A robust optimization approach for integrated steel production and batch delivery scheduling with uncertain rolling times and deterioration effect

Efficient collaboration between various sub-processes of steel production is of considerable significance, which directly affects a product’s production cycle and energy consumption. However, current collaborative optimisation models and methods in steel production are still limited: (1) Most of the current collaborative manufacturing problems in steel production focus on obtaining joint schedule between steel-making and continuous casting (SCC), and the works considering continuous casting and hot rolling (CCHR) are very few. (2) The processing time is assumed as a constant in most of the existing SCC scheduling models. However, the rolling time of a product in hot rolling operation is actually uncertain and deteriorating. (3) Exact algorithms cannot be applied to solve the complicated collaborative optimisation problems because of their high complexities. To address these problems, we propose an integrated CCHR and batch delivery scheduling model where interval rolling time and linear deterioration effect are considered. With the concept of min–max regret value, we formulate the collaborative optimisation problem as a robust optimisation problem. Instead of using the exact algorithm, we develop an Improved Variable Neighborhood Search (IVNS) algorithm incorporated a novel population update mechanism and neighbourhood structures to solve the robust optimisation problem. Moreover, we develop an exact algorithm that combines CPLEX solver and two dynamic programming algorithms to obtain the maximum regret value of a given rolling sequence. The results of computational experiments show the excellent performance of the proposed algorithms.Abbreviations: IVNS: improved variable neighbourhood search; TOPSIS: technique for order of preference by similarity to ideal solution; PUM-TOPSIS: population update mechanism based on TOPSIS; DP: dynamic programming; NSs-PUC: neighbourhood structures based on the parameterised uniform crossover; SNRT: shortest normal rolling time; SNRT-DP: DP algorithm based on SNRT rule; BRKGA: biased random-key genetic algorithm; SCC: steelmaking and continuous casting; MINP: mixed integer nonlinear programme; CCHR: continuous casting and hot rolling; PSO: particle swarm optimisation; GA: genetic algorithm; VNS-HS: variable neighbourhood search and harmony search; HPSO + GA: hybrid PSO and GA; SA: simulated annealing; B&B: branch-and-bound; TPSO: two-phase soft optimisation; TSAUN: tabued simulated annealing with united-scenario neighbourhood; VNS: variable neighbourhood search; ABC: artificial bee colony; PRVNS: population-based reduced variable neighbourhood search; NS1: neighbourhood structure 1; NS2: neighbourhood structure 2; DE: differential evolution; WSR: Wilcoxon signed-rank test; ENS: exchange neighbourhood structure; IVNS-ENS: IVNS with ENS; RPI: relative percentage increase; ARPI: average RPI; SD: standard deviation.