W e consider the problem of managing inventories and dynamically adjusting retailer prices in distribution systems with geographically dispersed retailers. More specifically, we analyze the following single item, periodic review model. The distribution of demand in each period, at a given retailer, depends on the item’s price according to a stochastic demand function. These stochastic demand fu...

In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. F...

This article provides an introduction to approximation algorithms in stochastic optimization models arising in various application domains, including central areas of operations management, such as scheduling, facility location, vehicle routing problems, inventory and supply chain management and revenue management. Unfortunately, these models are very hard to solve to optimality both in theory ...

In this work, we discuss the effect of risk measure selection in the determination of inventory policies. We consider an inventory system characterized by the loss function of Luciano et al. [2003. VaR as a risk measure for multi-period static inventory models. International Journal of Production Economics 81–82, 375–384]. We derive the optimization problems faced by risk neutral, quadratic uti...

Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n f...

We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value function with the sum of single-customer inventory value functions. The resulting approximation yield...

In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set distance to formulate a safety risk-constrained optimal control problem. Our reformulation method using an extremal representation of the safety risk measure ...

The optimal control of inventory in supply chains plays a key role in the competiveness of a corporation. The inventory cost can account for half of company’s logistics cost. The classical inventory models, e.g., newsvendor and EOQ models, assume either a single or infinite planning periods. However, these models may not be applied to perishable products which usually have a certain shelf life....

We introduce a class of models, called newsvendor networks, that allow for multiple products and multiple processing and storage points and investigate how their single-period properties extend to dynamic settings. Such models provide a parsimonious framework to study various problems of stochastic capacity investment and inventory procurement. Newsvendor networks can feature commonality, ßexib...