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.

Planning and Teaching Compliant Motion Strategies

This thesis presents a new high level robot programming system. The programming system can be used to construct strategies consisting of compliant motions, in which a moving robot slides along obstacles in its environment. The programming system is referred to as high level because the user is spared of many robot-level details, such as the specification of conditional tests, motion termination conditions, and compliance parameters. Instead, the user specifies task-level information, including a geometric model of the robot and its environment. The user may also have to specify some suggested motions. There are two main system components. The first component is an interactive teaching system which accepts motion commands from a user and attempts to build a compliant motion strategy using the specified motions as building blocks. The second component is an autonomous compliant motion planner, which is intended to spare the user from dealing with "simple" problems. The planner simplifies the representation of the environment by decomposing the configuration space of the robot into a finite state space, whose states are vertices, edges, faces, and combinations thereof. States are inked to each other by arcs, which represent reliable compliant motions. Using best first search, states are expanded until a strategy is found from the start state to a global state. This component represents one of the first implemented compliant motion planners. The programming system has been implemented on a Symbolics 3600 computer, and tested on several examples. One of the resulting compliant motion strategies was successfully executed on an IBM 7565 robot manipulator.