Benefits of Implementing Lean Practices and the Impact of the Lean Aerospace Initiative in the Defense Aerospace Industry and Government Agencies

In the 1980’s, many United States industrial organizations started developing new production processes to improve quality, reduce cost, and better respond to customer needs and the pressures of global competition. This new paradigm was coined Lean Production (or simply “Lean”) in the book The Machine That Changed The World published in 1990 by researchers from MIT’s International Motor Vehicle Program. In 1993, a consortium of US defense aerospace firms and the USAF Aeronautical Systems Center, together with the AFRL Materials and Manufacturing Directorate, started the Lean Aircraft Initiative (LAI) at MIT. With expansion in 1998 to include government space products, the program was renamed the Lean Aerospace Initiative. LAI’s vision is to “Significantly reduce the cost and cycle time for military aerospace products throughout the entire value chain while continuing to improve product performance.” By late 1998, 23 industry and 13 government organizations with paying memberships, along with MIT and the UAW were participating in the LAI.

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.