Dynamic programming for services scheduling with start time constraints in distributed collaborative manufacturing systems

In this paper, the service scheduling problem with start time constraints is considered for distributed collaborative manufacturing systems, which is different from the discrete time-cost tradeoff problem (DTCTP), well studied during the past decades. The assumption that the ability of services is unlimited in DTCTP is seldom true for practical settings. The fact that most services have limited capabilities, especially for manufacturing services results in constraint start times for requirements. Such a DTCTP is modeled as the DTCTP-STC (discrete time-cost tradeoff problem with start time constraints), also proved to be NP-hard. A service is just available at some time point, which can be assigned as the start time negotiated between a broker and a provider. An effective dynamic programming algorithm is proposed with the time complexity O(N²M^v+1) for the DTCTP-STC. The impact of the number of nodes, the number of modes, and the complexity of the network on the computation time is analyzed by experiments. Simulated experiments are performs on randomly generated instances. The results illustrated that the proposal is very effective for small size instances. As well, the proposal is more suitable for the DTCTP-STC than the DTCTP with faster convergent speed for those general instances with fixed fewer modes.