Scenario 1 : A company is taking bids on four construction jobs. Three contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the table below. (A dash indicates that the contractor did not bid on the given job.) Note: Contractor 1 can do only one job, but contractors 2 and 3 can each do up to two jobs. picture1

  • Determine the minimum cost assignment of contractors to jobs.
  • What is the “cost” of restricting Contractor 1 to only one job?
  • How much more can Contractor 1 bid for Job 4 and still get the job?


Scenario 2 : A brewery distributes kegs of beer through three warehouses in the greater New York City area, with current supplies, as shown in Figure 1. On a Thursday morning, they get their usual weekly orders from his four loyal customers, as shown in Figure 2. The brewery needs to determine the most cost-efficient plan to deliver beer to these four customers, knowing that the costs per keg are different for each possible combination of warehouse and customer (see Figure 3).picture2screen-shot-2016-11-06-at-9-46-19-pm

Scenario 3 : In treating a brain tumor with radiation, physicians want the maximum amount of radiation possible to bombard the tissue containing the tumors. The constraint is however that there is a maximum amount of radiation that normal tissue can handle without suffering tissue damage. Physicians must  decide how to aim the radiation so as to maximize the radiation that hits the tumor tissue subject to the beams available that can be aimed at a tumor. The region containing the tumor has been divided into 6 regions: 3 regions containing tumors and 3 regions of normal tissue. The amount of radiation delivered to each region by each type of beam is shown in the table below. If the each region of normal tissue can handle  at most 60 units of radiation which beams should be used to maximize the total amount of radiation received by the tumors? 



Scenario 4 : When you lease 800 phone numbers from AT&T for telemarketing, AT&T uses an optimization model to tell you where you should locate calling centers to minimize your operating costs over a 10-year horizon. To illustrate the model, suppose you are considering seven calling center locations: Boston, New York, Charlotte, Dallas, Chicago, Los Angeles, and Omaha. You know the average cost incurred if a telemarketing call is made from any these cities to any region of the country. See Table 1 below. Assume that an average number of calls made per day to each region of the country is listed in Table2. The cost(in millions of dollars) of building a calling center in each possible location and the hourly wage that you must pay workers in each city is listed in Table3. Each calling center can make up to 5000 calls per day.


Give this information, how can you minimize the discounted cost  ( at 10% per year) of running the telemarketing operation for 10 years? Assume all wage and calling costs are paid at the ends of the respective years.

a. Annual wage cost is (for each center) found from the following “units”equation: $/year=calls/day* days/year* minutes/call*hours/minute*$/hour

b. Total present value can be found from the PV function for the annual costs, but the one-time building cost must be outside the PV function.


Scenario 5: Tso’s Dumplings is building a new restaurant. To finish the project the following activities must be completed.


a. using only the ” most likely ” time estimates, how fast can this project be completed?

b. Which activities are on the critical path?