結合氮氣需求預測與系統操作限制之最適動態氣體生產規劃研究

Abstract

空氣分離系統乃分離空氣中主要氣體氮氣與氧氣供給鋼鐵生產之用，其中氧氣提供高爐煉鐵及轉爐煉鋼所需要的氧氧，氮氣則因性質穩定常被現場人員在製造程序作為輔助應用。本研究主要關心空氣分離系統在未來8小時計畫期間之生產規劃，以期最小化營運總成本。在進行生產計畫時，必須估算計畫期間內之氮氣的需求量作為輸入資料。而氮氣需求量因現場加工衍生，故與氧氧供給煉鋼與練鐵的需求量之間，存在時差之關係。因為個案公司沒有對於氮氣需求建立對應的量測設備，無法直接獲得氮氣需求量的估計量，本研究針對此部分運用向量自我迴歸模式進行分析，預測未來8小時計畫氮氣的需求量。另外，本研究針對C公司煉鋼廠之空氣分離系統的特性，考量:1)氧氣機組與氮壓機產能；2)液態氣體單位時間產量、氣態氮氣產量、氧氣機組調整量、貯槽容量的上限；3)氣態及液態氧氣（與氮氣）供給需求平衡；且4)必須滿足下游煉鋼之需求等限制，建立混合整數線性規劃模式，協助進行空氣分離系統最適中期動態生產計劃，規劃空氣分離系統氧氣與氮氣產量，與調節液態與氣態氣體貯槽存量，提高營運之效能，達到減少氧氣與氮氣排放量，達成最小化未來8小時計畫時程內之營運總成本的目標。本研究運用個案公司的歷史數據進行驗證與比較分析，數據實驗結果顯示其空氣分離系統8小時營運總成本改善率平均可達20%以上，顯示本研究所發展之求解方法為一優良的決策輔助工具。

An air separation system aims to supply oxygen, for the production of iron and steel via blast furnaces and rotary furnaces, and nitrogen, which is popularly used as an assisted air for manufacturing processes at the shop floor, due to its stable property. This study is concerned with the production plan of the air separation system so as to minimize the total operations cost in the planning horizon of the next 8 hours. We shall need the prediction of the demand of nitrogen in the planning horizon as the input data. Because being originated from the manufacturing operations at the shop floor, the demand of nitrogen arrives at a lag behind the demand of oxygen for the production of iron and steel. Since the case company did not install measurement instruments for the demand of nitrogen, there is no way of directly obtaining its estimate. Therefore, we propose a Vector Auto Regression model for the prediction of the demand of nitrogen in the planning horizon of the next 8 hours. Also, we formulate a mixed-integer linear programming model in this study by considering the operational characteristics of the air separation system, e.g., 1) the capacity of the air-production machines; 2) the upper bounds on the liquid air production per unit time, the capacity of air-phase nitrogen, the adjustment magnitude of oxygen, the capacity of storage tanks, 3) the balance equations for liquid-phase and gas-phase of oxygen and nitrogen, and 4) fulfill the demand of for the production of iron and steel. This model assists in the optimal midterm production planning of oxygen and nitrogen for the air separation system, determines the production quantity of oxygen and nitrogen, and adjust the inventory balance of storage tanks, so as to reduce the emission of oxygen and nitrogen, improve the efficiency of operations, and minimize the total operational costs in the next 8 hours. We conduct verification and comparison analysis using the historical data of the case company. Our numerical experiments show that the proposed model is able to obtain an average of 20% cost-saving in the planning horizon of 8 hours for the air separation system. We conclude that the proposed solution approach serves as a good one for the optimal dynamic production planning of the air separation system.