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In this study, a mathematical model for the integration of lot sizing and flow shop scheduling with lot streaming was proposed. A mixed-integer linear model for multi-product lot sizing and lot streaming problem was developed. Mixed-integer programming formulation is proposed which will enable user to identify optimal production quantities, inventory levels, sub lot sizes and sequences simultaneously. Two situations where considered: 1) all machines are available and 2) all machines need preventive maintenance tasks. For both situations a new mixed-integer formulation is developed. To demonstrate the practicality of the proposed model, numerical example was used. It is shown that, the best makespan can be achieved through consistent sublots with intermingling cases as compared to non-intermingling cases.

Mixed-integer Formulation for Integration of Lot Sizing and Lot Streaming Problem with Scheduled Preventive Maintenance