## 5 Implementation in AAC Industry (Numerical Case Study)  
The problem is in sharing total accessible budget in operations of supply--production--distribution manufacturing segments at Autoclaved Aerated Concrete (AAC) Blocks Plant plant as current case study. Through performances there are bottlenecks that increase the total cost and sometimes the production line stops the production suddenly, while the supply chain system cannot continue product enhancement. Though the implementations in each section of plant are complex, the performances are not similar in variant lines of production while having multifunctional machines that produce the product (light weighted blocks) in different size, which consume about five raw materials from varieties of suppliersthat decision makers will choose suppliers in priorities to provide the essentials in time and cost. The raw materials are included of cement, Aluminum mash, lime, Silica, Gypsum mash, and logistic costs are different in shipping. Also, delivery costs to end-users or customers are different. As the provided materials must be tested on normality and activation in chemical and physical laboratory before combining with the other normalized and activated materials in mixer, even though the quality of each one is different in degree of temperature in production, but without respecting this, we consider and measure the operation time of well-mixed material in each operational segment to identify the congestion and bottlenecks. In integrated model, the non-contractual time and cost can be used and consumed for the other postponed functions in process of supply chain, but in separate framework or model, the time for each operation is fixed and allocated to its applications as controlled by managers and decision makers of manufacturing, and the lack of time in operation according to contractual time reflects on the preparing the customer's demand and is chaos for the following sections in controlling that caused to bottleneck in supply chain system. Here, in this article, the problem is solved by using MINLP through MATLAB, a mathematical programming software to obtain the computations and present the plot for each operation while comparing together and with mixed integer modelling thoroughly. The programs are run on Windows 8. The multi- time step linear analytical data of supply model, production model and distribution model are considered from Tables 2-4. Each period depends on ordering time and delivery time that lasts 1-3 months. The result is obtained by MATLAB so that the parameters according to Table 2 in Supply Model are included of d(t), A\({}^{\text{Q}}\)(t), C\({}^{\text{Q}}\)(t), h\({}^{\text{Q}}\)(t), Z\({}^{\text{Q}}\)(t), \(X^{\text{Q}}\)(t) in certain periods of \(t_{1}\), \(t_{2}\), \(t_{3}\) and \(t_{4}\). In Table 2, the supply costs in period 2 and 3 are more than period 1 and 4. Meanwhile by spending higher cost in period 3, the sustainable production was in periods 2 and 4. As shown in distribution model in Table 3, with respect to constraint for demand responding in each period, it is signified to transfer the products as contractual value and quantity. In Table 4, the integrated total cost model is presented in supply, production, and distribution according to the area and circumstances for supply, production, and distribution manufacturing segments. The costs are scaled and estimated in each segment by range of implementation through manufacturing process according to amount of raw material, inventory, production, and logistics or transportation system from first to fourth period of time in this measurement. As depicted in Tables 2-5, the operation cost for the supply of raw materials for this plant is about 1148, while the operation cost for the production is 1674 and the operation cost for distribution channel is 2234. The total optimization cost for all three segments is measured about 5056 but by respecting to the total cost in integrated model in Table 5, it is calculated by MATLAB to be about 4058 (total cost reduced approximately 19.73%).