Assignment:
Northwest General, a large hospital in Providence, Rhode Island, has initiated a new procedure to ensure that patients receive their meals while the food is still hot as possible. The hospital will continue to prepare the food in its kitchen, but will now deliver it in bulk (not individual servings) to one of three new serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and wings of the hospital.
The three new serving stations are as efficiently located as possible to reach the various hallways in the hospital. The number of trays that each station can serve is shown below:
|
Location
|
Capacity (Meals)
|
|
Station 5A
|
200
|
|
Station 3G
|
225
|
|
Station 1S
|
275
|
There are six wings to Northwest General that must be served. The number of patients in each follows:
|
Wing
|
Patients
|
|
1
|
80
|
|
2
|
120
|
|
3
|
150
|
|
4
|
210
|
|
5
|
60
|
|
6
|
80
|
The purpose of the new procedure is to increase the temperature of the hot meals that the patient receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to wing. The table below summarizes the time associated with each possible distribution channel.
|
To
From
|
Wing 1
|
Wing 2
|
Wing 3
|
Wing 4
|
Wing 5
|
Wing 6
|
|
Station 5A
|
12
|
11
|
8
|
9
|
6
|
6
|
|
Station 3G
|
6
|
12
|
7
|
7
|
5
|
8
|
|
Station 1S
|
8
|
9
|
6
|
6
|
7
|
9
|
I already have the optimal solution and objective vaule (will list below) I just need to provide a summary and description of the overall problem. I am not the best when it comes to describing numerical analysis and solutions. I don't expect a full detailed explanation, just enough so that I can get started. Here is a quick list of what I need help with:
- An executive summary outlining the logistic problem, available business actions to solve the problem as well as the final decisions
- A logistic network diagram showing the origins and their capacities, destinations and their demands, all possible logistic connections (bounds) between these two groups of entities and their respective times
- An integer program (IP) formulation which is used to optimize this distribution system. Label or write remarks of the objective function and the various constraints.
- A brief narrative discussion describing the general problem as well as explaining the logistic model and how you perform the analysis and come up with the final decisions and recommendations.
General ideas and points I can elaborate on would be ideal!
My solution if this helps you:
|
Decision variable
|
|
|
|
|
|
|
|
|
x_ij
|
To
|
Wing 1
|
Wing 2
|
Wing 3
|
Wing 4
|
Wing 5
|
Wing 6
|
|
From
|
|
|
|
|
|
|
|
|
Station 1
|
|
0
|
55
|
5
|
0
|
60
|
80
|
|
Station 2
|
|
80
|
0
|
145
|
0
|
0
|
0
|
|
Station 3
|
|
0
|
65
|
0
|
210
|
0
|
0
|
Objective value = 4825 (minutes)