Homework for product mix and process selection:

Homework for product mix and process selection:

1. Formulate the Cargo balancing problem in Lindo format. Make sure you define each decision variable clearly. You do not have to solve the problem.

cij = the amount (per ton) of commodity i used in hold j, where

i = 1, 2, 3, 4 and j = F (front), C (center), R (rear)

Maximize the profit per ton of commodity i used, regardless of what hold it is used in

Max 6C1F + 6C1C + 6C1R + 8C2F + 8C2C + 8C2R + 5C3F + 5C3C + 5C3R + 7C4F + 7C4C + 7C4R

ST

!Weight Capacity Constraints per hold

C1F + C2F + C3F + C4F < 3000

C1C + C2C + C3C + C4C < 4000

C1R + C2R + C3R + C4R < 2500

!Volume Capacity Constraints per hold

60C1F + 50C2F + 25C3F + 40C4F < 155000

60C1C + 50C2C + 25C3C + 40C4C < 185000

60C1R + 50C2R + 25C3R + 40C4R < 145000

!Weight Distribution Requirements and Constraints

C1C + C2C + C3C + C4C - .9C1F - .9C2F - .9C3F - .9C4F - .9C1R - .9C2R - .9C3R - .9C4R < 0

C1C + C2C + C3C + C4C - 1.3C1F - 1.3C2F - 1.3C3F - 1.3C4F > 0

C1C + C2C + C3C + C4C - 1.3C1R - 1.3C2R - 1.3C3R - 1.3C4R > 0

C1F + C2F + C3F + C4F - .95C1R - .95C2R - .95C3R - .95C4R > 0

C1F + C2F + C3F + C4F - 1.05C1R - 1.05C2R - 1.05C3R - 1.05C4R < 0

!Limits on availability of each commodity

C1F + C1C + C1R < 5000

C2F + C2C + C2R < 3000

C3F + C3C + C3R < 1000

C4F + C4C + C4R < 1500

END

Homework for blending problem:

1. Formulate the heating oil problem (in my lecture notes) in Lindo format. Make sure you define each decision variable clearly. You do not have to solve the problem.

Let DiR represent the amount of distillate i used for regular oil (i = 1, 2 ,3),

Let DiN represent the amount of distillate i used for nontoxic oil (i = 1, 2 ,3),

Max 12D1R + 12D2R + 12D3R + 16D1N + 16D2N + 16D3N - 10D1R - 10D1N - 14D2R - 14D2N- 6D3R - 6D3N

ST

! Quality Requirements/Constraint

Rsulfur) 6D1R + 10D2R + 18D3R - 14D1R - 14D2R - 14D3R < 0

Nsulfur) 6D1N + 10D2N + 18D3N - 8D1N - 8D2N - 8D3N < 0

Rvapor) 16D1R + 8D2R + 4D3R - 6D1R - 6D2R - 6D3R > 0

Nvapor) 16D1N + 8D2N + 4D3N - 12D1N - 12D2N - 12D3N > 0

Rcontent) D3R - .8D1R - .8D2R - .8D3R < 0

Ncontent) D3N - .3D1N - .3D2N - .3D3N < 0

! Monthly Sales Constraints

Rsales) D1R + D2R + D3R < 10000

Nsales) D1N + D2N + D3N < 4000

! Availability per Distillate Constraints

Distil1) D1R + D1N < 3000

Distil2) D2R + D2N < 2000

Distil3) D3R + D3N < 10000

END

2. Solve the Chandler Oil problem by Excel.

Please click on the following link for Excel solution:

http://www.wsu.edu/~chenbi/decs344/Homework/HW4/Chandler.xlsHomework for covering problem:

1. Arlington Bank of Commerce and Industry is a busy bank that has requirements for between 10 and 18 tellers depending on the time of day. The lunch time, from noon to 2pm, is usually heaviest. The following table indicates the workers needed at various hours that the bank is open.PRIVATE

Time Period9-1010-1111-1212-11-22-33-44-5

# of tellers needed1012141618171510

The bank now employs 12 full-time tellers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly four hours per day, but can start anytime between 9am and 1pm. Part-time is fairly inexpensive labor pool, since no retirement or lunch benefits are provided them. Full-timers, on the other hand, work from 9am-5pm, but are allowed on hour for lunch. (Half of the full-timers eat at 11am, the other half at noon.) Full-timers thus provide 35 hours per week of productive labor time. By corporate policy, the bank limits part-time hours to a maximum of 50% of the day's total requirement. Part-timers earn $4 per hour (or $16 per day) on the average, while full timers earn $50 per day in salary and benefits, on the average. The bank would like to set a schedule that would minimize its total personnel costs. It will release one or more of its full-time tellers if it is profitable to do so. Set up and solve the problem by Excel and provide your recommendations to the Bank.

If you set up the problem such that the difference between the full timer having lunch at 11 oclock and the full timer having lunch at 12 oclock is no more than 1 person, then:

Please click on the following link for Excel solution:

http://www.wsu.edu/~chenbi/decs344/Homework/HW4/Arlington1.xlsIf you set up the problem such that the difference between the full timer having lunch at 11 oclock and the full timer having lunch at 12 oclock is zero (strictly 50-50 percent each), then:

Please click on the following link for Excel solution:

http://www.wsu.edu/~chenbi/decs344/Homework/HW4/Arlington2.xls2. Set up and solve the stock cutting problem (part c) in my lecture note by Excel

Please click on the following link for Excel solution:

http://www.wsu.edu/~chenbi/decs344/Homework/HW4/stockcutting.xlsHomework for DEA:

1. You have been commissioned by UW to evaluate the relative efficiency of four degree-granting units: Business, Education, Arts & Sciences, and Health, Physical Education, and Recreation (HPER). You are given the information in the following table. Use DEA to rank the four units. You need to determine the inputs and outputs for the problem first. Setup and solve this problem by Excel.

FacultyStaffBudget

(in millions)Credit Hours (in thousands)Research Publications

Business15070515.0225

Education602035.470

Arts&Science8001402056.01300

HPER301512.140

Please click on the following link for Excel solution:

http://www.wsu.edu/~chenbi/decs344/Homework/HW4/UWDEA.xls