We study the order acceptance and resource planning problem which has applications in many industries such as healthcare, logistics, and manufacturing. We extend the recent literature by considering two new features: the number of resources is a decision and processing times are uncertain....

Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the two-dimensional shelf space allocation problem (2DSSAP) with additional features motivated by literature and our...

Public service spending is an important issue with great economic, social and political ramifications. Consequently, correct measurements with respect to productivity evaluation of such expenditures is of paramount significance. Motivated by evaluating public services from a non-parametric...

Assessing determinants of health care quality and efficiency is of importance to researchers, policy-makers, and public health officials. Doing so allows for improved human capital and resource allocation as well as long-term fiscal planning. Statistical analysis has been used to understand...

We propose a computationally feasible inference method infinite games of complete information. Galichon and Henry (2011) and Beresteanu, Molchanov, and Molinari (2011) show that such models are equivalent to a collection of moment inequalities that increases exponentially with the number of...

We solve two related extremal problems in the theory of permutations. A set Q of permutations of the integers 1 to n is inversion-complete (resp., pair-complete) if for every inversion (j, i), where 1 <= i < j <= n, (resp., for every pair (i, j), where i not= j) there exists a permutation in Q where j is before i. It is minimally inversion-complete if in addition no proper subset of Q is inversion-complete; and similarly for paircompleteness. The problems we consider are to determine the maximum cardinality of a minimal inversion-complete set of permutations, and that of a minimal pair-complete set of permutations. The latter problem arises in the determination of the Carathéodory numbers for certain abstract convexity structures on the (n - 1)-dimensional real and integer vector spaces. Using Mantel's Theorem on the maximum number of edges in a triangle-free graph, we determine these two maximum cardinalities and we present a complete description of the optimal sets of permutations for each problem. Perhaps surprisingly (since there are twice as many pairs to cover as inversions), these two maximum cardinalities coincide whenever n >= 4.

In open pit mining, one must dig a pit, that is, excavate the upper layers of ground before reaching the ore. The walls of the pit must satisfy some geomechanical constraints, in order not to collapse. The question then arises how to mine the ore optimally, that is, how to find the optimal pit....

We consider multiobjective and parametric versions of the global minimum cut problem in undirected graphs and bounded-rank hypergraphs with multiple edge cost functions. For a fixed number of edge cost functions, we show that the total number of supported non-dominated (SND) cuts is bounded by a...

We study the computational complexity of finding extremal principal minors of a positive definite matrix. In particular, we focus on the NP-hard problem of maximizing the determinant over the set of principal submatrices of a given order. This problem arises in the area of statistical design,...

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show...