My dissertation focuses on stochastic dynamic inventory theory and its applications in inventory management, especially in perishable inventory systems.

Essay 1: We apply the concept of multimodularity in three stochastic dynamic inventory problems in which state and decision variables are economic substitutes. The first is clearance sales of perishable goods. The second is sourcing from multiple suppliers· with different leadtimes. The third is transshipment under capacity constraints. In all three problems, we establish monotone optimal polices with bounded sensitivity. Multimodularity proves to be an effective tool for these problems because it implies substitutability, it is preserved under minimization, and it leads directly to monotone optimal policies with bounded sens...[ Read more ]

My dissertation focuses on stochastic dynamic inventory theory and its applications in inventory management, especially in perishable inventory systems.

Essay 1: We apply the concept of multimodularity in three stochastic dynamic inventory problems in which state and decision variables are economic substitutes. The first is clearance sales of perishable goods. The second is sourcing from multiple suppliers· with different leadtimes. The third is transshipment under capacity constraints. In all three problems, we establish monotone optimal polices with bounded sensitivity. Multimodularity proves to be an effective tool for these problems because it implies substitutability, it is preserved under minimization, and it leads directly to monotone optimal policies with bounded sensitivity.

Essay 2: We study joint replenishment and clearance sales of perishable goods under a general finite lifetime and a last-in-first-out (LIFO) issuing rule, a problem common in retailing. We show that the optimal policies can be characterized by two thresholds for each age group of inventory: a lower one and a higher one. For an age group of inventory with a remaining lifetime of two periods or longer, clearance sales may take place when its inventory level is above its higher threshold. There is no clearance sale if its inventory level is below its lower threshold and the inventory levels in all the fresher age groups are also below their corresponding lower thresholds. The optimal policy for the age group of inventory with a one-period remaining lifetime is different. Clearance sales may occur if its inventory level is above its higher threshold or below its lower threshold. The phenomenon that a clearance sale happens when the inventory is low is driven by the need to segregate the newest inventory from the oldest inventory and is unique to the LIFO issuing rule. The optimal policy requires a full inventory record of every age group and its computation is challenging. We consider two myopic heuristics that require only partial information. The first requires only the information about the total inventory and the second requires the information about the total inventory as well as the information about the inventory with a one-period remaining lifetime. Our numerical studies show that the second outperforms the first significantly and its performance is consistently very close to that of the optimal policy.

Essay 3: Retailers of perishable goods are often faced with the choice between more expensive packaging that can extend shelf life of their products and less expensive packaging that cannot. Different choices will lead to different sales, costs, and waste, and different choices require different inventory control policies. In this paper, we study the coordination of inventory and packaging decisions in a retailing environment. Items in an active package have a longer lifetime than those in a regular package and cost more. We consider two types of customers: the selective customers only buy items with a sufficiently long remaining life; and the regular customers accept any on shelf but always pick items with a longer remaining lifetime first. Our study shows that under the optimal policy, in general, for a given initial inventory the retailer may either use both types of packaging or only one of them, depending on the context. While there are situations where the active packaging should not be adopted at all regardless of the initial inventory, using only active packaging regardless of the initial inventory is suboptimal. When the percentage of regular customers is high, the retailer may use either active packaging, or regular packaging, but not both in the same period. These results are very specific to the way perishable inventories are depleted in retailing. Our numerical results show that while the economic incentive for adopting active packaging may sometimes be low, waste reduction is always significant. In particular, adopting active packaging can consistently reduce waste by over 50%. This is true whether one uses only active packaging, or uses the optimal policy under which one uses both types of packaging.