An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS)

Guest editorial

We are glad to see the final version of this special issue of Decision Making in Manufacturing and Services (DMMS) on Optimization in Supply Chain Management take shape. It does not come as a surprise that we received a rather heterogeneous batch of submissions concerning different aspects of optimization focusing on applications in supply chain management (SCM). There seems to be no need to introduce the field of SCM here since it has been the focus of researchers and practitioners, for decades. This does not imply that there is no potential or no need for further improvement. With advances in hardware or algorithms, models have become more integrated over the years and there is no end to this development in sight. The mission of this special issue is to present new approaches on advancing optimization techniques with applications in SCM. It presents three papers in order to do so.

Shunting operations at flat yards : retrieving freight railcars from storage tracks

In this paper, we study the railcar retrieval problem (RRT) where specified numbers of certain types of railcars have to be withdrawn from the storage tracks of a flat yard. This task arises in the daily operations of workshop yards for railcar maintenance. The objective is to minimize the total cost of shunting via methods such as minimizing the usage of shunting engines. We describe the RRT formally, present a mixed-integer program formulation, and prove the general case to be NP-hard. For some special cases, exact algorithms with polynomial runtimes are proposed. We also analyze several intuitive heuristic solution approaches motivated by observed real-world planning routines. We evaluate their average performances in simulations with different scenarios and provide their worst-case performance guarantee. We show that although the analyzed heuristics result in much better solutions than the naive planning approach, they are still on average 30%-50% from the optimal objective value and may result in up to 14 times higher costs in the worst case. Therefore, we conclude that optimization should be implemented in practice in order to save valuable resources. Furthermore, we analyze the impacts of yard layout and the widespread organizational routine of presorting on the railcar retrieval cost