Bardia Kamrad

An Economic Model for Evaluating Mining and Manufacturing Ventures with Output Yield Uncertainty

This paper develops an operational risk management model for evaluating production efforts in manufacturing and mining industries where the resource to be exploited is nonhomogenous. Using acontingent claims methodology now commonly encountered in financial applications, we formulate a production control model in an environment characterized bymarket andprocess uncertainty. In our analysis, market risk is depicted by the output price while process uncertainty is captured by the random variability inherent in the outputs yield. In this light, adjustments to the rate of production are viewed as a sequence of (nested) real options affording operating flexibility. We account for an optimal sequence of production adjustments, over a preestablished production horizon, by taking the production rate as an adapted positive real-valued process. Accordingly, techniques of stochastic control theory and contingent claims analysis (CCA) are employed to ensure value maximizing production policies are rendered in a manner consistent with an equilibrium price structure.

A lattice claims model for capital budgeting

Techniques of contingent claims analysis (CCA), extend current capital budgeting practices in two specific ways. First, by explicitly accounting for project uncertainty and second, by quantifying the flexibility value afforded due to the presence of real options. When applied appropriately, CCA techniques can provide a powerful and robust valuation approach and are particularly useful in providing insight to key strategic factors that affect project value. These advantages, however, come at some expense as most applications of CCA to project valuation result in complex partial differential equations which cannot be solved for simple analytic formulas. This, combined with the intricate mathematical structure of these methods often make it difficult for an intuitive grasping and may result in implementation problems. The purpose of this article is to provide a prefatory perspective on the use of CCA techniques as applied to engineering, production, mining, and manufacturing projects. To that end, by using efficient numerical techniques this article formulates a simple and unified CCA framework for valuing a large class of projects that contain real options. The approach is straightforward, readily implementable, and computationally efficient. The framework presented in this paper also provides an important introduction to the use of CCA methods and the quantification of flexibility value in the management of operations. >

Production, operating risk and market uncertainty: a valuation perspective on controlled policies

This paper develops a contingent claims model of an optimally controlled production process characterized by financial and operational risks. Financial risk is depicted by the uncertainty in output prices as determined in competitive markets. Operational uncertainty is portrayed through the risk of system failures which we represent by a nonhomogeneous Poisson process. In the analysis, failure propensity is functionally specified by the systems age, rate of production, and system maintenance expenditures. In this environment, the model obtains an optimal production and maintenance policy maximizing the value of the production effort. Determination of the optimal policies results through the application of stochastic control techniques where production and maintenance expenditure rates are taken as adapted real-valued processes. Further extensions of the model include the analysis of an insurance option on failure repairs and the consequent moral hazard implications. We demonst rate that an appropriately established insurance premium must reflect the producers operating policy in place and the extent to which operating policies may be modified to maintain the same level of operating risk, as in the absence of an insurance option. The framework presented provides insight into key strategic factors that affect the management of process operations, operating flexibility issues and their resulting economic value.

Allocation of warehouse inventory with electronic data interchange and fixed order intervals

This paper considers the problem of allocating warehouse inventory to retailers where retailer orders and the replenishment of warehouse inventory occur periodically on a fixed schedule. We assume that the warehouse and the retailers have the opportunity to exchange demand information through Electronic Data Interchange (EDI). At the warehouse level, for instance, the available information on the retailers demand may be utilized in determining the shipment quantities needed to meet the desired service level to the retailers. Unlike similar models focusing primarily on optimizing systems wide performance measures, in this paper we focus on the service level furnished to the retailers by the warehouse. To this end, three different allocation policies are considered: static, myopic, and dynamic rules characterizing the impact of available demand information on the resulting service levels. Numerical illustrations exemplify the allocation rules considered. An interesting though counter intuitive observation is that the existence of additional demand information cannot, a prior, be assumed superior.

Valuing fixed price supply contracts

Abstract This article considers the problem of valuing a supply contract that requires the manufacturer to deliver fixed quantities of a product according to a predetermined schedule at fixed prices. Given that the raw material costs fluctuate randomly, the producer has capacity constraints, production costs depend on production rates, and that switching production rates result in additional charges, the problem is to establish an optimal production and inventory policy such that the schedule is met, and the value of the contract to the firm is maximized.

Estimating demand by using sales information: inaccuracies encountered

Abstract Demand data is integral to a company’s overall information requirement. This is particularly true for manufacturers and retailers with regard to capacity, production, and inventory planning. Notwithstanding the implicit inaccuracies encountered, companies are predisposed to employ sales data as a primary source of information for estimating future demand. In this paper, by adopting a two-product setting, we measure inventory cost inaccuracies that arise from using sales data in estimating demand. By analyzing these costs, we also explore the conditions under which the resulting inaccuracies are either “lessened” or become “acute.” In this context, the determining rule of an induced substitution structure between the two products during stockout occasions is explicitly analyzed. We use a newsboy framework, in a two product environment, wherein one product may be taken as a direct substitute for the other. We provide necessary and sufficient optimality conditions and an extensive computational study to illustrate and support our findings and to provide additional insights on the conditions characterizing optimal stocking policies.

Managing Supply Risk in Fixed Price Contracts: A Contingent Claims Perspective

The primary focus of this paper is supply risk mitigation. though, its objectives are twofold. First, we develop a generic contingent claims model framed as an exercise in stochastic optimal control. The model is easily adjusted to a number of risk-based operational problems. Second, we adapt the model to the problem of supply uncertainty and the valuation of a fixed price contract with a focus on managing supply uncertainty through a portfolio based risk sharing framework. The risk and reward tradeoffs characterizing our general findings in this chapter indicate a subtle balance between supply risk, sourcing allocations and related costs, and accordingly, the resulting operational strategies considered. Given this setup, increased supplier-portfolio risk is a defining measure in establishing optimal operating policies, with the caveat that increases in the supplier portfolio’s volatility, also increase shortages which lowers the contract’s value.

In Pursuit of Product Modularity: Impediments and Stimulants:

This article develops a framework, including a 2 × 2 matrix, to help guide firms in deciding when to design their products to be integral, modular-in-production, modular-in-use with a focus on selling “cartridges,” or modular-in-use with a focus on promoting numerous apps. Three key factors are as follows: the level of user heterogeneity, the disparity across components in frequency of updating, and the modularity/integrality penalty.

Option Pricing: Theory and Numerical Methods

In this article we will describe models, theory, and numerical methods for pricing derivative securities.