Linearity of the Optimal Income Tax: A Generalization

In an earlier paper, we examined the nature of individual and collective preferences over alternative income tax schedules in the context of a simple model in which individuals respond to high tax rates by working in an untaxed "sheltered" sector of the economy. There we established the social optimality of a linear income tax among the set of tax schedules that are continuous, nondecreasing convex functions of income. Here we relax the restrictions on tax schedules, most importantly allowing schedules to have concave (decreasing marginal tax rate) as well as convex (increasing marginal tax rate) regions. In fact, we prove that a linear income tax is socially preferred to any nonlinear lower semi-continuous tax schedule

Linearity of the Optimal Income Tax: A Generalization

In an earlier paper, we examined the nature of individual and collective preferences over alternative income tax schedules in the context of a simple model in which individuals respond to high tax rates by working in an untaxed "sheltered" sector of the economy. There we established the social optimality of a linear income tax among the set of tax schedules that are continuous, nondecreasing convex functions of income. Here we relax the restrictions on tax schedules, most importantly allowing schedules to have concave (decreasing marginal tax rate) as well as convex (increasing marginal tax rate) regions. In fact, we prove that a linear income tax is socially preferred to any nonlinear lower semi-continuous tax schedule

Retail Store Scheduling for Profit

In spite of its tremendous economic significance, the problem of sales staff schedule optimization for retail stores has received relatively scant attention. Current approaches typically attempt to minimize payroll costs by closely fitting a staffing curve derived from exogenous sales forecasts, oblivious to the ability of additional staff to (sometimes) positively impact sales. In contrast, this paper frames the retail scheduling problem in terms of operating profit maximization, explicitly recognizing the dual role of sales employees as sources of revenues as well as generators of operating costs. We introduce a flexible stochastic model of retail store sales, estimated from storespecific historical data, that can account for the impact of all known sales drivers, including the number of scheduled staff, and provide an accurate sales forecast at a high intra-day resolution. We also present solution techniques based on mixed-integer (MIP) and constraint programming (CP) to efficiently solve the complex mixed integer non-linear scheduling (MINLP) problem with a profit-maximization objective. The proposed approach allows solving full weekly schedules to optimality, or near-optimality with a very small gap. On a case-study with a medium-sized retail chain, this integrated forecasting–scheduling methodology yields significant projected net profit increases on the order of 2-3 % compared to baseline schedules

Approximation of System Components for Pump Scheduling Optimisation

© 2015 The Authors. Published by Elsevier Ltd.The operation of pump systems in water distribution systems (WDS) is commonly the most expensive task for utilities with up to 70% of the operating cost of a pump system attributed to electricity consumption. Optimisation of pump scheduling could save 10-20% by improving efficiency or shifting consumption to periods with low tariffs. Due to the complexity of the optimal control problem, heuristic methods which cannot guarantee optimality are often applied. To facilitate the use of mathematical optimisation this paper investigates formulations of WDS components. We show that linear approximations outperform non-linear approximations, while maintaining comparable levels of accuracy

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

Deterministic versus Stochastic Mechanisms in Principal–Agent Models

This paper shows that, contrary to what is generally believed, decreasing concavity of the agent’s utility function with respect to the screening variable is not sufficient to ensure that stochastic mechanisms are suboptimal. The paper demonstrates, however, that they are suboptimal whenever the optimal deterministic mechanism exhibits no bunching. This is the case for most applications of the theory and therefore validates the literature’s usual focus on deterministic mechanisms

Derivation of near-optimal pump schedules for water distribution by simulated annealing

The scheduling of pumps for clean water distribution is a partially discrete non-linear problem with many variables. The scheduling method described in this paper typically produces costs within 1% of a linear program-based solution, and can incorporate realistic non-linear costs that may be hard to incorporate in linear programming formulations. These costs include pump switching and maximum demand charges. A simplified model is derived from a standard hydraulic simulator. An initial schedule is produced by a descent method. Two-stage simulated annealing then produces solutions in a few minutes. Iterative recalibration ensures that the solution agrees closely with the results from a full hydraulic simulation