A novel mathematical model for the scheduling of a zero inventory production: an application of process scheduling in fog computing

One of the main production-related costs in manufacturing is inventory cost since manufacturing firms allocate a vast area to raw material, semi-processed, and final products in production lines and warehouses. Reducing the volume of these inventories leads to lower production-related costs. This paper presents a novel mathematical model for zero-inventory production scheduling. In this model, the jobs arrive at fixed times and are scheduled on a set of unrelated machines. The jobs have different operations that need to be processed one by one. Since the system has zero inventory, the jobs must be processed immediately upon arrival. Also, whenever a job’s operation is complete, the following operation must instantly start (no wait time). That operation is outsourced if no machines are available to process any of the job’s operations. The jobs’ operations are dispatched to the machines from a dispatching center, and there is a latency between the dispatching center, the machines, and the outsourcing center. We present a mixed-integer non-linear programming (MINLP) model to formulate this problem. Then, the MINLP model is turned into a mixed-integer linear programming (MILP) model by linearizing its constraints. Since many production scheduling problems are known to be NP-hard, particularly those involving unrelated parallel machines, precedence constraints, and time-dependent decisions like ours, we adopt two metaheuristics to solve the problem for large-scale cases where exact methods are computationally inefficient. The first is a Genetic Algorithm (GA), and the second is a Teaching-Learning-Based Optimization (TLBO) algorithm. The performance of these algorithms is tested against the optimal solutions obtained from CPLEX for a set of small-scale problems. We consider a real case study, an image processing system, to validate the proposed developments (the MILP model and the GA). The results show that the presented model and algorithm can reduce the system’s total cost by about 12.57% compared to the existing online dispatching rules.