The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

Enhanced skip -list search algorithm in 3-layer mediator framework

The Three-Layer distributed mediation architecture, designed by Secure System Architecture laboratory, employed a layered framework of presence, integration, and homogenization mediators. The architecture does not have any central component that may affect the system reliability. A distributed search technique was adapted in the system to increase its reliability. An Enhanced Chord-like algorithm (E-Chord) was designed and deployed in the integration layer. The E-Chord is a skip-list algorithm based on Distributed Hash Table (DHT) which is a distributed but structured architecture. DHT is distributed in the sense that no central unit is required to maintain indexes, and it is structured in the sense that indexes are distributed over the nodes in a systematic manner. Each node maintains three kind of routing information: a frequency list, a successor/predecessor list, and a finger table. None of the nodes in the system maintains all indexes, and each node knows about some other nodes in the system. These nodes, also called composer mediators, were connected in a P2P fashion. ^ A special composer mediator called a global mediator initiates the keyword-based matching decomposition of the request using the E-Chord. It generates an Integrated Data Structure Graph (IDSG) on the fly, creates association and dependency relations between nodes in the IDSG, and then generates a Global IDSG (GIDSG). The GIDSG graph is a plan which guides the global mediator how to integrate data. It is also used to stream data from the mediators in the homogenization layer which connected to the data sources. The connectors start sending the data to the global mediator just after the global mediator creates the GIDSG and just before the global mediator sends the answer to the presence mediator. Using the E-Chord and GIDSG made the mediation system more scalable than using a central global schema repository since all the composers in the integration layer are capable of handling and routing requests. Also, when a composer fails, it would only minimally affect the entire mediation system. ^