homework assignment

IEN642 Homework 2 Fall 2014 Due: 10/1/2014 (Wednesday) 1. You are working as an operations planner in a company which has two factories, one

in Atlanta, Georgia and one in St. Jose, California. In addition to the factories your

company has four depots with storage facilities in Miami, Baltimore, Denver and Seattle.

The company sells its products to six companies C1, C2…, C6. Customers can be

supplied either from a depot or from the factory directly as seen in the following figure:

The distribution costs are known and given in the Table (in $ per ton delivered).

Certain customers have expressed preferences for being supplied from factories or depots

which they are used to. The preferred supplier(s) for each customer are given below

C1 Atlanta (factory)

C2 Miami (depot)

C3 No preferences

C4 No preferences.

C5 Baltimore (depot)

C6 Seattle or Denver

Atlanta

St. Jose

Miami

Baltimore

Denver

Seattle

C1

C2

C3

C4

C5

C6

Factories Depots Customer

Each factory has a monthly capacity. Namely the capacities in Atlanta and St. Jose are

150,000 and 200,000 tons respectively. The maximum throughput for depots are 70000,

50000, 100000 and 40000 for Miami, Baltimore, Denver and Seattle respectively.

Supplied to Atlanta St. Jose Miami Baltimore Denver Seattle

Depots

Miami 0.5 -

Baltimore 0.5 0.3

Denver 1.0 0.5

Seattle 0.2 0.2

Customers

C1 1.0 2.0 - 1.0 - -

C2 - - 1.5 0.5 1.5 -

C3 1.5 - 0.5 0.5 2.0 0.2

C4 2.0 - 1.5 1.0 - 1.5

C5 - - - 0.5 0.5 0.5

C6 1.0 - 1.0 - 1.5 1.5

(A dash indicates the impossibility of certain suppliers for certain depots or customers)

Each customer has a monthly requirement given below which must be met

C1 50,000 tons

C2 10,000 tons

C3 40,000 tons

C4 35,000 tons

C5 60,000 tons

C6 20,000 tons

Your boss would like you to construct a model that will find an optimal distribution

pattern that minimizes overall cost.

First ignore the customer preferences. Suppose that you are free to use all “feasible”

channels to ship the products to the customers. Answer the following questions:

a) Write down the mathematical model as an LP

b) Solve the problem using MS Excel Solver (submit only hard copies of the model

and the solution sheet)

c) Solve the problem with AMPL (submit hardcopies of the model, data and output

files). You should use compound sets in your AMPL model.

d) Would it be possible to meet all customer preferences regarding suppliers and if

so what would be the extra cost of doing this? If it is not possible to satisfy all

preferences what does the company need to do to make it possible?

e) Suppose the customer preferences are not hard constraints. That is, a customer

may prefer being supplied from certain origin(s) even though she will still accept

shipments from other origins. Giving at most importance to customer satisfaction,

your company employs a policy that attempts to supply customers based on their

preferences first, before utilizing any other (un-preferred) origins. Find the

optimal distribution plan (algorithm) that minimizes the operational cost while

maximizing the customer preferences. Add and/or assume parameters and

constraints that you think necessary (Be reasonable and creative!). What is the

optimal cost and how is it different than the one found in the original problem?

f) Now treat preferences as requirements. That is, a customer will never accept a

shipment from an origin that is not included in her preferences list. Assuming that

the capacity at Baltimore Depot has been increased to 60,000 units find the

optimal distribution plan that minimizes the operational cost. Compare this result

to the case where there is no customer preferences (as in part a but now with new

Baltimore capacity)

You are expected to conduct your analysis using the features of AMPL whenever they are

useful except for parts a and b.

2. Write down the mathematical model for Problem 50 on Page 121 in the attached pages

and use AMPL to solve. Your model should “read” all the data from a text file.

3. Use AMPL to solve Exercise 2.4 in Textbook and make sure to use ordered sets in

your AMPL model.

4. Do Exercise 6.2 part A in the AMPL Book