Machine scheduling problem has been extensively studied by researchers for many decades in view of its numerous applications on solving practical problems. Due to the complexity of this class of scheduling problems, various approximation solution approaches have been presented in the literature....

The symmetric quadratic knapsack problem (SQKP), which has several applications in machine scheduling, is NP-hard. An approximation scheme for this problem is known to achieve an approximation ratio of (1+ϵ) for any ϵ0. To ensure a polynomial time complexity, this approximation scheme needs an...

Given k identical salesmen, where k⩾2 is a constant independent of the input size, the min–max k-traveling salesmen problem on a tree is to determine a set of k tours for the salesmen to serve all customers that are located on a tree-shaped network, so that each tour starts from and returns...

We consider a problem faced by a buying office for one of the largest retail distributors in the world. The buying office plans the distribution of goods from Asia to various destinations across Europe. The goods are transported along shipping lanes by shipping companies, many of which have...

The manufacturing base in the Pearl River Delta of China is moving westwards, where the Pearl River system has extensive coverage. This makes container barge transport a new growth area for Hong Kong Port. Traditionally, Hong Kong Port has been the main gateway for containers transported through...

We consider the problem of scheduling a given set of n jobs with equal processing times on m parallel machines so as to minimize the makespan. Each job has a given release date and is compatible to only a subset of the machines. The machines are ordered and indexed in such a way that a...

We consider the problem of scheduling a set of jobs with different release times on parallel machines so as to minimize the makespan of the schedule. The machines have the same processing speed, but each job is compatible with only a subset of those machines. The machines can be linearly ordered...