Multi-period inventory sharing between independent retailers : models for different degrees of information sharing - Zhang, Zhibin (Nanyang Technological University, 2020)
The problem of inventory sharing between independent retailers is studied. Current literature focuses on the single-period problem, of which a large majority is restricted to two retailers. In contrast, we consider the multi-period, multi-ordering problem that permits more than two retailers. In this research, we consider two related variants of the problem that are differed by the extent of inter-retailer information sharing: (1) “limited information sharing” and (2) “complete information sharing”. In “limited information sharing”, the retailers only share information on their up-to-date inventory levels. A sharing policy that is based on the concept of stock lending to control the sharing process for all possibilities is formulated. When designing the sharing policy, the key difficulty is to quantify the risk into a form of compensation to these retailers. This lending policy overcomes this difficulty. We first formulate the allocation rule for distributing the profit that are generated by reduction in backorder and holding cost. The rule that attains the essential optimality conditions of this problem, i.e., complete sharing and full inventory pooling is proved. Next, the lateral transshipment cost is included in the analysis and a transshipment rule for matching ”surplus” retailers with those in ”deficit” is developed. An upper bound of transshipment frequency for this rule is established, and it shows that under specific cost structure, the rule leads to complete sharing and guarantees additional profit for every retailer. In the “complete information sharing” problem, retailers share information on demands and order quantities (in addition to inventory information in “limited information sharing”). Information is characterized. It explains that how these information can be utilized to enhance sharing efficiency in terms of expectation and a modeling framework that determines each retailer’s optimal order quantity is developed. An analytical model is first developed, and then the complexity in obtaining the optimal solution and the difficulty in attaining the joint demand distribution (a key model input) in practice are demonstrated. A simulation approach that computes the optimal solution using the analytical model is then developed. The simulation avoids the need for the joint demand distribution by allowing demands to be characterized through demand sampling; this is enabled by an extension of the Leibniz Rule embedded in the analytical model, which allows for general demand distributions. The sharing problem without system-wide cooperation is first studied, then the concavity of the best response function is investigated. Unlike typical single-period problems in which the retailers have only one opportunity to order, retailers can choose their own order timing in the multi-period setting. Spreading the replenishment evenly over time (known as balanced ordering) can increase system-wide stock availability and consequently improve system efficiency. In addition, as a side benefit, the sequential ordering by the retailers considerably improves tractability by eliminating the possibility of game-based interactions.