Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.

Periodic review stochastic inventory models with service level constraint

Abstract: This article considers the periodic review stochastic inventory models with service level constraint to provide an improved solution procedure. The previous researchers assumed that the objective function is concave down in the lead time so that the minimum must occur on the boundary points of each sub-domain. In this article, we will show that their assumption is questionable since the minimum might not occur at the boundary points of each sub-domain. In a recent paper in International Journal of Systems Science, Ouyang and Chuang studied this problem. However, their solutions contained questionable results and their algorithm might not find the optimal solution due to flaws in their solution procedure. We develop some lemmas to reveal the parameter effects and then present our improved solution procedures for finding the optimal solution for periodic review stochastic inventory models in which the lead time demand is a normal distribution. The savings are illustrated by solving the same examples from Ouyang and Chuang's paper to demonstrate the improvement using our revised algorithm. In the direction of future research, we discuss the comparison between the reordered point being fixed and the reordered point as a new variable.

Concave Consumption Function under Borrowing Constraints

Abstract: This paper analyzes the optimal consumption behavior of a consumer who faces uninsurable labor income risk and borrowing constraints. In particular, it provides conditions under which the decision rule for consumption is a concave function of existing assets. The current study presents two main findings. First, it is shown that the consumption function is concave if the period utility function is drawn from the HARA class and has either strictly positive or zero third derivative. Second, it is shown that the same result can be obtained for certain period utility functions that are not in the HARA class.

Strategy-Proof Package Assignment

Abstract: We examine the strategy-proof allocation of multiple divisible and indivisible resources; an application is the assignment of packages of tasks, workloads, and compensations among the members of an organization. We find that any allocation mechanism obtained by maximizing a separably concave function over a polyhedral extension of the set of Pareto-efficient allocations is strategy-proof. Moreover, these are the only strategy-proof and unanimous mechanisms satisfying a coherence property and responding well to changes in the availability of resources. These mechanisms generalize the parametric rationing mechanisms (Young, 1987), some of which date back to the Babylonian Talmud.

On the Team Selection Problem

Abstract: We consider a team selection problem that requires to hire a team of individuals that maximizes a profit function defined as difference of the utility of production and the cost of hiring. We show that for any monotone submodular utility of production and any increasing cost function of the team size with increasing marginal costs, a natural greedy algorithm guarantees a 1− log(a)/(a− 1)– approximation when a ≤ e and a 1 − a/e(a − 1)–approximation when a ≥ e, where a is the ratio of the utility of production and the hiring cost of a profit-maximizing team selection. We also consider the class of test-score algorithms for maximizing a utility of production subject to a cardinality constraint, where the goal is to hire a team of given size based on greedy choices using individual test scores. We show that the existence of test scores that guarantee a constant-factor approximation is equivalent to the existence of special type of test scores – so called replication test scores. A set of sufficient conditions is identified that implies the existence of replication test scores that guarantee a constant-factor approximation. These sufficient conditions are shown to hold for a large number of classic models of team production, including a monotone concave function of total production, best-shot, and constant elasticity of substitution production function. We also present some results on the performance of different kinds of test scores for different models of team production, and report empirical results using data from a popular online labour platform for software development.

Conditions for boundedness in concave programming under reverse convex and convex constraints

Abstract: In this paper, we are concerned with the problem of boundedness in the constrained global maximization of a convex function. In particular, we present necessary and sufficient conditions for boundedness of a feasible region defined by reverse convex constraints and we establish sufficient and necessary conditions for existence of an upper bound for a convex objective function defined over the system of concave inequality constraints. We also address the problem of boundedness in the global maximization problem when a feasible region is convex and unbounded.