Rutgers university Distribution Network Design Project 1 Discussion

MIE 597SL Supply Chain LogisticsProf. Ana Muriel
Distribution Network Design Project
Creating hubs: the case of North Suburban Library Systems
Adapted from Prof. Karen Smilowitz, Northwestern University
Introduction
The North Suburban Library System (NSLS) is a state-funded library system that delivers
interlibrary loan items (books, video cassettes, etc.) to its member libraries in the suburbs north of
Chicago. Although NSLS counts with 769 member libraries, the 49 public libraries it serves
account for 89% of the total demand and are the focus of attention for NSLS management. The
system is undergoing a budget crisis due to stagnant state funding, while at the same time
experiencing a 35.8% increase in volume in the last year. This has prompted NSLS management
to reevaluate operations and explore new options.
Current Operations
Currently, four vans operate from a sorting facility (the depot), which is at the NSLS headquarters
in Wheeling, Illinois. Each van follows a delivery route and visits libraries to pick up outgoing
items and deliver incoming items. Vehicle capacity is not a problem, but vehicle tour lengths are
constrained by travel and library visit times. NSLS spends a significant amount on driver overtime.
At the end of the work day, the items that have been picked up are sorted at the depot for delivery
to their destination libraries when they are next visited.
Hub System
NSLS would like to provide the greatest possible visit frequency to its members. However, due to
budgetary restrictions and rising demand for service from libraries, NSLS is creating “hub”
libraries: the vans will visit only a subset of the 49 public libraries, which will act as hubs; the
other libraries will be responsible for collecting material from the hubs and delivering material to
the hubs. As a result of this change, NSLS will move from four vans to two vans and plan for no
driver overtime.
In the hub system, two van routes will connect the hubs and the NSLS headquarters. Access trips
will connect the non-hub libraries with hub libraries: When a patron uses interlibrary loan services
at a library that is not a hub, either the library staff or the patron must travel to the nearest hub. As
demand at non-hub libraries increases, the likelihood of travel increases.
In initial discussions of the development of the hub system, a few librarians have raised concerns
about the adverse effect these changes will have on the marginalized communities they serve.
Many of their patrons do not have access to transportation to collect their books from the hub
library. The limited personnel and budget at their particular facilities will make it very hard to
provide frequent visits to the hubs and adequate service.
MIE 597SL Supply Chain Logistics
Prof. Ana Muriel
Assignment
You are a team of business analysts from Minutemen Consulting. You have been hired by NSLS
to design this new hub system. In particular, NSLS would like you to design a simple solution
approach for them and use this approach to determine the hub locations and assignments for NSLS.
They want a solution approach that they can re-run as needed when their demand volumes and
other parameters change, without the support of Minutemen Consulting.
While the team should analyze the problem as given, where libraries are just distinguished by their
locations and demand volumes, management is also requesting recommendations to ensure
adequate service to a number of marginalized communities for whom the library services are an
essential gateway to knowledge and upward social mobility. There are plans to assess the
communities served by each of the libraries and identify which libraries should qualify for
increased service. Could the solution approach be adapted to incorporate these requirements later
on?
Note, some issues are purposely left vague as they would be in practice. Real projects are muddy:
objectives are not fully clear (different stakeholders may have different objectives), system
constraints need to be uncovered. As a team, you must make some assumptions about operations.
Justify each assumption you make. Be creative!
Your write-up should include:
•
Discussion of the problem, including the objective and constraints of the problem and
related decisions; you must justify your objective function, constraints, decision variables
and parameters
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Discussion of assumptions
•
PART 1:
o Provide a mathematical formulation for the problem of locating hubs; explain your
model clearly – show how your formulation matches your problem description
§
You can use the suggestions on Appendix 2 to approximate the two-van
constraint when modeling the hub location problem
o Optimal solution in AMPL or your mathematical programming language of choice
o Final recommendations for the design of the hub system and clear guidelines on
how to reassess and redesign the system when needed.
o Recommendations to better serve communities in greater need. How could the
models change to make sure that the solutions generated will provide appropriate
access for these patrons?
•
PART 2:
o Write a mathematical formulation for the problem of visiting the hubs in PART 1,
with the two available vans and no driver overtime.
o Solve the routing problem either through exact optimization or a heuristic approach.
MIE 597SL Supply Chain Logistics
Prof. Ana Muriel
Appendix 1 – Details on Delivery Route Operations
At each library the demand is composed of books lent and books borrowed. Management has
aggregated the full volume of total demand for each library into a daily demand figure in the
companion data file. Each van will depart from the depot, visit the hub libraries assigned to it, and
return to the depot. The stopping time (measured in minutes) necessary to drop-off books borrowed
and pick up books lent at a hub library is a function of the full demand the hub serves, which
management suggests can be well approximated by the formula:
Stop time = (1/10) * demand served by that hub
Finally, an important constraint to consider is driver shift length. Each driver can spend at most 6
hours making their route, so as to leave time for sorting at the depot.
Appendix 2 – Assumptions Suggested by Management
To make the problem easier when deciding which locations to use as hubs, management is
suggesting to simplify the travel time of the two van routes and assume that the travel time between
any two nodes (libraries or the depot) is 15 minutes. However, they feel strongly that the actual
distances between non-hub libraries and hub libraries be considered when evaluating the proposed
solutions, as they are a reflection of the level of service NSLS is providing to each library. They
have compiled a distance matrix in the companion data file.
In addition, NSLS management finds it reasonable to consider the driver availability constraint in
the aggregate:
total travel time of the vans + stopping time ≤ 2 * 6 hour driver limit
Once the hub locations have been identified, then accurate vehicle routes using the actual distances
can be created for the two vehicles to visit these locations.
MIE 597SL Supply Chain Logistics
Prof. Ana Muriel
Grading Rubric
Report Presentation
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Clarity of report/easy to understand
Organization
Self-contained
Good use of Figures and Appendix
Modeling Assumptions
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20 points
Explanation of solution method
Creativity of solution method
Ability of solution method to generate high quality solutions in reasonable time
Analysis and Conclusions
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20 points
Explanation of terms, decision variables, constraints and objective
Formulation matches modeling assumptions and goals
Solution Methods
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20 points
Are all the assumptions clearly stated (both those stated in the case study and those the
team develops)?
Are the assumptions reasonable and justified? Pros and cons evaluated?
Does the team consider the impact of the assumptions on the model results?
Formulation
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10 points
30 points
Appropriate cases are solved and using the formulation and solution method.
Sensitivity analysis, if appropriate.
Consideration of the impact of engineering solutions in global, economic, environmental,
and societal contexts, showing good understanding of ethical and professional
responsibility.
In this particular project, the needs of marginalized communities are of special interest.
Conclusions are well supported by the analysis and computational results