In this paper, we discuss fleet size decisions of an equipment rental firm. The availability of the rental equipment depends on the fleet size of the firm and has a direct impact on its profitability. In our setting, we allow for partial backordering, reneging, and finite commitment capacity. Moreover, we explicitly consider the breakdown possibility of the available equipment fleet. We develop an efficient recursive algorithm to solve the underlying two‐dimensional stochastic single‐player model. Our algorithm determines the global optimal fleet size of the firm for the same reneging and equipment return rates. Our extensive managerial insights quantify the behavior of various performance measures in the single‐player model with regard to repair performance of the firm, customer impatience level, traffic intensity, and equipment rental revenue. We demonstrate that by applying our model to a real case, there is a potential of more than a 4% (400,000 USD) increase in total daily profits. Extending our model to a two‐player game, we propose an approximation heuristic to derive closed‐form solutions to estimate equilibrium fleet sizes under complete information. Using our heuristic as the initial solution, we develop a simulation model to determine the exact equilibrium fleet sizes and draw a detailed comparison between the two‐player and single‐player models.
PurposeIncreasing scarcity of natural resources and the adverse effects of unsustainable practices call for more and more efficient management strategies in the energy industry. The quality of the coke plays a significant role in the quality and durability of the output steel which is produced using the energy from the coal. This paper aims to investigate the dynamic coal blending problem under overall cost and coke quality constraints in the steel industry within a periodic cycle of operations.Design/methodology/approachConsidering the variability of the natural properties over a periodic cycle, this study proposes a multi-period mixed-integer non-linear programming formulation to optimize the total blending costs while taking various coke quality constraints into account. Besides, this study applies factorial design to investigate about the significant effect of coal proportions as well as improvement into the overall cost of blending.FindingsIn this case study, utilizing real data from a coal blending facility in India, through a factorial design, the authors obtain optimal desirable levels of coal proportions and their criticality levels towards the total cost of blending (TCB) or objective function. This analysis reflects the role of the coke quality constraints in the objective function value while characterizing the price of sustainability for the case study among other critical insights.Originality/valueObjective function (or TCB) includes basic coal cost, movement cost and environmental costs during the coal and coke processing at a coke-oven and blast furnace of steel industry. The price of sustainability provides managerial insights on that sacrifices the industry has to make in order to become more “sustainable”.
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