In this paper, we study a multi-echelon uncapacitated lot-sizing problem in series (mULS), where the output of the intermediate echelons has its own external demand, and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two echelon case (2-ULS). Next, we present a family of valid inequaliti...

One method which has been used very successfully for finding optimal and provably good solutions for large instances of the Symmetric Travelling Salesman Problem (ST SP) is the branch and cut method. This method requires knowledge of classes of useful valid inequalities for the polytope associated with the ST SP, as well as efficient separation routines for these classes of inequalities. Recent...

We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequa...

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequal...

This note introduces an extension to the 0-1 knapsack cover inequalities to be used in a branchand-cut algorithm for the elementary shortest path problem with a capacity constraint. The extension leads to a set of valid inequalities that takes both the fractional usage of the edges and the capacity into account and are denoted the flow extended 0-1 knapsack cover inequalities. Computational exp...

Bansal and Kianfar introduced continuous multi-mixing set where the coefficients satisfy the so-called n-step MIR conditions and developed facet-defining inequalities for this set. In this paper, we first generalize their inequalities for the continuous multi-mixing set with general coefficients (where no conditions are imposed on the coefficients) and show that they are facetdefining in many c...

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit ine...