Optimal solution of a single machine scheduling problem with the option of batch outsourcing

Outsourcing is a prevalent strategy in the industry and business, which can enhance the performance of a company and rectify its constraints. This strategy can be integrated into various managerial aspects of a company, particularly the scheduling subject. In this paper, a single machine scheduling problem is investigated in which a set of jobs can be outsourced in a batch to a single subcontractor. It is supposed that the outsourcing time and cost of a job are proportional to its in-house processing time. In addition, a fixed logistics time and cost are also considered for the outsourcing batch. Moreover, the problem objective is to minimize the sum of the total completion time of the jobs and the total outsourcing cost.

To solve the problem, a set of optimal properties of the problem solution are proven via a lemma and a theorem to determine the optimal solution of the problem. Moreover, some computational experiments are also conducted at the end of the paper to examine the effect of the outsourcing strategy in the addressed problem.

By the developed solution approach, the structure of the optimal solution is determined, using which the optimal solution of the problem can be chosen among a limited set of candidate solutions via some simple computations. Moreover, the computational results indicate the remarkable possible role of outsourcing in decreasing the value of the objective function of the problem.

In this paper, a new practical problem in the research area of scheduling with outsourcing is defined and its optimal solution is determined via a detailed analysis. Furthermore, using computational experiments it is shown that the outsourcing strategy can have a great role to attain the problem objectives.