Ming Zhao We study a multiechelon supply chain model that consists of a production level and several transportation levels, where the demands can exist in the production echelon as well as any transportation echelons. With the presence of stationary production capacity and general cost functions, our model integrates production, inventory and transportation decisions and generalizes existing literature … Read more
The essential structure of the mixed–integer programming formulation for chance–constrained program (CCP) is the intersection of multiple mixing sets with a $0-1$ knapsack. To improve our computational capacity on CCP, an underlying substructure, the (single) mixing set with a $0-1$ knapsack, has received substantial attentions recently. In this study, we consider a CCP problem with … Read more
We study the set $S = \{(x, y) \in \Re_{+} \times Z^{n}: x + B_{j} y_{j} \geq b_{j}, j = 1, \ldots, n\}$, where $B_{j}, b_{j} \in \Re_{+} – \{0\}$, $j = 1, \ldots, n$, and $B_{1} | \cdots | B_{n}$. The set $S$ generalizes the mixed-integer rounding (MIR) set of Nemhauser and Wolsey and … Read more
Piecewise linear functions (PLFs) are commonly used to approximate nonlinear functions. They are also of interest in their own, arising for example in problems with economies of scale. Early approaches to piecewise linear optimization (PLO) assumed continuous PLFs. They include the incremental cost MIP model of Markowitz and Manne and the convex combination MIP model … Read more
We study the convex hull $P$ of the set $S = \{(x, y) \in \Re_{+} \times Z^{n}: x + B_{i} y_{ij} \geq b_{ij}, j \in N_{i}, i \in M\}$, where $M = \{1, \ldots, m\}$, $N_{i} = \{1, \ldots, n_{i}\}$ $\forall i \in M$, $\sum_{i = 1}^{m}n_{i} = n$, and $B_{1} | \cdots | B_{m}$. … Read more