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Business Applications of Operations Research
Bodhibrata Nag
In a sentence
This book demonstrates how to use mathematical Operations Research techniques and software to solve a wide range of common business problems and optimize decision-making across various management functions.
Operations Research provides a powerful bouquet of mathematical techniques to find the best solutions for the myriad decisions managers face, from daily operations to strategic planning. This book serves as a practical guide, demonstrating how to apply tools like linear and integer programming to solve real-world problems in operations, supply chain, finance, and marketing. The unique approach of this book is its focus on application over theory; using the LINGO software, you'll learn to model and solve complex issues like product mix, facility location, scheduling, and portfolio management. With detailed do-it-yourself instructions, you'll gain an intuitive understanding of these powerful tools, empowering you to build models for your own business needs and make optimal, data-driven decisions, even without a deep background in mathematics.
The four lenses
- Science
- Statistics
- Systems
- Strategy
The model
This model outlines the process by which structuring business problems with clear objectives and constraints, and applying Operations Research techniques, leads to optimal decisions and improved overall business performance.
Problem Structuringdesign lever
The process of formally defining a business problem by identifying key decision variables, formulating a clear objective function to be maximized or minimized, and specifying all relevant constraints and limitations.
Resource Constraintscontextual condition
The documented limitations on available resources, such as budget, time, production capacity, labor, and materials, that define the feasible solution space for a business problem.
Business Objectivescontextual condition
The clearly defined goals of the decision-making process, such as the maximization of profit or revenue, or the minimization of cost, risk, or distance.
Application of Operations Research Modelbehavioral pattern
The use of a mathematical technique (e.g., linear programming, integer programming) and solver software to analyze a structured problem and compute the optimal values for its decision variables.
Decision Optimalityoutcome metric
The degree to which a chosen course of action represents the best possible solution according to the model's objective function, given the specified constraints. This is the direct output of solving an OR model.
Business Performanceoutcome metric
The ultimate organizational outcomes resulting from the implementation of a decision, measured by key performance indicators such as profitability, cost savings, market share, or operational efficiency.
How they connect
- problem structuring → influences application of operations research model
- resource constraints → influences application of operations research model
- business objectives → influences application of operations research model
- application of operations research model → predicts decision optimality
- decision optimality → predicts business performance
The process
The book's overall playbook is a systematic approach to business decision-making using Operations Research (OR). The core process involves translating complex business problems into structured mathematical models. This begins with identifying key decisions to be made (decision variables), defining a clear goal to optimize, such as maximizing profit or minimizing cost (the objective function), and outlining all operational limitations, resource constraints, and requirements (the constraints). Once a problem is formulated as a mathematical model—typically a linear, integer, or non-linear program—it is solved using specialized software like LINGO to find the optimal solution. This foundational modeling process is applied across a wide array of business functions, creating a portfolio of problem-solving templates. In operations, it's used for optimizing product mix, production schedules, and staff shifts. For supply chain management, the playbook offers methods for facility location, transport planning, and vehicle routing. The book also extends these quantitative techniques to marketing for revenue management and to finance for capital budgeting, portfolio optimization, and asset-liability management. Some problems, like network design or vehicle routing, are addressed with heuristics—step-by-step algorithms that provide good, practical solutions when exact optimization is too complex. The combined set of processes equips a manager to move from ambiguous business challenges to data-driven, optimal decisions. By learning to model problems systematically, the practitioner can analyze trade-offs, understand sensitivities to changing conditions through the model's outputs (like dual prices and reduced costs), and ultimately make quantitatively-defensible choices that improve efficiency and profitability.
Formulating and Solving an Optimization Problem
To find the best possible solution (e.g., maximum profit, minimum cost) to a business problem with scarce resources by representing it as a mathematical model and solving it with software.
When to use: When a business needs to make optimal decisions regarding resource allocation, scheduling, planning, or design.
Step 1Identify and define the decision variables.
Entry: A clear understanding of the decision to be made is available.
Exit: All controllable quantities are represented by symbolic variables.
In: Problem description · Out: List of decision variables
Step 2Formulate the objective function.
Entry: Decision variables are defined and the goal is clear.
Exit: A single mathematical expression for the objective is created.
In: Decision variables, Coefficients for each variable in the objective (e.g., profit per unit) · Out: Objective function
Step 3Formulate the constraints.
Entry: Decision variables and system limitations are known.
Exit: All limitations are expressed as mathematical constraints.
In: Decision variables, Resource limits (RHS values), Technological coefficients (resource consumption per unit of decision variable) · Out: Set of constraints
Step 4Specify variable types.
Entry: The nature of the decision variables is understood.
Exit: All variable type constraints are defined.
In: Decision variables · Out: Variable type constraints
Step 5Enter the model into optimization software.
Entry: The complete mathematical model is formulated.
Exit: The model is correctly entered into the software.
In: Complete mathematical model · Out: Software-readable model script
Step 6Solve the model and interpret the solution.
Entry: Model is entered into the software.
Exit: An optimal solution or a status report (infeasible, unbounded) is generated.
In: Software-readable model script · Out: Solution report with optimal values
Step 7Perform sensitivity analysis.
Entry: An optimal solution for a linear program has been found.
Exit: Insights into the stability and sensitivity of the solution are gained.
In: Solution report · Out: Sensitivity analysis insights
Determining Optimal Product Mix
To determine the quantity of each product to manufacture to maximize total profit, given constraints on production capacity and market demand.
When to use: When planning weekly or monthly production to maximize profitability.
Step 1Define decision variables for the quantity of each product to produce.
In: List of products · Out: Decision variables
Step 2Formulate the objective function to maximize total profit.
In: Profit per unit for each product · Out: Objective function
Step 3Formulate constraints for resource availability.
In: Resource consumption per product, Total availability of each resource · Out: Resource constraints
Step 4Formulate constraints for market demand.
In: Maximum demand forecasts · Out: Demand constraints
Step 5Solve the integer programming model.
In: Complete model · Out: Optimal production quantities, Maximum total profit
Solving Facility Location Problems
To determine the optimal locations for new facilities (e.g., supermarkets, distribution centers) from a set of candidate sites to meet a specific objective, such as maximizing population coverage or minimizing total costs.
When to use: During network design or expansion planning for retail, logistics, or service operations.
Step 1Define binary decision variables for facility location and customer assignment.
In: List of candidate facility sites, List of customer locations · Out: Decision variables
Step 2Formulate the objective function based on the goal.
In: Population data, Distance matrix, Transportation costs, Facility capital costs · Out: Objective function
Step 3Formulate constraints for the number of facilities.
In: Number of facilities to build · Out: Facility count constraint
Step 4Formulate constraints for customer assignment and service.
Out: Assignment and linking constraints
Step 5Add optional capacity constraints.
In: Facility capacities, Customer demand data · Out: Capacity constraints
Step 6Solve the integer programming model.
In: Complete model · Out: Optimal facility locations, Customer-to-facility assignments
Designing a Minimum Spanning Tree
To design a network (e.g., for laying cables) that connects a set of nodes (e.g., towns) with the minimum possible total length of connections, ensuring all nodes are connected.
When to use: When planning the layout of a utility or communication network to minimize material or construction costs.
Step 1Initialize sets for the heuristic.
Entry: A list of all towns (nodes) and the distances between them is available.
Exit: Sets P, Q, and R are initialized.
In: List of nodes, Distance matrix between nodes · Out: Initialized sets P, Q, R
Step 2Select a starting town.
Entry: Sets are initialized.
Exit: Set P contains one town, and set Q contains the rest.
Step 3Iteratively add the closest town.
Entry: Set P is not empty and set Q is not empty.
Exit: The shortest link between the connected and unconnected sets of towns is identified.
In: Current sets P and Q, Distance matrix · Out: The next connection to add
Step 4Update the sets.
Entry: The next connection has been identified.
Exit: Sets P, Q, and R are updated.
In: Identified connection · Out: Updated sets P, Q, R
Step 5Repeat until all towns are connected.
Entry: Set Q is not empty.
Exit: Set Q is empty and set R contains the complete network layout.
Out: Optimal network layout (set R), Total minimum length of the network
Planning Service Capacity with Queuing Theory
To determine the appropriate service capacity (e.g., number of check-in counters, servers) to manage customer waiting lines effectively by balancing service costs and waiting times.
When to use: When designing or evaluating a service system to predict performance metrics like average queue length and waiting time.
Step 1Model the customer arrival process.
Entry: Data on customer arrivals is available.
Exit: The average arrival rate λ is calculated.
In: Historical arrival data · Out: Average arrival rate (λ)
Step 2Model the service process.
Entry: Data on service times is available.
Exit: The average service rate μ is calculated.
In: Historical service time data · Out: Average service rate (μ)
Step 3Verify system stability.
Entry: λ and μ are calculated.
Exit: System is confirmed to be stable (μ > λ).
In: λ, μ
Step 4Calculate key performance metrics.
Entry: The system is stable.
Exit: Performance metrics are calculated.
In: λ, μ · Out: Average queue length, Average waiting time
Step 5Adjust service rate to meet performance goals.
Entry: Performance metrics are calculated and compared against goals.
Exit: A satisfactory service rate is determined.
- Is the current service rate adequate?
In: Performance metrics, Service level goals · Out: Required service rate or number of servers
Scheduling a Production Line
To determine the optimal start time for each job on each machine in a production line to minimize the total time required to complete all jobs (makespan).
When to use: When creating a detailed production schedule to optimize throughput and minimize completion time.
Step 1Define decision variables for the start time of each operation.
In: List of jobs, List of machines, Processing sequence for each job · Out: Decision variables
Step 2Formulate the objective function to minimize the makespan.
Out: Objective function
Step 3Formulate precedence constraints for job sequences.
In: Processing sequence for each job, Processing times · Out: Precedence constraints
Step 4Formulate disjunctive constraints for machine capacity.
In: Processing times · Out: Disjunctive constraints
Step 5Link the makespan to the completion times of all jobs.
In: Processing times, Final machine for each job · Out: Makespan constraints
Step 6Solve the mixed-integer programming model.
In: Complete model · Out: Optimal job schedule, Minimum makespan
Planning Shift Staff
To determine the minimum number of staff required to start shifts at different times of the day to meet fluctuating hourly staffing requirements.
When to use: When creating weekly or monthly staff schedules to minimize labor costs while ensuring service levels.
Step 1Define decision variables for the number of staff starting each shift.
Entry: Shift start times and durations are known.
Exit: A decision variable is defined for each possible shift start time.
In: Possible shift start times (e.g., every hour) · Out: Decision variables
Step 2Formulate the objective function to minimize total staff.
Out: Objective function
Step 3Formulate constraints for hourly staff requirements.
Entry: Minimum staff requirements for each hour are known.
Exit: A constraint is created for each time period with a requirement.
In: Hourly minimum staff requirements, Shift patterns (e.g., 8 hours with a 2-hour break) · Out: Staffing constraints
Step 4Solve the integer programming model.
In: Complete model · Out: Optimal number of staff per shift, Total minimum staff required
Multi-Period Production Planning
To determine the optimal production quantity (using regular and overtime labor) and inventory levels for each period in a planning horizon to meet fluctuating demand at minimum cost.
When to use: For medium-term (e.g., monthly over six months) production planning.
Step 1Define decision variables for production and inventory.
In: Planning horizon (number of periods), Labor types (regular, overtime) · Out: Decision variables
Step 2Formulate the objective function to minimize total cost.
In: Production cost per unit (regular/overtime), Inventory holding cost per unit per period · Out: Objective function
Step 3Formulate constraints for monthly production capacity.
In: Regular time production capacity, Overtime production capacity · Out: Production capacity constraints
Step 4Formulate constraints to meet demand in each period.
In: Demand forecast for each period · Out: Demand satisfaction constraints
Step 5Formulate constraints for inventory limits.
In: Maximum storage capacity, Inventory shelf-life rules · Out: Inventory constraints
Step 6Solve the linear programming model.
In: Complete model · Out: Optimal production plan, Inventory plan, Minimum total cost
Solving a Blending Problem
To determine the optimal mix of raw ingredients to produce a final product that meets specific quality or nutritional requirements at the minimum cost.
When to use: When formulating recipes or blends to meet product specifications cost-effectively.
Step 1Define decision variables for the quantity of each ingredient.
In: List of available ingredients · Out: Decision variables
Step 2Formulate the objective function to minimize total cost.
In: Cost per unit of each ingredient · Out: Objective function
Step 3Formulate constraints for nutritional or quality requirements.
In: Nutritional/quality content of each ingredient, Specification for the final product (min/max levels) · Out: Blending constraints
Step 4Solve the linear programming model.
In: Complete model · Out: Optimal blend recipe, Minimum cost of the blend
Optimizing Cutting Stock
To determine the best way to cut large standard-sized rolls or sheets of material (e.g., paper, steel) into smaller, required sizes to meet demand while minimizing waste or material cost.
When to use: When planning production runs that involve cutting raw materials to fulfill a set of orders for various smaller sizes.
Step 1Identify all possible cutting patterns for each standard roll size.
Entry: Standard roll sizes and required final sizes are known.
Exit: A comprehensive list of feasible cutting patterns is generated.
In: Standard roll widths, Required final widths · Out: List of cutting patterns
Step 2Define decision variables for the length of each standard roll cut using each pattern.
In: List of cutting patterns · Out: Decision variables
Step 3Formulate the objective function to minimize total material cost.
In: Cost per foot of each standard roll · Out: Objective function
Step 4Formulate constraints to meet demand for each required size.
In: Demand (required length) for each final width · Out: Demand constraints
Step 5Formulate constraints for the availability of standard rolls.
In: Available length of each standard roll · Out: Availability constraints
Step 6Solve the linear programming model.
In: Complete model · Out: Optimal cutting plan, Minimum material cost
Planning Multicommodity Transport
To design a distribution network by selecting optimal locations for distribution centers (DCs) and determining product flows from plants to customers via these DCs to minimize total costs.
When to use: During strategic supply chain network design or redesign.
Step 1Define decision variables for facility location, customer assignment, and product flow.
In: Lists of plants, candidate DCs, customers, and commodities · Out: Decision variables
Step 2Formulate the objective function to minimize total system cost.
In: Transportation costs, Fixed and variable DC costs · Out: Objective function
Step 3Formulate constraints for plant production capacity.
In: Production capacities · Out: Capacity constraints
Step 4Formulate constraints to satisfy customer demand.
In: Customer demand data · Out: Demand satisfaction constraints
Step 5Formulate constraints for DC operation and assignment.
In: DC throughput limits, Maximum number of DCs to open · Out: DC operational constraints
Step 6Solve the mixed-integer programming model.
In: Complete model · Out: Optimal network design
Routing a Single Delivery Truck (TSP Heuristic)
To find a short, feasible route for a single truck that starts at a depot, visits a set of customer locations exactly once, and returns to the depot, minimizing the total distance traveled.
When to use: When planning a daily delivery route for one truck.
Step 1Start with an initial feasible route.
Entry: A list of locations and a distance matrix are available.
Exit: An initial route and its distance are established.
In: List of locations, Distance matrix · Out: Initial route R, Initial distance d
Step 2Iterate through pairs of towns in the route to attempt an interchange.
Entry: An initial or improved route exists.
Exit: All pairs of towns have been considered for a swap.
In: Current best route R
Step 3Evaluate the interchanged route.
Entry: A pair of towns to swap has been selected.
Exit: The feasibility and distance of the potential new route are determined.
- Is the new route feasible?
In: Current route R, Selected pair of towns · Out: New route R', New distance d'
Step 4Update the best route if an improvement is found.
Entry: A feasible new route has been evaluated.
Exit: The best known route is updated if an improvement was found.
- Is d' < d?
In: d', d · Out: Updated best route R, Updated best distance d
Step 5Stop when no further improvements can be found.
Entry: A full cycle of iterations completes with no change to the best route.
Exit: The final, locally optimal route is determined.
Out: Final shortest route
Routing Multiple Delivery Trucks (VRP Heuristic)
To assign customers to multiple capacity-constrained trucks and determine the delivery route for each truck to minimize the total distance traveled by all trucks.
When to use: When planning daily delivery routes for a fleet of trucks.
Step 1Find the shortest possible route through all towns.
Entry: A list of locations, demands, and a distance matrix are available.
Exit: An ordered sequence of all towns to visit is created.
In: List of locations, Distance matrix · Out: Shortest TSP route/sequence
Step 2Initialize the first truck.
In: Truck capacity
Step 3Sequentially assign towns to the current truck.
Entry: There are unassigned towns.
Exit: The next town in the sequence is either assigned or skipped.
- Does the truck have enough remaining capacity for this town's demand?
In: TSP sequence, Town demands, Truck's remaining capacity · Out: Updated truck assignment, Updated remaining capacity
Step 4Start a new truck when capacity is exceeded.
Entry: The current truck's capacity is insufficient for the next town.
Exit: A new truck is initialized and the town is assigned to it.
Out: A new truck route is started
Step 5Repeat until all towns are assigned.
Entry: There are still unassigned towns in the sequence.
Exit: All towns are assigned to a truck route.
Out: A set of truck routes with assigned towns
Selecting Suppliers with Multiple Criteria (AHP & IP)
To select the best suppliers and determine optimal order quantities by systematically evaluating them against multiple, weighted criteria using the Analytic Hierarchy Process (AHP) and then using those results in an optimization model.
When to use: When making a complex supplier selection decision for a critical component or service.
Step 1Determine weights for selection criteria using AHP.
Entry: Selection criteria are defined.
Exit: A weight is calculated for each criterion, summing to 1.
In: List of criteria (price, quality, etc.), Expert judgments on relative importance · Out: Criterion weights
Step 2Score each supplier on each criterion using AHP.
Entry: Criterion weights are determined.
Exit: Each supplier has a performance score for each criterion.
In: List of suppliers, Expert judgments on supplier performance · Out: Supplier performance scores per criterion
Step 3Calculate a final, overall score for each supplier.
Entry: Supplier scores and criterion weights are available.
Exit: Each supplier has a final overall score.
In: Criterion weights, Supplier performance scores · Out: Final supplier scores
Step 4Formulate an integer programming model for order allocation.
Entry: Final supplier scores and order constraints are known.
Exit: A complete IP model is formulated.
In: Final supplier scores, Total demand, Supplier capacities and lot sizes · Out: Order allocation optimization model
Step 5Solve the model to determine the optimal order quantities.
In: Complete model · Out: Optimal order allocation
Airline Revenue Management
To determine the optimal number of seats to allocate to different fare classes on each flight leg of an airline's network to maximize total revenue.
When to use: When setting booking limits for different fare classes for future flights.
Step 1Define decision variables for seat allocation.
In: Flight network (legs), Fare classes · Out: Decision variables
Step 2Formulate the objective function to maximize total revenue.
In: Fare for each class on each leg · Out: Objective function
Step 3Formulate constraints for aircraft capacity.
In: Aircraft capacity, Flight routes · Out: Capacity constraints
Step 4Formulate constraints for demand forecasts.
In: Demand forecast per fare class per O-D pair · Out: Demand constraints
Step 5Solve the integer programming model.
In: Complete model · Out: Optimal seat allocation plan, Maximum expected revenue
Optimizing an Investment Portfolio
To determine the optimal allocation of funds across a set of stocks to minimize the portfolio's risk (measured by variance) for a given minimum level of expected return.
When to use: When constructing or rebalancing an investment portfolio.
Step 1Gather historical data and calculate key statistics.
Entry: A set of potential stocks for investment is identified.
Exit: Expected returns, variances, and a covariance matrix are computed.
In: Historical stock price/return data · Out: Expected returns (E(S_i)), Variances (var(S_i)), Covariance matrix (cov(S_i, S_j))
Step 2Define decision variables for the amount to invest in each stock.
In: List of stocks · Out: Decision variables
Step 3Formulate the objective function to minimize portfolio variance.
In: Variances, Covariance matrix · Out: Quadratic objective function
Step 4Formulate a constraint for the total investment budget.
In: Total investment budget · Out: Budget constraint
Step 5Formulate a constraint for the minimum expected return.
In: Expected returns, Target portfolio return · Out: Return constraint
Step 6Solve the quadratic programming model.
In: Complete model · Out: Optimal investment allocation, Minimum portfolio risk (variance)
Capital Budgeting
To select the optimal combination of available investment projects to undertake in order to maximize the total return (Net Present Value), subject to budget constraints in multiple time periods.
When to use: During the annual or periodic strategic planning and budgeting process.
Step 1Define binary decision variables for project selection.
In: List of potential projects · Out: Decision variables
Step 2Formulate the objective function to maximize total NPV.
In: NPV for each project · Out: Objective function
Step 3Formulate budget constraints for each time period.
In: Cash outflow schedule for each project, Annual budgets · Out: Budget constraints
Step 4Solve the integer programming model.
In: Complete model · Out: Optimal set of projects to fund, Maximum total NPV
Bank Asset Liability Management
To manage a bank's balance sheet by optimally allocating funds from various liabilities (deposits, borrowings) to various assets (loans, investments) across different time horizons (buckets) to maximize profit while ensuring liquidity and adhering to regulatory norms.
When to use: For periodic strategic planning by a bank's Asset-Liability Committee (ALCO).
Step 1Define decision variables for asset and liability amounts in each time bucket.
In: List of asset categories, List of liability categories, Time buckets · Out: Decision variables
Step 2Formulate the objective function to maximize profit.
In: Interest rates/returns for each asset, Interest rates/costs for each liability · Out: Objective function
Step 3Formulate liquidity constraints.
In: Estimated deposit levels (which are fixed inputs) · Out: Liquidity/balance sheet constraints
Step 4Formulate regulatory and policy constraints.
In: Regulatory requirements, Internal risk policies · Out: Regulatory and policy constraints
Step 5Solve the linear programming model.
In: Complete model · Out: Optimal asset and liability structure, Maximum profit
Constructing an Index Fund
To select a small subset of stocks (an index fund) from a larger population of stocks that best represents the movement of the entire population, by maximizing the correlation between the population and the chosen subset.
When to use: When creating a new index fund or exchange-traded fund (ETF).
Step 1Calculate the correlation matrix for the stock population.
Entry: A population of stocks is defined.
Exit: A complete correlation matrix is generated.
In: Historical return data for all stocks in the population · Out: Correlation matrix
Step 2Define binary decision variables for stock selection and representation.
Out: Decision variables
Step 3Formulate the objective function to maximize total correlation.
In: Correlation matrix · Out: Objective function
Step 4Formulate constraints for the index fund structure.
In: Desired size of the index fund · Out: Structural constraints
Step 5Solve the integer programming model.
In: Complete model · Out: Optimal set of stocks for the index fund
Designing an Airline Network
To determine which flight routes to operate and with what type and frequency of aircraft to satisfy passenger demand across a network of cities at minimum total operating cost.
When to use: When an airline is planning a new network, expanding, or restructuring its routes.
Step 1Define decision variables for flight frequency and passenger flow.
In: List of cities, Aircraft types · Out: Decision variables
Step 2Formulate the objective function to minimize total operating cost.
In: Operating cost per mile for each aircraft type, Distance matrix between cities · Out: Objective function
Step 3Formulate capacity constraints for each flight leg.
In: Passenger demand between all city pairs, Aircraft seating capacities · Out: Flight leg capacity constraints
Step 4Formulate demand satisfaction constraints.
Out: Demand satisfaction constraints
Step 5Add operational restrictions.
In: Operational rules · Out: Operational constraints
Step 6Solve the mixed-integer programming model.
In: Complete model · Out: Optimal flight schedule (routes and frequencies), Passenger routing plan
Measuring Performance with Data Envelopment Analysis (DEA)
To measure the relative efficiency of a set of peer decision-making units (DMUs), such as railroads, banks, or schools, which use multiple inputs to produce multiple outputs.
When to use: When conducting a benchmarking study to identify best practices and areas for improvement among a group of similar organizations.
Step 1Select the Decision Making Units (DMUs) and define inputs and outputs.
Entry: A benchmarking study is initiated.
Exit: A complete dataset of inputs and outputs for all DMUs is compiled.
In: List of peer organizations, Performance data · Out: Input/output data table
Step 2Formulate a linear programming model for one DMU.
Entry: Data is compiled.
Exit: An LP model is formulated for the target DMU.
In: Input/output data for all DMUs · Out: DEA linear programming model
Step 3Add constraints to the model.
Out: Constraints for the LP model
Step 4Linearize and solve the model.
Entry: The complete fractional model is formulated.
Exit: The efficiency score for the target DMU is calculated.
In: DEA model · Out: Efficiency score (between 0 and 1)
Step 5Repeat for all DMUs.
Entry: The first DMU has been evaluated.
Exit: All DMUs have an efficiency score.
Out: A list of efficiency scores for all DMUs
Step 6Analyze the results.
Entry: All efficiency scores are calculated.
Exit: Efficient and inefficient units are identified, along with their reference sets.
In: List of efficiency scores · Out: Performance analysis report
The story
The reader A manager, business professional, or student who is responsible for making complex decisions regarding operations, finance, or supply chains. They want to improve efficiency, increase profits, and make the best possible choices, but are often faced with too many variables and constraints to rely on intuition alone.
External problem
Facing complex business problems—such as determining the optimal product mix, locating facilities, scheduling production, routing vehicles, or allocating budgets—where finding the best solution is critical but difficult due to numerous options and constraints.
Internal problem
Feeling uncertain or intimidated by the complexity of quantitative analysis, and frustrated by making suboptimal decisions based on guesswork or overly simplistic spreadsheets. They worry they are leaving money on the table or are not as efficient as they could be.
Philosophical problem
It's just plain wrong to make critical business decisions with significant financial implications based on gut feel when a scientific, proven method exists to find the optimal solution and maximize value from scarce resources.
The plan
- Learn the fundamental concepts of Operations Research tools like Linear and Integer Programming.
- Follow step-by-step examples showing how to model diverse business problems from operations, supply chain, marketing, and finance.
- Use the provided LINGO code and do-it-yourself instructions to solve these problems and gain hands-on experience.
Success
- Becoming a more effective and confident decision-maker, capable of tackling complex business problems with a structured, analytical approach.
- Achieving significant, measurable improvements in your area of responsibility, such as increased profits, reduced costs, and optimized resource allocation.
- Gaining a powerful new skill set in quantitative modeling that enhances your career prospects and makes you an invaluable asset to your organization.
At stake
- Continuing to make suboptimal decisions based on intuition or incomplete analysis, leading to wasted resources and missed opportunities.
- Falling behind competitors who leverage operations research to optimize their processes and gain a competitive edge.
- Remaining unable to provide a rigorous, data-driven justification for critical business decisions, leaving your strategies vulnerable to questioning.
Chapter by chapter
ch02Product Mix
This chapter discusses optimizing product mix decisions in a manufacturing context by employing operations research techniques to maximize profit while adhering to production constraints.
- Maximizing profit in a manufacturing context requires a precise understanding of resource allocation and demand constraints.
- Integer decision variables are essential in formulating complex optimization problems in product mix scenarios.
- Employing software tools like LINGO can significantly enhance the accuracy and efficiency of production planning.
- Strategic scheduling can lead to more profitable outputs while adhering to operational limitations.
ch04Cable Layout
This chapter addresses how to optimize the layout of cables connecting ten neighboring towns through a step-by-step heuristic approach that minimizes the total distance of cable required.
- Efficient cable layout can significantly reduce resource expenditure in utility planning.
- The heuristic method presented allows practitioners to visualize and solve complex connectivity issues systematically.
- Iterative processes are essential in optimizing network design, facilitating proactive adjustments based on real-time data.
- Establishing clear sets for problem components helps simplify multifaceted challenges in operations research.
ch05Planning Check-in Counters
This chapter examines the mathematics of customer queue dynamics, focusing on how arrival and service rates impact customer wait times and service efficiency at a fast-food drive-in counter.
- Understanding customer arrival and service time distributions is crucial for effective queue management.
- Poisson distributions model customer arrivals while exponential distributions are best for service times in queuing environments.
- Optimizing service rates is key to reducing wait times and enhancing customer satisfaction.
- The interplay between customer arrival and service rates directly influences queue dynamics and customer experience.
ch07Shift Staff Planning
This chapter tackles the complexities of workforce scheduling in environments with fluctuating demand, such as call centers, and presents a systematic approach to optimizing staff allocation to meet hourly requirements.
- Effective staff planning is essential in service industries facing fluctuating demand, particularly in call centers.
- Utilizing integer programming can significantly enhance the decision-making process for optimal staff allocation.
- Balancing staffing levels not only affects operational costs but also impacts overall service quality and employee satisfaction.
- The integration of software solutions like LINGO provides a concrete method for executing complex staffing strategies efficiently.
ch09Blending of Dog Diet
This chapter addresses the complexities of formulating a nutritionally balanced and cost-effective diet for dogs, emphasizing a systematic approach grounded in operations research to optimize pet nutrition.
- An 80-pound dog requires a minimum of 2000 calories daily, with specific limits on protein, carbohydrates, and vegetable content.
- The application of operations research can provide a structured approach to solving complex dietary challenges for pet nutrition.
- Underutilized ingredients can lead to higher costs and inadequate nutrition if not calculated properly.
- The recommended dietary solution for an 80-pound dog includes 29.5 ounces of raw meat, 7.5 ounces of brown rice, and 0.6 ounces of vegetables.
ch10Paper Roll Trimming
This chapter explores optimal strategies for cutting large rolls of paper into smaller sizes to meet production requirements while minimizing costs, demonstrating a practical application of operations research methods.
- Effective roll trimming requires balancing cost-efficiency with production demands.
- Mathematical modeling, especially constraint programming, is crucial for optimizing resource allocation.
- Visual tabulation of requirements can aid in understanding complex relationships between materials and outputs.
- LINGO and similar optimization tools can significantly enhance decision-making processes.
ch15Revenue Management
The chapter dissects the complexities of revenue management in the airline industry, emphasizing how effective seat allocation based on demand forecasting can maximize airline revenue.
- Effective revenue management relies on a mathematical understanding of optimization and demand forecasting.
- Real-time data integration is critical in dynamically adjusting seat allocation for maximizing revenue.
- Integer programming serves as a powerful tool for operational decision-making in the airline industry.
- The iterative process of re-evaluating constraints has a tangible impact on airline profitability.
Questions this book answers
- How can mathematical modeling and optimization be used to solve practical business problems?
- What are the core tools of Operations Research, such as linear and integer programming, and how are they applied in areas like operations, supply chain, finance, and marketing?
- How can managers use software like LINGO to formulate and solve complex optimization problems without needing to understand the underlying mathematical algorithms?
- How can a business determine the optimal product mix, facility locations, production schedules, or investment portfolios to maximize profit or minimize cost?
Glossary
- Problem Structuring
- The process of translating a complex, real-world business problem into a formal, mathematical structure suitable for optimization analysis. This involves identifying the core decisions to be made, the goal to be achieved, and the rules that must be followed.
- Resource Constraints
- The set of real-world limitations and requirements that restrict the possible choices or actions in a business decision context. These can include physical, financial, legal, or policy-based restrictions.
- Business Objectives
- The primary, quantifiable goal that the organization seeks to achieve through the decision-making process, such as maximizing financial gain or minimizing operational costs.
- Application of Operations Research Model
- The act of employing a formal optimization technique and computational software to analyze a structured problem and derive a solution.
- Decision Optimality
- The quality of a decision, defined as being the best possible choice among all feasible alternatives that achieves the maximum (or minimum) value of the stated objective.
- Business Performance
- The aggregate, real-world outcomes and results of an organization's operations and strategies, reflecting its overall effectiveness and financial health.
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