Multi-item capacitated lot-sizing problems with setup times and pricing decisions

We study a multi-item capacitated lot-sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot-sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch-and-price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65027/1/20394_ftp.pd

On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (1991) (M&M). We follow a ‘logical experimentation’ perspective by computing and com- paring the results of three models: (i) The M&M model, (ii) a modified version of M&M where the planning horizon is infinite, and (iii) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon, or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitiv- ity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models (Mesak, 1996).MINECO under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU)

Some numerical methods for solving stochastic impulse control in natural gas storage facilities

The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP

Utility-Based Hedging of Stochastic Income

In this dissertation, we study and examine utility-based hedging of the optimal portfolio choice problem in stochastic income. By assuming that the investor has a preference governed by negative exponential utility, we a derive a closed-form solution for the indifference price through the pricing methodology based on utility maximization criteria. We perform asymptotic analysis on this closed form solution to develop the analytic approximation for the indifference price and the optimal hedging strategy as a power series expansion involving the risk aversion and the correlation between the income and a traded asset. This gives a fast computation route to assess these quantities and perform our analysis. We implemented the model to perform simulations for the optimal hedging policy and produce the distributions of the hedging error at terminal time over many sample paths histories. In turn, we analyze the performance of the utility-based hedging strategy together with the strategy which arises from employing the traded asset as a substitute for the stochastic income