Reference no: EM133954388
Problem 1:
The City of Port Charles has two hospitals. (Bayview Hospital and Lakeshore Hospital) Bayview Hospital has 4 ambulances and Lakeshore Hospital has 2 ambulances. Queueing theory (done outside of this problem)indicates that Bayview can be assigned up to 4.9 calls per hour and that Lakeshore can be assigned up to 1.5 calls per hour. Port Charles has been divided into 12 districts. The travel time per call in each district and the average number of calls per hour emanating from each district are given in table to the left.
The objective is to minimize the average travel time needed to respond to a call. Determine the proper assignment of districts (NOT individual ambulances) to hospitals. A given district's calls do not all have to be assigned to the same hospital. Since these are averages, fractional assignments are expected. HINT: you are not scheduling individual ambulances, only allocating calls per hour to each hospital. This has similarities to a network. Get professional assignment help from qualified experts—on time, every time.
a. Formulate the written model and develop the solver model in this spreadsheet, then solve using solver.
b. Are there alternative optimal solutions where Lake Shore is assigned a different district from one on your solution? (Suppose for instance that your original solution in part a assigns calls from Districts 3, 4, and 5 to Lake Shore. Is there a solution where at least one of those districts is not assigned to Lake Shore but the objective value is still the same as the original - an alternate optimal solution?)
c. Is the solution value different if each district is assigned a unique hospital? In other words,
Problem 2:
PART A:
You need to withdraw money from an interest-bearing savings account A into a short-term, daily use cash account B, where B is much like a petty cash account. You move money from A to B so that you can pay for various needs. Every time you withdrawal money from A and put it into B, you must pay a $10 service few no matter how much you withdraw. You must have enough in account B to meet any requirements for that day - you must pay on time. So for instance, if you move 6,000 into acount B on Day 1 so that you can meet payments of 4,000 today (Day 1) and 2,000 tomorrow (Day 2), then you will need to withdraw more on Day 3 to meet whatever requirements you might have.
On Monday morning, you have $3000 in cash on hand in the daily use account. For the next seven days, the cash requirements are given and these must be met. At the beginning of each day, you must decide how much money (if any) to withdraw from the interest-bearing account into the daily cash account. It costs $10 to make a withdrawal of any size. You believe that the opportunity cost of having $1 of cash on hand for a year is $0.20. Assume that opportunity costs are incurred on each day's ending balance ($0.20/365). If you pull money from an account that pays interest when you don't need it that day, then you are forgoing the interest for that day - an opportunity cost. Determine how much money you should withdraw from the bank during each of the next seven days. Formulate the written model and develop the solver model in this spreadsheet, then solve using solver.
PART B:
Assume that the third period (Wednesday) requirement is not known for certain. It could be either 3000 or 9000. This won't be known until after Tuesday's transaction has been made. Therefore the withdrawal schedule can be changed for Wednesday through Sunday, after Tuesday, and upon learning the real demand for Wednesday.
The primary question is what is the "best decision" in period 1 - what should the withdrawal be on Monday? And what kind of errors are involved with making the wrong assumption about the demand for cash on Wednesday. If you make the wrong decision, how much could this "mistake" cost you? This is not simply a question of running an optimization of the two situations.
Determine the best withdrawal schedule - which can include a change in the original plan. Determine also the percent error of making a decision based on one of the two possible options for Wednesday's demand.
Hint: Notice that the objective function value is different for the two scenario optimal solutions, so determining the error is based on the two scenarios.
Problem 3:
Sailboat Extension - Part A
This sheet shows where we ended after class.
Assume that we still want to limit OT each quarter to <=100.
In addition, suppose there is a desire to keep the OT difference across the total of the summer months (2 and 3) and the total of the winter months (1 and 4) to be less than 80.
Right now the summer months total is 180 and the winter months total is 0, for a difference of 180 which is >80.
Remember that this needs to be linear and solved with Simplex LP.
Sailboat Extension - Part B
This sheet shows where we ended after class.
Assume that we still want to limit OT each quarter to <=100.
In addition, suppose there is a desire to keep the OT difference across all months to be less than 60.
Right now the highest month is 100 and the lowest is 0, and thus the difference is 100 which is > 60.
Remember that this needs to be linear and solved with Simplex LP.
Sailboat Extension - Part C
This sheet shows where we ended after class.
Assume that we still want to limit OT each quarter to <=100.
In addition, suppose there is a desire to keep the OT difference across adjacent months to be less than 60.
Right now the highest adjacent difference is 100 and the lowest is 0, and thus the difference is 100 which is > 60.
Remember that this needs to be linear and solved with Simplex LP.
Attachment:- Solver mode.rar