum expected system costs are obtained. Based on the bounds, an algorithm is developed for finding an optimal or near-optimal solution. A method is proposed for evaluating the quality of the solution. It is shown that the algorithm proposed in this paper finds a solution that is (i) optimal/near-optimal and/or (ii) significantly better than the optimal solution with unlimited resource.

On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers

This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded.

A two-demand-class inventory system with lost-sales and backorders

A periodic review inventory system serves two demand classes with different priorities. Unsatisfied demands in the high-priority class are lost, whereas those in the low-priority class are backlogged. We formulate the problem as a dynamic programming model and characterize the structure of the optimal replenishment policy.

Stability of a priority queueing system with customer transfers

This paper is concerned with the stability of a preemptive priority queueing system with customer transfers. Conditions for the queueing system to be stable/unstable are found. An interesting result is that the stability/instability conditions are independent of the service rates of lower priority customers and the transfer rates.

Risk Mitigation Benefit from Backup Suppliers in the Presence of the Horizontal Fairness Concern

The backup supply strategy is demonstrated as an effective approach to mitigating supply risk. We study a supply chain in which a leader manufacturer designs a contract to a potential backup supplier to mitigate the yield uncertainty of the primary supplier. In this context, the backup supplier may compare with the primary supplier and have horizontal fairness concerns. We model the contract design problem using a Stackelberg game and characterize the optimal decisions for the manufacturer and backup supplier, in both fairness and off-fairness settings. The theoretical results show that the leader manufacturer must sacrifice his own payoff to balance the payoffs of both suppliers. As a result, using a self-interested backup supplier is the dominating strategy, whereas using a fair-minded backup supplier is only suggested when the reliability of the primary supplier is low and the fairness concern of the backup supplier is not strong. Additionally, the backup supplier only benefits from fairness concerns when the level is not exceeding a threshold value. With regard to high fairness levels beyond this threshold, fairness concern has negative effects on the monetary payoff and even might lead to loss of the business. By conducting laboratory experiments, we provide evidence of the horizontal fairness concern from the backup supplier. Further, we show that if the primary supplier also has horizontal fairness concerns, the leader manufacturer can conditionally benefit from a promoted yield reliability due to an extra effort from the primary supplier

On supplier encroachment with retailer's fairness concerns

We introduce the retailers fairness concerns into the supplier encroachment problem.The retailers profit may decrease in her disadvantageous-inequality aversion degree.The supplier has more flexibility to encroach.The retailer has more possibility to benefit from supplier encroachment. With the development of e-commerce, many wholesale suppliers establish direct channels competing with their retailers. Such competition is often referred to as supplier encroachment. Previous studies assume the perfect rationality of retailers. However, supplier encroachment may trigger the fairness concerns of the retailers as a supplier is also a competitor of its retailer if the supplier encroaches. Thus, we introduce retailers fairness concerns into the encroachment problem and explore its impact. It is shown that encroachment may be detrimental to the supplier when the retailer has strong fairness concerns and a significant marketing advantage. If the retailer has a significant marketing advantage, retailers profit may decrease as her fairness concerns become much stronger. Numerical illustrations demonstrate that, when the retailer is fairness concerned, the supplier has more flexibility to encroach and the retailer has more possibility to benefit from encroachment in most cases. Moreover, retailers fairness concerns can bring a remarkable improvement to the system profit.

Revisiting prospect theory and the newsvendor problem

Abstract Many experimental studies have demonstrated that human decision-makers exhibit the pull-to-center effect in newsvendor decision. It has been shown in the literature that prospect theory with a decision-dependent reference point can predict the pull-to-center effect for the newsvendor problem by assuming a uniform distribution of demand. In this paper, we prove this result for a general case: prospect theory with a decision-independent reference point can predict the pull-to-center effect for the newsvendor problem with a general distribution of demand.

On elicitation-method effect in game experiments: a competing newsvendor perspective

To test the behavioral validity of the strategy method in a setting of operations management, we experimentally investigate competing newsvendor behavior under incomplete information with both the strategy method and the direct-response method. We observe that the “pull-to-center” effect exists only with low margin; mean order quantity with high margin does not significantly deviate from equilibrium prediction. We build a behavioral model based on overestimation and mean anchoring to explain competing newsvendor behavior. Estimates of the behavioral model confirm the existence of the behavioral biases. Meanwhile, order levels are not significantly different between the strategy method and the direct-response method. Hence, we suggest that the strategy method should lead to similar decisions in newsvendor settings compared to the direct-response method and may be adopted in most operations management settings associated to the newsvendor problem to improve the efficiency of experimental studies.