Posted: September 13th, 2017

TO DECISION SCIENCES

TO DECISION SCIENCES
THE CLASS PROJECT BELOW INCLUDES TWO CASES. FOR FULL CREDIT,
WRITEUPS FOR BOTH CASES MUST BE COMPLETED!!!!!! FOR EACH CASE,
INCLUDE A BRIEF SUMMARY OF THE CASE, A MODEL FORMULATION, WITH
ANY DEFINITION OF VARIABLES, OBJECTIVE FUNCTION, AND CON-
STRAINTS, IF APPROPRIATE. SHOW ANY WORK AND TABLES, AS APPRO-
PRIATE. ALSO, INCLUDE ANY CONCLUSIONS OR RECOMMENDATIONS YOU
FEEL ARE RELEVANT. REMEMBER TO COMPLETE BOTH CASES!!!!! YOU
CAN WORK IN GROUPS OF UP TO FIVE. HOWEVER, INDIVIDUAL SUBMIS-
SIONS (OR SMALLER GROUPS) ARE O.K. ALSO!!!!!!!! MAKE SURE TO
DETERMINE TOTAL COSTS AND/OR STAFFING AS APPROPRIATE IN EACH
CASE!!!!!

10 PTS. I) THE KRETSCHMER WHEATGERM DISTRIBUTION COMPANY

THE KRETSCHMER WHEATGERM DISTRIBUTION COMPANY DISTRIBUTES WHEAT
GROWN IN NEBRASKA TO PROCESSING CENTERS IN ILLINOIS. THE WHEAT
IS STORED IN DISTRIBUTION CENTERS IN THE MIDWEST, AT
WHICH IT IS KEPT IN SPECIAL, TEMPERATURE CONTROLLED SILOS.
WHEN NEEDED, THE WHAT IS SHIPPED TO THE PROCESSING
CENTERS IN ILLINOIS, WHERE IT IS PROCESSED AND PACKAGED
FOR FURTHER DISTRIBUTION AROUND THE U.S. OR FOR EXPORT AROUND THE
WORLD. THE KRETSCHMER CO. CURRENTLY MAINTAINS FIVE DISTRIBUTION
CENTERS IN THE MIDWEST WHICH SHIP TO SIX PROCESSING CENTERS IN THE
STATE OF ILLINOIS.
KURT TOMS, THE MANAGER FOR THE COMPANY WISHES TO DETERMINE A
SHIPPING PATTERN OF WHEAT FROM DISTRIBUTION CENTERS TO PROCESSING
CENTERS IN AN APPROPRIATE MANNER. THE TABLE BELOW INDICATES THE
COSTS PER BUSHEL OF WHEAT FOR SHIPPING FROM DISTRIBUTION CENTERS
TO PROCESSING CENTERS. ALSO SHOWN IN THE TABLE ARE THE MONTHLY
SUPPLIES (IN BUSHELS) OF WHEAT AVAILABLE AT EACH DISTRIBUTION
CENTER AND THE MONTHLY DEMAND FOR WHEAT (ALSO IN BUSHELS) AT EACH
PROCESSING CENTER. THE OBJECTIVE IS TO MINIMIZE THE COST OF SHIPPING.

YOU ARE TO ADVISE THE MANAGER ON APPROPRIATE SHIPPING PATTERNS
USING:

A) THE NORTHWEST CORNER RULE
B) THE LEAST-COST METHOD

IN YOUR RESULTS MAKE SURE TO SHOW THE SHIPPING PATTERNS FOR
EACH METHOD. ALSO, CALCULATE THE TOTAL SHIPPING COST FOR EACH
METHOD. COMPARE THESE COSTS AND SUMMARIZE YOUR RECOMMENDATIONS.
NOTE THAT ALL COSTS IN THE TABLE ARE IN DOLLARS ($), AND REPRES-
ENT THE COST OF SHIPPING ONE BUSHEL OF WHEAT FROM THE CORRESPON-
DING DISTRIBUTION CENTER TO THE APPROPRIATE DESTINATION (PROCESSING
CENTER).
DISTRIB- DESTINATION (PROCESSING CENTER)
UTION
CENTER A B C D E F SUPPLY
(BUSHELS)
1 $ 58.43 57.25 56.54 59.27 56.37 59.04 700
2 57.62 49.55 58.87 57.64 49.37 66.78 500
3 49.88 58.99 59.52 55.98 57.23 56.97 900
4 58.01 57.66 49.70 56.45 58.27 59.33 500
5 56.42 67.87 49.22 66.71 48.88 66.33 400
DEM-
AND 425 575 550 450 350 650
(BUSH-
ELS)
10 PTS.II) SCHEDULING CRANE OPERATORS AT THE PORT OF OAKLAND

THE MANAGER OF THE PORT OF OAKLAND WISHES TO SCHEDULE CRANE
OPERATORS ON A DAILY BASIS. OPERATORS ARE SCHEDULED TO WORK
FOR SIX CONTINUOUS HOURS, WHICH IS THE LENGTH OF THEIR SHIFT.
SHIFTS ARE SCHEDULED FOR A CONTINUOUS 24 HOUR DAY OPERATION.
THE CRANE OPERATORS ARE PAID $60 PER HOUR BETWEEN THE HOURS
OF 9:00 A.M. AND 9:00 P.M. OTHER HOURS (EARLY AND LATE HOURS)
ARE COMPENSATED AT A RATE OF $80 PER HOUR. THE REQUIRED STAF-
FING LEVELS OF CRANE OPERATORS FOR EACH THREE HOUR TIME PERIOD
DURING THE DAY ARE AS SHOWN BELOW: (NOTE THAT ALL SHIFTS ARE
SCHEDULED TO START ON THE HOUR.)

OPERATORS
TIME PERIOD REQUIRED

3 AM – 6 AM 7
6 AM – 9 AM 11
9 AM – 12 PM 15
12 PM – 3 PM 20
3 PM – 6 PM 16
6 PM – 9 PM 13
9 PM – 12 AM 10
12 AM – 3 AM 6

ZACK WINSTON, THE OPERATIONS MANAGEMENT RESPONSIBLE FOR
PERSONNEL SCHEDULING AT THE PORT OF OAKLAND HAS BEEN COM-
MISSIONED BY THE PORT MANAGER TO BE RESPONSIBLE FOR DEVEL-
OPING A SCHEDULE OF CRANE OPERATORS IN SUCH A WAY AS TO
MINIMIZE THE DAILY COST OF STAFFING.
A) DEVELOP A SCHEDULE OF CRANE OPERATORS USING A SIMPLE
TABULAR PROCEDURE OF YOUR OWN CHOOSING. DETERMINE THE
DAILY STAFFING COST OF THE CRANE OPERATORS USING THIS SCHEDULE.
(NOTE THAT YOU DO NOT NEED THE COMPUTER TO DO THIS!!!) MAKE
SURE TO DETERMINE THE TOTAL DAILY COST OF STAFFING AND THE
TOTAL NUMBER OF OPERATORS YOU WILL NEED IN YOUR RECOMMENDATION.

B) FORMULATE THIS PROBLEM AS AN INTEGER PROGRAMMING PROBLEM.
(YOU DO NOT HAVE TO SOLVE!!!!) MAKE SURE TO DEFINE YOUR VARI-
ABLES, AND WRITE YOUR OBJECTIVE FUNCTION AND CONSTRAINTS. NOTE
THAT YOUR OBJECTIVE IS TO MINIMIZE THE DAILY TOTAL COST OF STAFF-
ING THE CRANE OPERATORS. EXPLAIN WHY YOU WOULD USE INTEGER PRO-
GRAMMING AND NOT LINEAR PROGRAMMING.

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