Optimal Inventory Control and Allocation for Sequential Internet Auctions

We study an optimal inventory scrapping and allocation problem for a retailer who uses sequential online auctions with reserve price. It is assumed that the buyers arrive according to a Poisson process or constant case with uniform bid distributions and multi-unit Vickrey auction mechanism is employed in each auction. We build a Markov decision process model for the retailer’s lot-size decision in these auctions with reserve price. It is shown that the single-auction expected revenue function satisfies a second order condition, leading to the retailer’s optimal lot-size policy. That is, the optimal inventory-scraping policy is a threshold policy and the optimal lot-size policy is a monotone staircase with unit jumps policy when we introduce the reserve price in sequential online auction systems. We also show these results for the case where the reserve price is a decision variable.

Inventory Models with Delivery Upgrade

We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy. Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4–7.3% revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100%. These results explain why yield management has become so essential to fashion retailing and travel service industries.

Minimizing Risk Models in Markov Decision Processes with Policies Depending on Target Values

Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes

Optimal supplier inventory control policies when buyer purchase incidence is driven by past service

Optimal eviction policies for stochastic address traces

Ratchet consumption over finite and infinite planning horizons

Fuzzy Logic is used to derive the optimal inventory policies in the Supply Chain (SC) numbers. We examine the performance of the optimal inventory policies by cutting the costs and increasing the supply chain management efficiency. The proposed inventory policy uses multi-agent and Fuzzy logic, and provides managerial insights on the impact of the decision making in all the SC numbers. In particular, we focus on the way in which our agent purchases components using a mixed procurement strategy (combining long and short term planning) and how it sets its prices according to the prevailing market conditions and its own inventory level (because this adaptivity and flexibility are key to its success). In modern global market, one of the most important issues of the supply chain (SC) management is to satisfy changing customer demands and enterprises should enhance the long-term advantage through the optimal inventory control. In this paper an intelligent multi-agent system to simulate supply chain management has been developed.

In the highly competitive retail industry many retailers bundle goods with optional value-added packages to enhance the attraction of the goods and increase their revenue. Offering such packages affects the sales and hence the inventory management of the goods. To maximize the benefits of bundling, the package offerings should vary with the inventory level of the goods. In this paper we propose a model to analyze the joint optimal management of a single good and its associated package offering and inventory control for the good. We define a procedure to construct superior offerings, which are shown to contain the optimal package offerings for all inventory levels of the goods. After obtaining the structural properties of the superior offerings and applying an existing result on the optimal inventory control, we deduce that the optimal inventory management policy is of the reorder-point, order-up-to-level, or (s, S), type, and the optimal choice of the package offering at any given inventory level of the goods is one of the superior offerings. Numerical examples show that the joint optimization model can substantially improve profitability over the policy of offering the same packages all of the time.

Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models

Single item periodic review inventory control with sales dependent stochastic return flows

Optimal inventory control and design refresh selection in managing part obsolescence

We study a stochastic inventory model of a firm that periodically orders a product from a make-to-order manufacturer. Orders can be shipped by a combination of two freight modes that differ in lead-times and costs, although orders are not allowed to cross. Placing an order as well as each use of each freight mode has a fixed and a quantity proportional cost. The decision of how to allocate units between the two freight modes utilizes information about demand during the completion of manufacturing. We derive the optimal freight mode allocation policy, and show that the optimal policy for placing orders is not an (s,S) policy in general. We provide tight bounds for the optimal policy that can be calculated by solving single period problems. Our analysis enables insights into the structure of the optimal policy specifying the conditions under which it simplifies to an (s,S) policy. We characterize the best (s,S) policy for our model, and through extensive numerical investigation show that its performance is comparable with the optimal policy in most cases. Our numerical study also sheds light on the benefits of the dual freight model over the single freight models.

Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control using the estimated distributions. These approaches often lead to fragile solutions whenever the preselected family of distributions was inadequate. In this article, we propose a minimax robust model that integrates data fitting and inventory optimization for the single‐item multi‐period periodic review stochastic lot‐sizing problem. In contrast with the standard assumption of given distributions, we assume that histograms are part of the input. The robust model generalizes the Bayesian model, and it can be interpreted as minimizing history‐dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular, we analyze the robust model based on the chi‐square goodness‐of‐fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under generous conditions. Its effectiveness is also validated by numerical experiments.