Business Decision Making Through Advanced Analytics
BUS 4024
Assignment #2 – Linear Programming Applications
Assignment Objective:
In this assignment, you will be demonstrating the basic skills to implement a range of linear
programming approaches across a
oad cross section of managerial problems.
Deliverables:
Please Note: All requested submissions for this assignment must be uploaded as
attached files in the assignment folder. To ensure accuracy of feedback, please ensure
that written responses to questions are clearly identified by question number.
In this assignment you will be producing a written report FOR EACH case study, containing the following
deliverables:
Component 1: Executive Summary of Solution Approach and Recommendations (/40)
• For each solution implementation provide a
ief summary of; Presenting Problem,
Solution Approach (include assumptions and sensitivities), Recommendations.
• Your audience is a business sponsor (not a management scientist) and information
should be summarized in that context (2 to 3 paragraphs max)
• Ensure that all responses to case study questions are addressed (and clearly labelled)
and integrated into your executive summary.
• For each model implementation, review the solution and sensitivity output reports and
provide a
ief written summarization (i.e. one to two paragraphs max) of; constraint
impacts, marginal values, sensitivity ranges, scenario analysis showing the effects of
added
emoved constraints or variables, shadow prices. Do not simply produce the
eports, but provide a summary interpretation of the key insights. You’ll be evaluated
on how effectively you use these reports to better qualify and contextualize you
solution recommendations12
1 In terms of sensitivity analysis, although there's not much in terms of reporting from Solver for integer problems, you can still run different
scenarios on either the parameters or the constraints to see the impact of the solution. Having reports makes it a lot more convenient,
however often times you can accomplish similar analysis by rerunning the model under specific changes to see the impact. Obviously, there's
an infinite number of scenarios of sensitivity analysis that you can do, but what I'm looking for is for you to demonstrate some reflection on the
solution and consider from a management perspective anticipating and addressing some of the issues that may arise from your model that may
e relevant to the situation. There's no one "co
ect" answer for doing sensitivity analysis, - but there are some that are useful, while others
are not that pertinent to the problem. Focus on sensitivities around binding constraints that you consider more "negotiable" - or look at the
effect of changes in objective function parameters where you feel there's some potential variability or uncertainty, and you can subjectively run
alternative "best case" or "worst case" scenarios, on the uncertain parameters.
2 In order to receive a proficient evaluation, you will be expected to formulate additional “what if” scenarios that extend beyond the baseline
case solution and demonstrate an ability to think beyond getting the “co
ect answer” and demonstrate an ability to anticipate other potential
questions or inquiries from management. Your evaluation will be based on the value and relevance of these additional scenarios.
• In the APPENDIX of each Case Report please include the following:
1. The mathematically modelled solution(s) must be written in Standard LP
Formulation (using an equation editor, not hand written) with; variable names,
model constraints and objective function clearly defined (i.e. NOT X1, X2, … etc.
or Constraint1, Constraint2, … etc.)
2. Include clearly labelled and commented copies of all output solution and
sensitivity reports for each executed solution scenario in your case
• Submit the completed report as XX_Case_Name_Report.doc file. (where XX is the
enrolled group number (or First and Last Initials if a non-group assignment), followed by
the Case Name)
• Solutions must be executable (in either .xls followed by the Case Name)
Component 2: Executable Solution Implementation and Program Solution and Sensitivity
output (/10)
• Submit your executable implementation as a separate additional file named
XX_Case_Name_LP_Implementation. (where XX is the enrolled group number (or First
and Last Initials if a non-group assignment), followed by the Case Name)
• Solutions must be executable (in either .xls or .sas or .py file formats)
Case 1: Heinz Tomatoes (Ref:241_5.4)
The Heinz Company produces a tomato product at three plants. This product can be shipped directly to
the company’s two customers or it can first be shipped to the company’s two warehouses and then to
the customers. The Figure below is a network representation of Heinz’s problem. Nodes 1, 2, and 3
epresent plants (these are the origins denoted by “S” for Supplier), nodes 4 and 5 represent the
warehouses (these are the transshipment points, denoted by “T”), and nodes 6 and 7 represent the
customers (these are the destinations, denoted by “D”). Shipments are allowed among plants, among
warehouses, and among customers. Where arcs have a
ows on both ends indicates that flow is
allowed in either direction.
The cost of producing the product is the same at each plant, so Heinz is concerned with minimizing the
total shipping cost incu
ed in meeting customer demands. The production capacity of each plant (in
tons per year) and the demand of each customer are shown in the figure. For example, Plant 1 (Node 1)
has a capacity of 200, and Customer 1 (Node 6) has a demand of 400. In addition, the cost (in $ 000s) of
shipping a ton of the product between each pair of locations is listed in the following table:
From
To
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
6 1
7 7
Where there are no values in the table, assume that it’s not possible to ship any product via those node
pairs. Also, assume that at most, 200 tons of product can be shipped between any two nodes. Heinz
wants to determine a minimum-cost shipping schedule to ship the tomato product from suppliers to
customers, possibly through warehouses, so that customer demands are met and supplier capacities are
not exceeded.