This paper introduces a new notion related to the traveling salesperson problem (TSP) — the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i ∈ I is the difference between the length of the optimal tour on I and the length of the optimal tour on I...

A single machine scheduling problem is described which covers earliness costs, tardiness costs and setup costs. Setups are needed whenever a switch is made to a job of another product family. All jobs within the same product family have the same processing time. Besides setup costs also setup times are involved. Idle time is allowed, preemption is not allowed. Both a mixed integer programming f...

background: breast cancer is the most frequently diagnosed cancer and the leading global cause of cancer death among women worldwide. radiotherapy plays a significant role in treatment of breast cancer and reduces locoregional recurrence and eventually improves survival. the treatment fields applied for breast cancer treatment include: tangential, axillary, supraclavicular and internal mammary ...

Sheet metal bending press-brakes can be setup to produce more than one type of part without requiring a setup change. To exploit this flexibility, we need setup planning techniques so that press-brake setups can be shared among many different parts. In this paper, we describe algorithms for partitioning a given set of parts into setup compatible part families that can be produced on the same se...