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# 数学代考|运筹学代写Operations Research代考|MAST30013 sCenaRio 1: suPPly is moRe than demand

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## 数学代考|运筹学代写Operations Research代考|sCenaRio 1: suPPly is moRe than demand

Due to production constraints such as maintenance, breakdowns, variation in the availability of raw material, etc., the manufacturer, in this case, Musashi Auto Parts Michigan, tends to produce and stock finished auto parts even before the order is placed. This is done to avoid any bottlenecks in production when the process of fulfillment of an order begins. The amount of overproduction is based on previous demand of three consumers. Thus, considering both production and demand constraints, three supply centres were able to produce a maximum of 65,50 and 35 (in thousands) units. The demand for all three destinations was at a fixed level. Estimate the most viable route to supply and minimum total transportation cost.
Step 1: Formulation of model:
As discussed in the previous section, the notation for different variables would be:
$\mathrm{x}{\mathrm{ij}}=$ number of units to be transported from supply centre $\mathrm{i}$ to demand centre $\mathrm{j}$. $\mathrm{b}{\mathrm{i}}=$ maximum production capacity of supply centre $i$.
$\mathrm{c}{\mathrm{j}}=$ fixed demand of destination $\mathrm{j}$. Constraints regarding both supply and demand constraints are formulated by using a linear programming method. Supply of each source is not fixed and is given at maximum production capacity. This would involve construction of supply constraints with $\leq$ inequality. Demand for each destination is kept at a fixed level, keeping demand constraints with equality constraint function. Thus, Constraints pertaining to demand would be: \begin{aligned} &\mathrm{x}{11}+\mathrm{x}{21}+\mathrm{x}{31}=\mathrm{c}{1} \ &\mathrm{x}{12}+\mathrm{x}{22}+\mathrm{x}{32}=\mathrm{c}{2} \ &\mathrm{x}{13}+\mathrm{x}{23}+\mathrm{x}{33}=\mathrm{c}_{3} \end{aligned}

## 数学代考|运筹学代写Operations Research代考|sCenaRio 2: demand is moRe than suPPly

This case takes into consideration the scenario of fixed production capacity and estimated demand of three destinations. Performing under normal conditions three supply centres were producing a fixed quantity of 55,40 and 25 (in thousands) units. The data corresponded with requirement data indicated the difference between capacity and increased demand of three destinations. To offset this Musashi mostly resort to producing in advance resulting in creation of stock and increase in inventory cost. The varying demand data of past 6 months show that minimum requirement of auto parts from D1 was 75,000 units whereas that D2 was found to be 60,000 units. Finally, data showed a marginal decrease in demand from D3 for last 6 months. But due to approaching festive season, plant at D3 estimated to sell at least 15,000 units.

## 数学代考|运筹学代写Operations Research代考|sCenaRio 1: suPPly is moRe than demand

Xij=从供应中心运送的单位数量一世到需求中心j. b一世=供应中心最大产能一世.
Cj=目的地固定需求j. 通过使用线性规划方法制定有关供需约束的约束。每个来源的供应不是固定的，而是以最大生产能力提供的。这将涉及构建供应约束≤不等式。每个目的地的需求保持在一个固定的水平，保持需求约束与等式约束函数。因此，与需求有关的约束将是：X11+X21+X31=C1 X12+X22+X32=C2 X13+X23+X33=C3

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