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.

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed 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 maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. 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.

Measuring Value in Product Development

“What is value in product development?” is the key question of this paper. The answer is critical to the creation of lean in product development. By knowing how much value is added by product development (PD) activities, decisions can be more rationally made about how to allocate resources, such as time and money. In order to apply the principles of Lean Thinking and remove waste from the product development system, value must be precisely defined. Unfortunately, value is a complex entity that is composed of many dimensions and has thus far eluded definition on a local level. For this reason, research has been initiated on “Measuring Value in Product Development.” This paper serves as an introduction to this research. It presents the current understanding of value in PD, the critical questions involved, and a specific research design to guide the development of a methodology for measuring value. Work in PD value currently focuses on either high-level perspectives on value, or detailed looks at the attributes that value might have locally in the PD process. Models that attempt to capture value in PD are reviewed. These methods, however, do not capture the depth necessary to allow for application. A methodology is needed to evaluate activities on a local level to determine the amount of value they add and their sensitivity with respect to performance, cost, time, and risk. Two conceptual tools are proposed. The first is a conceptual framework for value creation in PD, referred to here as the Value Creation Model. The second tool is the Value-Activity Map, which shows the relationships between specific activities and value attributes. These maps will allow a better understanding of the development of value in PD, will facilitate comparison of value development between separate projects, and will provide the information necessary to adapt process analysis tools (such as DSM) to consider value. The key questions that this research entails are: · What are the primary attributes of lifecycle value within PD? · How can one model the creation of value in a specific PD process? · Can a useful methodology be developed to quantify value in PD processes? · What are the tools necessary for application? · What PD metrics will be integrated with the necessary tools? The research milestones are: · Collection of value attributes and activities (September, 200) · Development of methodology of value-activity association (October, 2000) · Testing and refinement of the methodology (January, 2001) · Tool Development (March, 2001) · Present findings at July INCOSE conference (April, 2001) · Deliver thesis that captures a formalized methodology for defining value in PD (including LEM data sheets) (June, 2001) The research design aims for the development of two primary deliverables: a methodology to guide the incorporation of value, and a product development tool that will allow direct application.