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）
On most U.S. university campuses, students are contracted by academic departments to do errands, such as answering the phone and typing. The need for such service fluctuates during work hours (8:00 A.M. to 5:00 P.M.). In one department, the minimum number of students needed is 2 between 8:00 A.M. and 10:00 A.M., 4 between 10:01 A.M. and 11:00 A.M., 3 between 11:01 A.M. and 1:00 P.M., and 2 between 1:01 P.M. and 5:00 P.M. Each student is allotted 3 consecutive hours (except for those starting at 3:01, who work for 2 hours, and those who start at 4:01, who work for 1 hour). Because of their flexible schedule, students can usually report to work at any hour during the work day, except that no student wants to start working at lunch time (12:00 noon). Develop the LP model, and determine a time schedule specifying the time of the day and the number of students reporting to work. Use AMPL, Solver, or TORA to determine the solution.
Let $x_i=$ Number of students starting in period $i$ ( $i=1$ for 8:01 A.M., $i=9$ for 4:01 P.м.)
$$
\begin{gathered}
\text { Minimize } z=x_1+x_2+x_3+x_4+x_6+x_7+x_8+x_9 \text { subject to } \
x_1 \geq 2, x_1+x_2 \geq 2, x_1+x_2+x_3 \geq 4, \
x_2+x_3+x_4 \geq 3, x_3+x_4 \geq 3, x_4+x_6 \geq 2, \
x_6+x_7 \geq 2, x_6+x_7+x_8 \geq 2, x_7+x_8+x_9 \geq 2 \
x_5=0, \text { all other variables are nonnegative }
\end{gathered}
$$
Solution: $x_1=x_3=2, x_4=x_6=x_7=x_9=1$, total hired $=8$. Problem has alternative optima.
A hardware store packages handyman bags of screws, bolts, nuts, and washers. Screws come in 100-lb boxes and cost $\$ 120$ each, bolts come in 100-lb boxes and cost $\$ 175$ each, nuts come in 80 -lb boxes and cost $\$ 75$ each, and washers come in 30-lb boxes and cost $\$ 25$ each. The handyman package weighs at least $1 \mathrm{lb}$ and must include, by weight, at least $10 \%$ screws and $25 \%$ bolts, and at most $15 \%$ nuts and $10 \%$ washers. To balance the package, the number of bolts cannot exceed the number of nuts or the number of washers. A bolt weighs 10 times as much as a nut and 50 times as much as a washer. Develop an LP model to determine the optimal mix of the package, and find the solution using AMPL, Solver, or TORA.
Let $x_s=1 \mathrm{~b}$ of screws/package, $x_b=1 \mathrm{~b}$ of bolts/package, $x_n=1 \mathrm{~b}$ of nuts/package, $x_w=1 \mathrm{~b}$ of washers/package
$$
\begin{aligned}
& \text { Minimize } z=1.2 x_s+1.75 x_b+\left(\frac{75}{80}\right) x_n+\left(\frac{25}{30}\right) x_w \text { subject to } \
& \qquad \begin{aligned}
y & x_s+x_b+x_n+x_w \
& y \geq 1, x_s \geq .1 y, x_b \geq .25 y, x_n \leq .15 y, x_w \leq .1 y \
& \left(\frac{1}{10}\right) x_b \leq x_n,\left(\frac{1}{50}\right) x_b \leq x_w \
& \text { All variables are nonnegative }
\end{aligned}
\end{aligned}
$$
Solution: $z=\$ 1.26, y=1, x_s=.5, x_b=.25, x_n=.15, x_w=.1$.
Two different products, $P 1$ and $P 2$, can be manufactured by one or both of two different machines, $M 1$ and $M 2$. The unit processing time of either product on either machine is the same. The daily capacity of machine $M 1$ is 200 units (of either $P 1$ or $P 2$, or a mix of both), and the daily capacity of machine $M 2$ is 250 units. The shop supervisor wants to balance the production schedule of the two machines such that the total number of units produced on one machine is within 5 units of the number produced on the other. The profit per unit of $P 1$ is $\$ 10$ and that of $P 2$ is $\$ 15$. Set up the problem as an LP in equation form.
Let $x_{i j}=$ Units of product $i$ produced on machine $j$.
Maximize $z=10\left(x_{11}+x_{12}\right)+15\left(x_{21}+x_{22}\right)$ subject to
$$
\begin{gathered}
x_{11}+x_{21}-x_{12}-x_{22}+s_1=5 \
-x_{11}-x_{21}+x_{12}+x_{22}+s_2=5 \
x_{11}+x_{21}+s_3=200 \
x_{12}+x_{22}+s_4=250 \
s_i, x_{i j} \geq 0, \text { for all } i \text { and } j
\end{gathered}
$$
JoShop manufactures three products whose unit profits are $\$ 2, \$ 5$, and $\$ 3$, respectively. The company has budgeted $80 \mathrm{hrs}$ of labor time and $65 \mathrm{hrs}$ of machine time for the production of the three products. The labor requirements per unit of products 1,2 , and 3 are 2,1 , and $2 \mathrm{hrs}$, respectively. The corresponding machine-time requirements per unit are 1,1 , and $2 \mathrm{hrs}$. JoShop regards the budgeted labor and machine hours as goals that may be exceeded, if necessary, but at the additional cost of $\$ 15$ per labor hour and $\$ 10$ per machine hour.
Formulate the problem as an LP, and determine its optimum solution using TORA, Solver, or AMPL.
Let $x_j=$ Units of product $j, j=1,2,3$.
$$
\begin{gathered}
\text { Maximize } z=2 x_1+5 x_2+3 x_3-15 x_4^{+}-10 x_5^{+} \text {subject to } \
2 x_1+x_2+2 x_3+x_4^{-}-x_4^{+}=80 \
x_1+x_2+2 x_3+x_5^{-}-x_5^{+}=65 \
x_1, x_2, x_3, x_4^{-}, x_4^{+}, x_5^{-}, x_5^{+} \geq 0
\end{gathered}
$$
Optimum solution: $x_2=65$ units, $x_4^{-}=15$ units, all others $=0, z=\$ 325$.
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