MIXED INTEGER PROGRAMMING
project代做 | 代写Objective | unity | lab – 本题是一个利用unity进行练习的代做, 对unity的流程进行训练解析, 包括了Objective/unity等方面, 这是值得参考的lab代写的题目
Department of Management Sciences
MSCI 331: Introduction to Optimization
Winter 2021
COURSE PROJECT
PHASE II: MIXED INTEGER PROGRAMMING
Phase II of the project focuses on Integer Programming and computational analysis. It includes ( 3 ) parts (a)-
(c) and a bonus part (d).
In order to limit the carry over mistakes in parts (b)-(d) related to the core formulation, we will provide you
with feedback on your models, exclusively for part (a). If you would like to receive a feedback, you must submit
your work by Friday, March 19 at 11:59pm (EST). Submission instructions are posted on LEARN.
The course project must be completed with your teammate collaboration among teams is not allowed and
will not be tolerated.
If you use resources from the internet or another source to solve a particular problem, you need to cite the
resources properly. Academic dishonesty will not be tolerated.
The deliverables of both phases of the project are due April 23, 9:00am (EST).
As a consequence of the current COVID-19 crisis, Canadian Blood Services (CBS) wants to run a pilot program for setting up community-based blood collection centres in the KW region to reduce the risk to blood donors. Before launching the project, CBS has decided to establish a new clinic and a laboratory to serve this region. Each day, a nurse will start his/her trip from the new clinic and visit each of the comm unity centres one-by-one to collect blood. At the end of the day, s/he will return all of the collected blood to the new laboratory for testing.
CBS has determined a set of candidate locations for the new clinic and the new laboratory, and is asking you to help them select the best location for each of these facilities and the optimal schedule for the nurse such that the total cost is minimized. A pilot dataset including information of community centres in the KW area is provided to be used in this project. The time horizon being considered for the project is 1 year ( days).
Problem Description:
Let the set of candidate locations for the clinic and the lab be denoted by ={,} and ={,}, respectively. The yearly fixed cost of opening a clinic at location {,} is , and the yearly fixed cost for opening a laboratory at location {,} is . Let the set of community centres be denoted by the set ={,,,,}. It is known that sets H, L and P are disjoint sets (there are no overlaps in their locations). Let denote the parameter for the time required to go from any location {,…} to any location
{,…} in minutes (from/to locations can be from any of the sets ,,).* Assume that the travel cost is per minute. All registered community centres ( P) must be visited by the nurse before the nurse goes to
the laboratory. Assume that the same set of community centres should be visited every single day (365 days) of the year, i.e., the nurse will complete his/her daily trip 365 times in a year.
Each community centre requests a specific time window for the arrival of the nurse. Let and represent the earliest and latest arrival time preferred by the community centre located at location . Violation of these time window requirements will cause CBS to incur a penalty cost of per minute for early arrival and per minute for late arrival. Assume the nurse spends 30 minutes at each community centre. The regular working hours of the nurse are 8am to 4pm. If necessary, he/she can work overtime after 4pm, which will cost CBS an additional per hour.
Formulate and solve a mathematical programming model to find the optimal location of the new clinic and the laboratory as well as the optimal route (starting from the clinic and ending at the laboratory) and schedule (what time each community centre is visited) of the nurse such that all the requirements above are explicitly taken into account. The goal is to minimize total cost including the fixed cost of locating facilities as well as the annual cost for overtime, travel, and the penalty for time-window violation.
*In order to understand the structure of the given data better, please check the unique data set file you received.
Deliverables:
(a) ( 40 %) Mathematical Formulation: Formulate a mathematical model for this problem. Nonlinear
formulations are not accepted. Include clear explanations on your modeling assumptions, parameters,
decision variables, Objective function, and each constraint that you have written.
(b) ( 40 %) Computational Analysis: Using your unique dataset, solve your mathematical model using
Microsoft Excel Solver*. All key findings and outcomes (including but not limited to computation
time, objective function value, facility locations, interpretation of nurse schedule), as well as relevant
sensitivity analyses and/orwhat-if analyses, should be provided. We encourage you to visualize the
solutions that you obtained on maps.
*Note: Please do not forget to set the integer optimality (%) to a value below 0.05 on Excel Solver options.
(c) ( 20 %) Conclusions and Recommendations: Provide uantitative as well as qualitative conclusions
justified by your results. Describe your optimal recommendation to CBS.
(d) (5%) Bonus: Think of a new requirement that CBS could ask for in this problem setting that might
make it infeasible. By providing a what-if analysis, identify a modification to the range of values
related to this new requirement so that the problem maintains feasibility.