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Solutions Manual For Introduction To Operations Research 10th Edition By Frederick Hillier

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Operations Research

Degree concentration for phd, industrial engineering.

Operations Research (OR) is the application of scientific and especially mathematical methods to the study and analysis of problems involving complex systems. 

PhD students interested in OR apply methods such as mathematical programming, stochastic modeling, and discrete-event simulation to the solution of problems in complex systems such as logistics, supply chain optimization, long-range planning, energy and environmental systems, urban and health systems, and manufacturing.

We have an active student body - in fact, UB hosts one of the founding chapters of Omega Rho, the National Operations Research Honor Society. Students are also active participants in the Institute for Operations Research and the Management Sciences (INFORMS).

Our faculty and students conduct OR research funded by such agencies as the National Science Foundation, the Office of Naval Research, the Air Force Office of Scientific Research, the Department of Homeland Security, the Department of Transportation and the National Institute of Justice, as well as national and local corporations and foundations such as United Airlines, Praxair, Lockheed Martin, Boeing, and the Fire Protection Research Foundation. We often work in teams with faculty and students with research interests in manufacturing, production systems and human factors to solve problems beyond the expertise of any single discipline.

Graduating students take positions in national and international corporations, academic institutions and research laboratories. 

Required Core Courses

ISE PhD students who concentrate in OR complete at a minimum:

• IE 572 Linear Programming
• IE 573 Discrete Optimization
• IE 575 Stochastic Methods
• IE 576 Applied Stochastic Processes
• IE 5xx/6xx Operations Research/IE Elective
• IE 555 Programming for Analytics (Must be completed within the first two years of the program) 

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Transformations That Work

• Michael Mankins
• Patrick Litre

More than a third of large organizations have some type of transformation program underway at any given time, and many launch one major change initiative after another. Though they kick off with a lot of fanfare, most of these efforts fail to deliver. Only 12% produce lasting results, and that figure hasn’t budged in the past two decades, despite everything we’ve learned over the years about how to lead change.

Clearly, businesses need a new model for transformation. In this article the authors present one based on research with dozens of leading companies that have defied the odds, such as Ford, Dell, Amgen, T-Mobile, Adobe, and Virgin Australia. The successful programs, the authors found, employed six critical practices: treating transformation as a continuous process; building it into the company’s operating rhythm; explicitly managing organizational energy; using aspirations, not benchmarks, to set goals; driving change from the middle of the organization out; and tapping significant external capital to fund the effort from the start.

Lessons from companies that are defying the odds

Idea in Brief

The problem.

Although companies frequently engage in transformation initiatives, few are actually transformative. Research indicates that only 12% of major change programs produce lasting results.

Why It Happens

Leaders are increasingly content with incremental improvements. As a result, they experience fewer outright failures but equally fewer real transformations.

The Solution

To deliver, change programs must treat transformation as a continuous process, build it into the company’s operating rhythm, explicitly manage organizational energy, state aspirations rather than set targets, drive change from the middle out, and be funded by serious capital investments.

Nearly every major corporation has embarked on some sort of transformation in recent years. By our estimates, at any given time more than a third of large organizations have a transformation program underway. When asked, roughly 50% of CEOs we’ve interviewed report that their company has undertaken two or more major change efforts within the past five years, with nearly 20% reporting three or more.

• Michael Mankins is a leader in Bain’s Organization and Strategy practices and is a partner based in Austin, Texas. He is a coauthor of Time, Talent, Energy: Overcome Organizational Drag and Unleash Your Team’s Productive Power (Harvard Business Review Press, 2017).
• PL Patrick Litre leads Bain’s Global Transformation and Change practice and is a partner based in Atlanta.

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An open-source framework for solving shop scheduling problems in manufacturing environments

• Original Research
• Published: 27 April 2024

Cite this article

• Carlos R. H. Márquez 1 ,
• Vanessa Braganholo 1 &
• Celso C. Ribeiro   ORCID: orcid.org/0000-0002-9478-2351 1  

Scheduling problems refer to the decision-making process of allocating tasks to resources, usually scarce and in high demand, to optimize different performance measures. We consider the class of shop scheduling problems arising in the context of manufacturing systems, which are often NP-hard and challenging to solve. Exact methods have limitations in finding optimal solutions in reasonable computation times, even for instances of moderate size. Therefore, in real-life production environments, finding high-quality solutions is often satisfactory, even if they are not optimal. We contribute to the solution of shop scheduling problems with the design and implementation of the SSP-3M framework, oriented by three main guidelines: versatility, extensibility, and independence of the optimization method. These characteristics reduce the gap between scheduling theory and practice in real-life environments and improve the integration of the scheduling framework with other process planning or functions such as Computer-aided Process Planning, Advanced Planning and Scheduling, Integrated Process Planning and Scheduling, and Computer Integrated Manufacturing. The problem and solution representations adopted in our framework design make it possible to handle six shop scheduling problem variants, illustrating its versatility: job shop, flow shop, permutation flow shop, generalized flow shop, flexible flow shop, and flexible job shop. SSP-3M is open-source and can be used by any interested party. Our experimental evaluation shows that it can successfully be integrated with external optimization methods. We claim that SSP-3M is a good choice for companies that need free and quick-to-develop solutions to shop scheduling problems.

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Data availability

The data that support the findings of this study are available from repositories at http://people.brunel.ac.uk/~mastjjb/jeb/orlib/flowshopinfo.html (Beasley, 2023 ), http://people.brunel.ac.uk/~mastjjb/jeb/orlib/jobshopinfo.html (Beasley, 2023 ), and https://people.idsia.ch/~monaldo/fjsp.html (Mastrolilli, 2023 ). Full numerical results are available at the project repository at https://github.com/cherreram2012/jssp-framework/wiki/Benchmark-results (Márquez, 2023 ).

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Acknowledgements

The work of Celso C. Ribeiro was supported by research grants CNPq 309869/2020-0 and FAPERJ E-26/200.926/2021. Vanessa Braganholo was supported by research grant CNPq 305020/2019-6.

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Institute of Computing, Universidade Federal Fluminense, Niterói, Brazil

Carlos R. H. Márquez, Vanessa Braganholo & Celso C. Ribeiro

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Correspondence to Celso C. Ribeiro .

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The open-source, ready-to-use framework SSP-3M coded in C++ is available at the project repository at https://github.com/cherreram2012/jssp-framework (Márquez, 2023 ).

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Appendix A: Greedy randomized G &T algorithm

The greedy randomized G &T algorithm of Giffler and Thompson ( 1960 ) takes as input the set of jobs \(J=\{J_1,\ldots ,J_n\}\) , the set of machines \(M=\{M_1,\ldots ,M_m\}\) , and, for each job \(J_i\) , \(i=1,\ldots ,n\) , the number of operations \(\#op(i)\) to be processed, a list \(L^i = [L^i[1],\ldots ,L^i[\#op(i)]]\) with the sequence of machines where it has to be processed, and the processing times \(p_{i,1},\ldots ,p_{i,\#op(i)}\) of each operation. The algorithm outputs a schedule represented by an operation sequence (possibly with repetitions), with each operation defined by a job, a machine, and the time this job should start to be processed in this machine. The main steps of its pseudo-code appear in Algorithm 1, which is our formalization of the original algorithm textually described in Giffler and Thompson ( 1960 ).

Line 1 initializes the set A that stores the candidate operations, i.e., those that are ready to be scheduled. Each iteration \(i=1,\ldots ,n\) of the loop in lines 2 to 6 places the first operation of job \(J_i\) in the candidate set A in line 3 and sets its starting time to 0 in line 4. Line 5 sets to 1 the position of the first operation of job \(J_i\) ready to be scheduled. Line 7 sets to 0 the counter of scheduled operations. The while loop in lines 8 to 20 runs until all operations are scheduled. Line 9 selects from the candidate set A the operation \(o_{i',k'}\) with the shortest completion time, corresponding to the execution of job \(J_{i'}\) in machine \(M_{k'}\) . Line 10 creates the set \(B \subseteq A\) formed by the candidate operations that guarantee the construction of an active schedule. It contains all operations that use machine \(M_{k'}\) and may start before the shortest completion time determined in line 9. Line 11 randomly selects an operation \(o_{i^*,k^*}\) from B . Line 12 removes the newly selected operation from the candidate set A . Line 13 updates the counter of scheduled operations, and line 14 schedules operation \(o_{i^*,k^*}\) in this position of the operation sequence. Line 15 checks if operation \(o_{i^*,k^*}\) is not the last of job \(J_{i^*}\) . In this case, line 16 updates the position of the subsequent operation of job \(J_{i^*}\) ready to be scheduled. Line 17 adds the next operation of job \(J_i\) to the candidate set A , and its starting time is set to the completion time of operation \(o_{i^*,k^*}\) in line 18. Line 21 returns the schedule represented as an operation sequence.

G &T algorithm

We remark that other dispatching rules can be used at step 11 instead of a simple random choice, such as shortest processing time (SPT), longest processing time (LPT), start as-early-as-possible (SEP), earliest completion time (ECT), earliest due date (EDD), longest number of successors (LNS), and shortest number of successors (SNS). They all lead to active schedules and different variants of the algorithm (Pfeiffer et al., 2006 ).

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Márquez, C.R.H., Braganholo, V. & Ribeiro, C.C. An open-source framework for solving shop scheduling problems in manufacturing environments. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05995-6

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Received : 01 September 2023

Accepted : 08 April 2024

Published : 27 April 2024

DOI : https://doi.org/10.1007/s10479-024-05995-6

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