MY-ASSIGNMENTEXPERT™可以为您提供utasKMA255 Operations research运筹学的代写代考和辅导服务！
这是塔斯马尼亚大学 运筹学的代写成功案例。
KMA255课程简介
This unit teaches students skills and techniques that are used to answer practical questions arising in Operations Research. These questions typically also arise in Engineering, Management, Finance, Economics, and Teaching. For example, How long do I expect to have to wait for the next bus? How should I balance the products my factory makes, to maximise my profit? and What is the best way to send electricity from this set of power stations to these homes, to minimise power loss?
Operations Research includes the solution of optimization problems, modelling, and simulation. This unit provides necessary background in probability and graph theory, and then using those tools introduces students to methods in modelling stochastic systems as Discrete Time Markov Chains, and analysing their expected behaviour. It also gives students tools, such as the Simplex Method, to solve Linear Programming optimization and Transportation problems, and heuristic methods to solve computationally intractable problems like the Travelling Salesman Problem.
This unit is a required component of the Statistics and Decision Science major in the BSc.
Prerequisites
- Explain and apply fundamentals of probability and graph theory relevant to operations research.
- Analyse short- and long- term behaviour of discrete time Markov chains.
- Solve problems in linear programming using standard techniques.
- Select and apply standard heuristic methods to computationally intractable problems in operations research.
- Interpret and communicate mathematical arguments using appropriate terminology and notation, as they relate to problems in operations research.
KMA255 Operations research HELP（EXAM HELP， ONLINE TUTOR）
Let
$x_i=$ Dollars invested in project $i, i=1,2,3,4$
$y_j=$ Dollars invested in bank in year $j, j=1,2,3,4$
Maximize $z=y_5$ subject to
$$
\begin{aligned}
& x_1+x_2+x_4+y_1 \leq 10,000 \
& .5 x_1+.6 x_2-x_3+.4 x_4+1.065 y_1-y_2=0
\end{aligned}
$$
\begin{gathered}
.3 x_1+.2 x_2+.8 x_3+.6 x_4+1.065 y_2-y_3=0 \
1.8 x_1+1.5 x_2+1.9 x_3+1.8 x_4+1.065 y_3-y_4=0 \
1.2 x_1+1.3 x_2+.8 x_3+.95 x_4+1.065 y_4-y_5=0 \
x_1, x_2, x_3, x_4, y_1, y_2, y_3, y_4, y_5 \geq 0
\end{gathered}
Optimum solution:
$$
\begin{gathered}
x_1=0, x_2=\$ 10,000, x_3=\$ 6000, x_4=0 \
y_1=0, y_2=0, y_3=\$ 6800, y_4=\$ 33,642 \
z=\$ 53,628.73 \text { at the start of year } 5
\end{gathered}
$$
Let $x_{i A}=$ Amount invested in year $i$ using plan $A, i=1,2,3$
$x_{i B}=$ Amount invested in year $i$ using plan $B, i=1,2,3$
Maximize $z=3 x_{2 B}+1.7 x_{3 A}$ subject to
$$
\begin{array}{rlrl}
x_{1 A}+x_{1 B} & \leq 100(\text { start of year } 1) \
-1.7 x_{1 A}+x_{2 A}+x_{2 B} & =0 & (\text { start of year } 2) \
-3 x_{1 B}-1.7 x_{2 A}+x_{3 A} & =0 & (\text { start of year } 3) \
x_{i A}, x_{i B} \geq 0, i & =1,2,3
\end{array}
$$
Optimum solution: $x_1=324.32, x_2=216.22, x_3=540.54, z=\$ 41,081.08$
Let $x_{i j}=$ Quantity produced by operation $i$ in month $j, i=1,2, j=1,2,3$
$I_{i j}=$ Entering inventory of operation $i$ in month $j, i=1,2, j=1,2,3$
$$
\begin{array}{r}
\text { Minimize } z=\sum_{j=1}^3\left(c_{1 j} x_{1 j}+c_{2 j} x_{2 j}+.2 I_{1 j}+.4 I_{2 j}\right) \text { subject to } \
.6 x_{11} \leq 800, .6 x_{12} \leq 700, .6 x_{13} \leq 550 \
.8 x_{21} \leq 1000, .8 x_{22} \leq 850,8 x_{23} \leq 700
\end{array}
$$
\begin{gathered}
x_{1 j}+I_{1, j-1}=x_{2 j}+I_{1 j}, x_{2 j}+I_{2, j-1}=d_j+I_{2 j}, j=1,2,3 \
I_{1,0}=I_{2,0}=0, \text { all variables } \geq 0 \
d_j=500,450,600 \text { for } j=1,2,3 \
c_{1 j}=10,12,11 \text { for } j=1,2,3 \
c_{2 j}=15,18,16 \text { for } j=1,2,3
\end{gathered}
Optimum: $x_{11}=1333.33$ units, $x_{13}=216.67, x_{21}=1250$ units, $x_{23}=300$ units, $z=\$ 39,720$.
Let $x_i\left(y_i\right)=$ Number of $8-\mathrm{hr}(12-\mathrm{hr})$ buses starting in period $i$. Objective function coefficients 1 and 1.75 are relative cost weights per bus for 8 -hr and 12 -hr operations, respectively.
$$
\begin{aligned}
\text { Minimize } z & =\sum_{i=1}^6 x_i+1.75 \sum_{i=1}^6 y_i \text { subject to } \
& x_1+x_6+y_1+y_5+y_6 \geq 4, x_1+x_2+y_1+y_2+y_6 \geq 8, \
x_2 & +x_3+y_1+y_2+y_3 \geq 10, x_3+x_4+y_2+y_3+y_4 \geq 7 \
& x_4+x_5+y_3+y_4+y_5 \geq 12, x_5+x_6+y_4+y_5+y_6 \geq 4
\end{aligned}
$$
All variables are nonnegative
Solution: $x_1=4, x_2=4, x_4=2, x_5=4, y_3=6$, all others $=0$. $z=24.5$. Total number of buses $=20$. For the case of 8 -hr shift, number of buses $=26$ and comparable $z=1 \times 26=26$. Thus, $(8-\mathrm{hr}+12$-hr $)$ shift is better.
MY-ASSIGNMENTEXPERT™可以为您提供utasKMA255 Operations research运筹学的代写代考和辅导服务！
