Revenue maximization in the dynamic knapsack problem

Abstract

We analyze maximization of revenue in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially arriving agents. Each agent is described by a two-dimensional type that reflects his capacity requirement and his willingness to pay per unit of capacity. Types are private information. We first characterize implementable policies. Then we solve the revenue maximization problem for the special case where there is private information about per-unit values, but capacity needs are observable. After that we derive two sets of additional conditions on the joint distribution of values and weights under which the revenue maximizing policy for the case with observable weights is implementable, and thus optimal also for the case with twodimensional private information. In particular, we investigate the role of concave continuation revenues for implementation. We also construct a simple policy for which per-unit prices vary with requested weight but not with time, and we prove that it is asymptotically revenue maximizing when available capacity and time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing.

Dynamic Pricing Behavior in Perishable Goods Markets: Evidence from Secondary Markets for Major League Baseball Tickets

“…On Stubhub, sellers list tickets at fixed prices, with potential buyers observing the section and row of each listing (e.g., Loge Box 512 row D at Yankee Stadium), the number of tickets available, and an indicator for whether fewer tickets can be purchased, and the price per seat. 17 They do not observe anything about the seller, which is possible because Stubhub provides a guarantee that anyone buying from its site will receive tickets at least as good as those listed. Stubhub collects 25% commissions on each transaction and also sets shipping costs.…”

Dynamic Assignment of Objects to Queuing Agents

“…time is only used to break ties among applicants with the same score. 5 Finally, lotteries are used in New York to allocate subsidized housing managed by private and nonprofit developers and listed by NYC Housing connect. Eligible applicants to affordable housing units are chosen by a uniform random draw.…”

Genetic Algorithm Solution of the Knapsack Problem Used in Finding Full Issues in the Holy Quran Based on the Number (19)

“…The knapsack problem can be defined as the problem of selecting a number of items to be put into a knapsack that has a certain capacity. The selected objects must have a high value as well as a suitable weight since the total weight cannot exceed the capacity of the knapsack (Dizdar et al, 2009). Therefore, the knapsack problem has a huge space of suggested solutions; and so, finding the best solution possible for the problem requires a long search time.…”