The Supplying Chain Scheduling with the Cost Constraint and Subcontracting

We propose an analytical scheduling model with subcontracting. Each job can be processed either on a single machine at a manufacturer or outsourced to a subcontractor, possibly at a higher cost. For a given set of jobs, the decisions the manufacturer needs to make include the selection of a subset of jobs to be outsourced and the schedule of all the jobs. The objective functions are to minimize the commonly used scheduling measures, subject to a constraint on the total production and subcontracting cost. We show the NP-hardiness for the problems with different objective functions and develop dynamic programming algorithms for solving them. 1. Introduction and Problem Description With widespread globalization, subcontracting is widespread in many industries. Subcontracting is the procurement of an item or service that a firm is normally capable of producing using its own facilities. Subcontracting can be used as a strategic tool to reduce operation cost and as a means to hedge against the capacity shortage when facing a large demand. When a firm subcontracts out some orders, this allows it to concentrate on its core competencies and improve its response to customer demand. Furthermore, subcontracting lowers investment requirements and the financial risk of the firm. However, in making subcontracting decisions, many factors need to be taken into account, such as production cost, subcontracting cost, customer demand, and delivery lead times. Obviously, analytical models and problem-solving tools are needed if a manufacturer is to optimize the tradeoffs from those factors. In this paper, we propose an analytical scheduling model for a firm with an option of subcontracting. In our model, we assume that there is a single machine at the manufacturer’s plant and there is a subcontractor, who has a sufficient number of identical parallel machines, such that each of these machines will handle at most one job, possibly at a higher cost. Each job can be processed either at the manufacturer’s plant or outsourced to a subcontractor. The objective functions are to minimize the common scheduling measures, subject to a constraint on the total production and subcontracting cost. Given a set of orders, the manufacturer needs to determine which orders should be scheduled in-house and which should be outsourced. While controlling the production and subcontracting costs, the manufacturer needs to consider in-house scheduling and subcontracting simultaneously. The study of subcontracting under machine scheduling models just started recently. Chung et al. [1] considered a job