Optimal monopoly investment and capacity utilization under random demand

Unique value-maximizing programs of irreversible capacity investment and capacity utilization are described and shown to exist under general conditions for monopolist exhibiting capital adjustment costs and serving random consumer demand for a nondurable good over an infinite horizon. Stationary properties of these programs are then fully characterized under the assumption of serially independent demand disturbances. Optimal monopoly behavior in this case includes acquisition of a constant and positive level of capacity, the maintenance of a positive expected value of excess capacity in each period, and an asymmetrical response of price to unanticipated fluctuations in consumer demand. Under a general form of Markovian demand, the effect of uncertainty on irreversible capacity investment is also described in terms of the discounted flow of expected revenue accruing to the marginal unit of existing capacity and the option value of deferring the acquisition of additional capital. The option value of deferring such acquisition, created by the irreversibility of capacity investment, is characterized directly in terms of the value function of the firm, and is then shown to be zero in a stationary equilibrium with serially independent demand disturbances. The response of investment to increase demand uncertainty depends, as a result, directly on the properties of the marginal revenue product of capital. A non-negative response of optimal capacity to increased uncertainty in market demand is demonstrated for a general class of aggregate consumer preferences.Industrial capacity

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/1/poms12221-sup-0001-OnlineSupplement.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/2/poms12221.pd

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy.Singapore-MIT Alliance (SMA

Going Bunkers: The Joint Route Selection and Refueling Problem

Managing shipping vessel profitability is a central problem in marine transportation. We consider two commonly used types of vessels—“liners” (ships whose routes are fixed in advance) and “trampers” (ships for which future route components are selected based on available shipping jobs)—and formulate a vessel profit maximization problem as a stochastic dynamic program. For liner vessels, the profit maximization reduces to the problem of minimizing refueling costs over a given route subject to random fuel prices and limited vessel fuel capacity. Under mild assumptions about the stochastic dynamics of fuel prices at different ports, we provide a characterization of the structural properties of the optimal liner refueling policies. For trampers, the vessel profit maximization combines refueling decisions and route selection, which adds a combinatorial aspect to the problem. We characterize the optimal policy in special cases where prices are constant through time and do not differ across ports and prices are constant through time and differ across ports. The structure of the optimal policy in such special cases yields insights on the complexity of the problem and also guides the construction of heuristics for the general problem setting

Optimizing flow rates in a queueing network with side constraints

Network Analysis;operations research

airline revenue management

With the increasing interest in decision support systems and the continuous advance of computer science, revenue management is a discipline which has received a great deal of interest in recent years. Although revenue management has seen many new applications throughout the years, the main focus of research continues to be the airline industry. Ever since Littlewood (1972) first proposed a solution method for the airline revenue management problem, a variety of solution methods have been introduced. In this paper we will give an overview of the solution methods presented throughout the literature.revenue management;seat inventory control;OR techniques;mathematical programming

Dynamic pricing models for electronic business

Dynamic pricing is the dynamic adjustment of prices to consumers depending upon the value these customers attribute to a product or service. Today’s digital economy is ready for dynamic pricing; however recent research has shown that the prices will have to be adjusted in fairly sophisticated ways, based on sound mathematical models, to derive the benefits of dynamic pricing. This article attempts to survey different models that have been used in dynamic pricing. We first motivate dynamic pricing and present underlying concepts, with several examples, and explain conditions under which dynamic pricing is likely to succeed. We then bring out the role of models in computing dynamic prices. The models surveyed include inventory-based models, data-driven models, auctions, and machine learning. We present a detailed example of an e-business market to show the use of reinforcement learning in dynamic pricing