Suppose there is a seller that has an unlimited number of units of a single product for sale. The seller at each moment of time posts a price for his/her product. Based of the posted price, at each moment of time, a b...
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(纸本)3540645640
Suppose there is a seller that has an unlimited number of units of a single product for sale. The seller at each moment of time posts a price for his/her product. Based of the posted price, at each moment of time, a buyer decides whether or not to buy a unit of that product from the seller. The only information about the buyer to the seller is the seller's sales history. Further, we assume that the maximal unit price the buyer is willing to pay does not change over time. The question then is how should the seller price his/her product to maximize profits? To address this question, we use the notion of loss functions. Intuitively, a loss function is a measure, at each moment of time, of the lost opportunity to make a profit. In particular, we provide a polynomial-time algorithm that finds a pricing algorithm (strategy) for the seller that minimizes the average (total) losses over time. Further, we present preliminary results on pricing strategies that minimize the maximum possible loss at every moment of time. We also show that there is no strategy minimizing both the total loss and the maximum loss at the same time.
This paper presents the theoretical foundations for controlling pile-up systems. A pile-up system consists of one or more stacker cranes picking up bins from a conveyor and placing them onto pallets with respect to co...
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This paper presents the theoretical foundations for controlling pile-up systems. A pile-up system consists of one or more stacker cranes picking up bins from a conveyor and placing them onto pallets with respect to costumer orders. The bins usually arrive at a conveyor from an orderpicking system. We give a mathematical definition of the pile-up problem, define a data structure for control algorithms, introduce polynomial time algorithms for deciding whether a system can be blocked by making bad decisions, and show that the pile-up problem is in general NP-complete. For pile-up systems with a restricted storage capacity or with a fixed number of pile-up places the pile-up problem is proved to be solvable very efficiently. (C) 1997 Elsevier Science B.V.
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