Section: New Results

Scheduling and Clustering Problems

In [19] we consider the unrelated parallel machine scheduling problem with setup times to minimize a general objective function. In this work we present a novel exact algorithm that is capable of solving this problem $R|r_j,s_{ij}^k|\sum f_j\left(C_j\right)$ and the large class of problems that can be derived as particular cases from it. The proposed algorithm consists of a branch-cut-and-price approach that combines several features such as non-robust cuts, strong branching, reduced cost fixing and dual stabilization. To our knowledge, this is the first exact algorithm for unrelated machines with earliness and/or tardiness criteria that can solve consistently instances with more than 20 jobs. We report improved bounds for instances of problems $R|r_j,s_{ij}^k|\sum w_j^{\text{'}}{E}_j+w_j{T}_j$ and $R\left|\right|\sum w_j^{\text{'}}{E}_j+w_j{T}_j$ with up to 80 and 120 jobs, respectively.

A cross-docking terminal is a transshipment facility in supply chains, where products transported by inbound trucks are unloaded at inbound doors, sorted, and reloaded on outbound trucks at outbound doors. In [16], we address the truck-to-door scheduling problem at a multi-door cross-docking terminal where temporary storage is considered. We propose two types of time-indexed formulation for the problem to assign trucks to dock doors and determine their arrival and departure times so that tadiness and earliness as well as unsatisfied demand are minimized. We examine the effectiveness of the proposed formulations by numerical experiment.