A Linear Programming Approach for Different Serial Machines Scheduling with Optimizing Batch Size in a Flow Oriented Synchronized Production

Linear Programming (LP) models are widely used by companies to meet the demand for a variety of products efficiently. In a flow-shop, each product has to be processed by a number of machines in synchronized lines. This work presents a novel interactive linear programming approach for solving the multiproduct aggregate production planning problem with precise forecast demand, related operating costs, capacity and production-inventory model with constant/stock dependent demand. The proposed approach attempts to minimize total costs with reference to inventory levels, overtime, subcontracting and backordering levels, and machine and warehouse capacity. In this study, the problem of scheduling a set of parts with sequence-dependent setup times is considered. The production smoothing problem under presence of setup and processing times vary among the products. The master production-inventory problem of the firm was divided into two sub-problems which were concerned with determining the batch sizes and production sequences of products, respectively.