AMPL Forum

Industry Use Cases

Learn how AMPL is used in real-world situations to improve the performance of companies big and small.

Use Cases


Extraction planning under capacity uncertainty at the Chuquicamata underground mine

The proposed extraction schedule for the Chuquicamata underground copper mine in Chile maximizes profits while adhering to all operational and geomechanical requirements involved in proper removal of the material and includes extraction capacity uncertainties due to failure in equipment, specifically to the overland conveyor, which was found to be the most critical component in the extraction process.


Allocating Students to Multidisciplinary Capstone Projects Using Discrete Optimization

A distinguishing feature of the Capstone projects is that they are multidisciplinary. Each project must involve students from at least two disciplines. This is an instance of a bipartite many-to-one matching problem with one-sided preferences and with additional lower and upper bounds on the number of students from the disciplines that must be matched to projects. This leads to challenges in applying many existing algorithms. It was proposed to use discrete optimization to find an allocation that considers both efficiency and fairness.


Kaiser Permanent Oakland Medical Center Optimizes Operating Room Block Schedule for New Hospital

In developing the new schedule for the Oakland Medical Center, the key decisions the staff would have to make were the type of block (i.e., a combination of surgery types that can be performed in the same operating room on the same day) to assign to each operating room on each day of the planning horizon. This article reports on the development and implementation of an integer programming model to generate a near-optimal block schedule, and differs from many in the literature because it considers both direct nursing costs and patient-related costs, and can accommodate a variety of practical constraints.


Neonatal Physician Scheduling at the University of Tennessee Medical Center

A common issue faced by physician groups is how to schedule 24-7 coverage for hospital units such as an emergency department. The first step is to determine the shifts to be covered. The second step, assigning physicians to specific shifts, is complicated because shifts vary with respect to duration, day of week, time of day, and desirability. To ensure workload fairness, physician groups often create “equality” schedules in which they evenly divide shifts, by type, among physicians. This problem can be readily modeled and solved via optimization. This paper presents a novel approach that incorporates individual physician shift-type preference and seeks, for each physician, a schedule that is superior to his or her equality schedule.


Open-Pit Block-Sequencing Formulations: A Tutorial

A classical problem in the mining industry for open-pit mines involves scheduling the production of notional three-dimensional production blocks, each containing a predetermined amount of ore and waste. That is, given operational resource constraints on extraction and processing, we seek a net present value-maximizing schedule of when, if ever, to extract each block in a deposit. We present a version of the problem, which some literature refers to as (CPIT). This constrained ultimate pit limit problem (i.e., open-pit production-scheduling problem variant) produces a sequence of blocks to extract given minimum and maximum bounds on production and processing capacity, and geospatial precedences.


A Decision-Making Tool for a Regional Network of Clinical Laboratories.

For healthcare systems that operate in large, geographically dispersed areas, the quality of the services provided requires the effective management of a complex transportation problem. We present a decision support system to help healthcare managers improve the delivery of biological samples collected from patients in hospitals and outpatient clinics to laboratories that perform tests on them. This is the development of an optimization model for supporting strategic decisions on the transport of samples and the assignment of work in a large healthcare network with geographically dispersed hospitals, clinics, and testing laboratories. The tool proved invaluable in helping the Andalusian Healthcare System obtain significant improvements in efficiency, quality of service, and outsourcing costs.


Carlson Rezidor Hotel Group Maximizes Revenue Through Improved Demand Management and Price Optimization

Under changing market conditions for the hospitality industry, the Carlson Rezidor Hotel Group (CRHG) collaborated with JDA Software Group to use operations research to drive higher revenue for its hoteliers and to stay ahead of the competition. This highly innovative revenue optimization project, Stay Night Automated Pricing (SNAP), started with enterprise demand forecasting across 600 US hotels in 2007. It was followed by a large-scale network optimization solution to dynamically optimize hotel room rates based on price elasticity of demand, competitor rates, availability of remaining inventory, demand forecasts, and business rules.


Building Cyclical Schedules for Emergency Department Physicians

Physicians at a branch of the emergency department at Cincinnati Children’s Hospital Medical Center complained that their schedules were too erratic because of the multitude of operating requirements, regulatory constraints, physician preferences, and holiday requests. The issue was addressed by using integer programming to build cyclic schedules that can be repeated throughout the year. These schedules are flexible enough to handle incorporating holidays, work assignments, and vacation requests ex post. After we rolled out the calendar-year-based cyclic schedule, statistics were captured to assess the viability and the quality of the yearly schedule generated. Surveys of the physicians and the scheduler after implementation showed that the new schedule provides predictability and well-balanced work patterns.


Norske Skog Improves Global Profitability Using Operations Research

Many businesses, including global papermaker Norske Skog, are uncertain of how the economic recession will affect demand for their services and products. The company has experienced declining demand for its products as electronic media have replaced newsprint publications. Operations research (OR) models have become a vital part of Norske Skog’s decision-making process, helping the company to significantly reduce costs and enabling senior managers to make difficult choices with confidence that their solutions are the best possible. The tactical use of OR models has provided solutions that enable Norske Skog to save $8 million and $10 million USD annually in Australasia and Europe, respectively. In 2008, the Norske Skog Board used a model to make a strategic decision to close two paper mills and a paper machine, saving the company US$100 million annually, compared with the status quo.


Motion Robotics on designing aircrafts

Motion Robotics develops and sells electric flying vehicles including drones and related infrastructure (i.e. docking stations), electric motors containing highly efficient radial design, and designs drones for specific applications. 

The goal was to create a new electric aircraft and to evaluate the many possibilities of design, architecture and flight path. 

Case study coming soon


Transfreight Reduces Cost and Balances Workload at Georgetown Crossdock

Transfreight, LLC, is a third-party logistics provider that supports Toyota Motor Manufacturing’s operations in North America. As part of its logistical support, the company operates several crossdocks that facilitate Toyota’s focus on lean manufacturing principles. In this paper, the development is described of a mixed-integer linear program that provides optimal allocation of inbound trailers to docks at a crossdock facility. The focus is on improving its operational efficiency and balancing the workload of the crossdock workers. Transfreight’s successful implementation is discussed of a model for its inbound trailer assignments at its largest crossdock in Georgetown, Kentucky. This work has provided Transfreight with significant cost savings and growth opportunities.


Improving Customer Service Operations at Amazon

The success of Amazon depends on its providing high-quality customer service. Amazon’s customer service operations consist of internally and externally managed contact centers. Amazon must size its contact centers appropriately, deciding about hiring and training at internally managed centers, and the volume of voice calls and e-mail messages to allocate to external service providers. An approach was developed based on mathematical programming that Amazon uses in planning capacity, reducing the average cost of handling a customer contact, and increasing the service level provided customers.



Research was conducted to enable the US Minerals Management Service (MMS) to maximize natural gas royalties. MMS is the agency of the US Department of the Interior responsible for managing mineral royalties. As part of managing royalties, MMS decides whether to accept royalties in value (cash payment, RIV) or in kind (physical transfer of gas, RIK). When MMS collects RIK, it also decides how to transport, process, and sell the natural gas. The author used an optimization model to evaluate conversion and contract alternatives so as to maximize total royalties.


Implementing a Production Schedule at LKAB's Kiruna Mine

LKAB’s Kiruna Mine, located in northern Sweden, produces about 24 million tons of iron ore yearly using an underground mining method known as sublevel caving. To efficiently run the mills that process the iron ore, the mine must deliver planned quantities of three ore types. A mixed-integer program was used to schedule Kiruna’s operations, specifically, which production blocks to mine and when to mine them to minimize deviations from monthly planned production quantities while adhering to operational restrictions. These production schedules save costs compared to schedules produced manually by meeting desired production quantities more closely and reducing employee time spent on preparing schedules.


Implementing a Pool Distribution Network at Schneider Logistics Application of P-Median Model for Distribution-Network Design

A pool-distribution network operates on a simple principle—groups of customer orders are consolidated into full truckloads and shipped to pool points where the individual orders are deconsolidated and delivered to the end customers assigned to each pool point. By leveraging the use of full truckload transportation for the movement of goods into the local market, the manufacturer reduces freight costs, improves transit time, and minimizes product damage.


NBC's Optimization Systems Increase Revenues and Productivity

NBC television network, a subsidiary of the General Electric Company (GE), uses optimization-based sales systems to improve its revenues and productivity. GE’s corporate research and development center (CRD) developed these systems using operations research and management science techniques to improve NBC’s sales processes. These systems remove bottlenecks caused by manual development of sales plans, helping NBC to respond quickly to client requests with sales plans that meet their requirements. These systems also enable NBC to make the most profitable use of its limited inventory of valuable advertising slots by estimating demands for airtime by show and by week and to schedule commercials. Between 1996 and 2000, the systems increased revenues by over $200 million, improved sales-force productivity, reduced rework by over 80 percent, and improved customer satisfaction.


Underground Planning at Stillwater Mining Company

As part of a new expansion effort, Stillwater Mining Company needed a tool for analyzing development and production scenarios in a new area of an underground platinum and palladium mine in Stillwater, Montana. A large mixed-integer programming model was developed that takes as input the planned mine layout, projected ore quality, and projected costs for basic mining activities, and produces as output a near-optimal schedule of activities that maximizes discounted ore revenue over a given planning horizon. This model was used to evaluate various planning scenarios and make recommendations about development and production in this new area.


Implementing and Evaluating SilverScreener: A Marketing Management Support System for Movie Exhibitors

Every Monday morning, Pathé Theaters in the Netherlands decides which movies in its cinemas to retain and which to replace. It must choose replacement movies from those available at that time. A mathematical-programming system was implemented [Swami, Eliashberg, and Weinberg 1999] to help Pathé managers make those decisions for one six-screen theater and tested its performance against the performance of two unaided similar multiscreen cinemas. Using Pathé’s historical data, managerial judgment, and theater-specific factors, an attendance-forecasting system was developed.


Supply-Chain Analysis at Volkswagen of America

A while back, Volkswagen of America began a review of its vehicle-distribution system looking for opportunities to improve customer responsiveness and simultaneously reduce system costs. An analytical tool was required to evaluate alternative designs in terms of cost and customer service level, both of which are functions of probabilistic and dynamic elements. These elements include inventory policies, demand seasonality and volume, customer-choice patterns, and transportation delays. By using an innovative combination of simulation and discrete optimization models, the problem was addressed of analyzing a large number of alternatives efficiently. The analysis indicated opportunities for significant savings in estimated annual transportation costs, and it provided insights on how to implement the proposed system.


US Airways Automates Its Weekend Fleet Assignment

Assigning fleets of aircraft to a weekend schedule is more difficult than assigning them to a weekday schedule. The reason is that you must balance two conflicting objectives. You must meet passenger demand that is different from weekday demand. You must also minimize the costs of realigning airport facilities and personnel that would incur by changing flight patterns too much. To support US Airways’ schedule planners in this balancing act, a specialized fleet-assignment model was built and integrated it into a graphical environment for schedule development. The planners use the system to create safe, profitable, and robust flight plans.