The proposed study addresses a two-echelon sustainable supply chain (SC) model with single-vendor and single-buyer by considering the detrimental impacts of environmental pollution due to production. Moreover, an estimation function measure production is developed through separate modelling. In entire chain, we assume deterioration rate increases time it also depends on product’s expiration dat...

We present a supervised learning to rank algorithm that effectively orders images by exploiting the structure in image sequences. Most often in the supervised learning to rank literature, ranking is approached either by analyzing pairs of images or by optimizing a list-wise surrogate loss function on full sequences. In this work we propose MidRank, which learns from moderately sized sub-sequenc...

Distributive supermatroids generalize matroids to partially ordered sets. Completing earlier work of Barnabei, Nicoletti and Pezzoli we characterize the lattice of flats of a distributive supermatroid. For the prominent special case of a polymatroid the description of the flat lattice is particularly simple. Large portions of the proofs reduce to properties of weakly submodular rank functions. ...

A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the quasisymmetric functions associated to matroids by the Hopf algebra morphism F of Billera, Jia, and Reiner [3]. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as wel...

This paper presents a representation theory for permutation-valued functions, which in their general form can also be called listwise ranking functions. Pointwise ranking functions assign a score to each object independently, without taking into account the other objects under consideration; whereas listwise loss functions evaluate the set of scores assigned to all objects as a whole. In many s...

Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [1]. In [2], Berkovich and Garvan found theta series representations for the t-core generating functions P n≥0 at,j(n)q , where at,j(n) denotes the number of t-cores of n with BG-rank = j. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme value...

This paper presents the first combinatorial polynomial algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. Since the rank functions of delta-matroids are bisubmodular, the scaling algorithm naturally leads to the first combinatorial polynomial algorithm for testing membership in delta-matro...

In this paper the problem of comparing several treatments with a control in a one-way repeated measures design is considered. Multiple testing procedures based on rank transformation data are proposed for determining which treatments are more effective than the control. The results of a Monte Carlo level and power study are presented.