MaxHedge: Maximising a Maximum Online

We introduce a new online learning framework where, at each trial, the learner is required to select a subset of actions from a given known action set. Each action is associated with an energy value, a reward and a cost. The sum of the energies of the actions selected cannot exceed a given energy budget. The goal is to maximise the cumulative profit, where the profit obtained on a single trial is defined as the difference between the maximum reward among the selected actions and the sum of their costs. Action energy values and the budget are known and fixed. All rewards and costs associated with each action change over time and are revealed at each trial only after the learner's selection of actions. Our framework encompasses several online learning problems where the environment changes over time; and the solution trades-off between minimising the costs and maximising the maximum reward of the selected subset of actions, while being constrained to an action energy budget. The algorithm that we propose is efficient and general in that it may be specialised to multiple natural online combinatorial problems.Comment: Published in AISTATS 201

An approximation algorithm for a facility location problem with stochastic demands

In this article we propose, for any $\epsilon>0$, a $2(1+\epsilon)$-approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs). \u

Standard-Rate Wage Setting, Labor Quality, and Unions

"Standard rate" wage policies, under which all workers in a particular job receive the same wage, are common for blue-collar workers, especially those covered by collective bargaining agreements and those who work for large employers.This paper analyzes the impact of standard-rate wage setting.There are two important conclusions. First,a standard-rate rule which leaves the employer free to set the rate can either increase or reduce the quality of labor hired. Given empirically likely distributions of alternative wages for workers, it pushes employers toward the middle of the quality distribution. Second, union standard-rate policies allow union?ununion differences in wages for workers of a given qualityto exist even when union employers are free to alter the quality of their workforces.

The Expectation-Based Loss-Averse Newsvendor

We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to Koszegi and Rabin (2006, 2007). Expectation-based loss aversion leads to an endogenous psychological cost of leftovers as well as stockouts. If there are no monetary stockout costs, then the loss-averse newsvendor orders a quantity lower than the quantity ordered by a profit-maximizing newsvendor. If there are positive monetary costs associated with stockouts, then the loss-averse newsvendor places suboptimal orders, which can be either too high or too low

Majority Voting and the Welfare Implications of Tax Avoidance

A benchmark result in the political economy of taxation is that majority voting over a linear income tax schedule will result in an ine±ciently high tax rate whenever the median voter has a below average income. The present paper examines the role of tax avoidance for this welfare assessment. We find that the inefficiency in the voting equilibrium is the lower, the higher the average level of tax avoidance in the economy, or equivalently, the lower the median voter's amount of avoidance. The result holds for endogenous avoidance and labor choice and, under certain conditions, for an endogenous enforcement policy.Tax avoidance, welfare analysis, majority voting, median voter equilibrium

Assigning Orders to Suppliers with Linear Piecewise Concave Costs

Purpose: Once a set of suppliers has been determined, according to criteria of quality, price and reliability, among others, there remains the problem of assigning orders to the selected suppliers, in order to cover the needs at the lowest cost. We consider the case in which the needs of a component for a set of plants should be covered by suppliers with linear piecewise concave cost functions, a lower bound on the order size for the non-zero deliveries and a capacity constraint. The purpose is to design procedures for solving this problem. Design/methodology/approach: With the aim of providing practical tools to solve the problem of assigning orders to suppliers with linear piecewise concave costs, two mixed integer linear programs are proposed. Findings: The two MILP models are compared through an extensive computational experiment. This shows that both models, with a slight advantage for one of them, can be solved within a very short time, even when the dimensions of the instance largely exceed those that can occur in real cases. Originality/value: The paper proposes novel models that can be used to solve the problem to optimality in reasonable times and with standard optimization software.Peer Reviewe

Upward Pricing Pressure As A Predictor Of Merger Price Effects

We use Monte Carlo experiments to evaluate whether “upward pricing pressure” (UPP) accurately predicts the price effects of mergers, motivated by the observation that UPP is a restricted form of the first order approximation derived in Jaffe and Weyl (2013). Results indicate that UPP is quite accurate with standard log-concave demand systems, but understates price effects if demand exhibits greater convexity. Prediction error does not systematically exceed that of misspecified simulation models, nor is it much greater than that of correctly-specified models simulated with imprecise demand elasticities. The results also support that UPP provides accurate screens for anticompetitive mergers