Glossary

Business model in which a company buys warehousing, transport, distribution or value-added logistics services from an external specialist provider rather than running them in-house.

Statistical-OR practice of inspecting a random sample of n items from a lot and deciding to accept or reject the entire lot based on whether the number of defects is below or above an acceptance threshold c.

Medium-term OR/MS problem of jointly setting production rate, inventory, regular workforce, hiring/firing, overtime, subcontracting and backlog across a multi-product, multi-period horizon (typically 3-18 months) to minimise total cost.

An MCDM technique that decomposes a decision into a goal-criteria-alternatives hierarchy, extracts weights from pairwise comparison matrices via the principal eigenvector, and validates judgments using a consistency ratio.

A classic MCDM method that decomposes a complex multi-criteria decision into hierarchical layers, derives weights through pairwise comparisons, and checks judgment consistency.

OR problem of assigning indivisible tasks under precedence to ordered stations on a serial assembly line so the cycle time (takt) is not exceeded; SALBP-1 minimises station count, SALBP-2 minimises takt.

Matching a set of resources (people, vehicles, machines) to a set of tasks at minimum cost or maximum benefit.

Selecting which products to carry in a retail store or e-commerce category, given limited shelf or page space.

OR problem of forecasting each ATM's cash demand, deciding replenishment timing and amount, and balancing the immobilisation cost (interest opportunity + security risk) of idle in-ATM cash against the stock-out cost (customer complaints + lost transactions) of an empty ATM; joins forecasting + stochastic inventory + cash-in-transit (CIT) routing.

A customer order accepted in spite of no on-hand stock, awaiting future delivery — the deliberately planned shortage mode of inventory policy.

The decision problem of which patient is admitted to which ward and bed, and when — under clinical compatibility, isolation, gender-separation and nurse-staffing constraints.

Recursive value-function equation that captures the necessary and sufficient condition for an optimal policy in dynamic programming; formalized by Bellman (1957) as the principle of optimality.

The hierarchical tree that, at each level of a manufactured product, lists the immediate components and their quantities, recursively down to raw materials.

The problem of placing objects of various sizes into fixed-capacity bins so as to minimize the number of bins used.

The resource, station, or process step in a production or service system with the lowest capacity or highest utilization, which determines the overall system throughput.

Foundational exact solution method for mixed-integer programming (MIP) and general combinatorial optimization; explores a tree of subproblems and prunes nodes using LP-relaxation bounds; introduced by Land and Doig (1960).

The exact MIP solution framework that combines branch-and-bound with cutting-plane methods — at each node of the search tree, valid inequalities (cuts) tighten the LP relaxation before branching.

Amplification of demand variance as orders travel up the supply chain, so that the manufacturer-end signal swings far more wildly than actual end-consumer demand.

Designing minimum-cost vehicle routes that start and end at a single depot, visit each customer exactly once, with total demand per route not exceeding vehicle capacity.

The accounting-finance distinction between capital expenditure (long-lived asset acquisition, depreciated over useful life) and operating expenditure (consumed within the current period); the central axis for buy-vs-lease, on-premise-vs-cloud, and subscription decisions.

The composition, weight, and distribution of patient types a hospital treats — the key input to operational planning.

Operational routing of armoured cash-transport vehicles visiting a bank's ATMs and branches for refill. A VRP variant shaped by security (route unpredictability), tight time windows, denomination considerations and regulatory monitoring.

Classical actuarial loss-reserving method that derives development factors from cumulative ratios in a loss development triangle.

Strategic OR problem of selecting locations, types (AC slow vs DC fast) and counts of public EV charging stations to deploy in a region, balancing capital and operational cost against expected user coverage and waiting time.

The actuarial process of estimating future claim payments for events that have already occurred.

Classical 1964 heuristic for the Capacitated Vehicle Routing Problem: start with each customer on its own route, iteratively merge pairs of routes that yield the largest 'savings' in distance, until capacity blocks further merges.

A large-scale optimization method that generates candidate decisions (columns) on demand instead of enumerating all of them upfront.

Optimization paradigm where the focus is on a solution satisfying a set of constraints — particularly strong for scheduling and assignment problems.

The problem of placing parcels and pallets into one or more containers or trucks; the 3D-BPP extended with practical side constraints.

The problem of assigning courses to teachers, classes, rooms, and times in schools or universities without conflicts.

The longest chain of dependent tasks running from project start to finish — the chain that drives the delivery date.

Foundational deterministic project-network technique: given activities with fixed durations and precedence, compute earliest and latest start/finish times and identify the longest path that drives project duration.

A distribution model in which incoming shipments move directly from receiving dock to shipping dock with no shelf-storage step — effectively zero warehousing.

Method that iteratively tightens the LP relaxation of an integer program with valid inequalities that preserve all integer-feasible solutions while cutting off the fractional LP optimum; introduced by Gomory (1958) for integer programming.

The problem of extracting required pieces from standard rolls or sheets with the least waste.

Average inventory held to cover normal demand between two consecutive orders — half the order quantity, Q/2.

The actual processing time spent at a station between the start of one unit and the start of the next.

Non-parametric LP-based frontier-efficiency method that measures the relative technical efficiency of similar units (DMUs) operating with multiple inputs and multiple outputs.

Specification of which days in a weekly or n-week cycle an employee works versus rests, under consecutive-day-off, weekend-fairness and ergonomic limits.

Unit of analysis in DEA — a similar entity (one of N homogeneous organisations) being benchmarked; consumes multiple inputs to produce multiple outputs.

Quantitatively predicting future demand using history, seasonality, events, and external signals.

An energy-management approach that optimizes when loads run on the consumer side, based on the tariff, system conditions, or incentives.

Edsger Dijkstra's (1959) polynomial-time algorithm for single-source shortest paths in graphs with non-negative edge weights; greedy — extract the unvisited node with smallest tentative distance from a priority queue and relax its neighbours; O((V+E) log V) with a binary heap.

Broader class of OR pricing problems where item value declines over time (fresh food, fashion, electronics with new generations, hotel rooms past arrival date) and prices must adapt — monotonically decreasing or up-down.

The OR / computer-science technique for solving multi-stage decision problems by recursive decomposition into overlapping subproblems with stored intermediate results; introduced by Bellman (1957).

The classic inventory formula for the most economic order quantity to place with a supplier.

The family of relaxations and extensions to the classical Economic Order Quantity model — quantity discounts (all-units / incremental), planned shortages / backordering, finite replenishment rate (EPQ), perishable / shelf-life constraints, multi-item joint ordering, and inflation-adjusted variants.

Formula giving the probability that an arriving customer must wait in an M/M/c queue; the call-center staffing standard.

Operational OR problem of deciding when and at what power level to charge each EV in a fleet or queue, subject to deadline, grid power limits, battery SoC bounds, time-of-use pricing and battery-aging cost.

Choosing where to place a new facility (warehouse, plant, branch, hospital) — mathematical optimization across demand points and costs.

A scheduling rule that limits worker fatigue in safety-critical roles — minimum rest, max consecutive nights, weekly hours, weekend balance.

The set of processes covering installation, maintenance, or repair performed at customer locations — technician assignment, routing, and customer notification.

FIFO issues oldest stock first, LIFO issues newest first — the two basic rules governing both physical rotation of perishables and accounting-tax-driven inventory valuation.

The fraction of units that pass quality inspection on the first try without rework or repair, relative to the total units produced.

Operational sub-problem of determining how often each transit line is served (e.g., one bus every 6, 10, 20 minutes) per time band, based on demand profile, available fleet and target service quality.

Population-based metaheuristic that mimics natural selection and genetic transmission, evolving a population of candidate solutions through selection, crossover, and mutation operators.

Class of constructive algorithms that builds a solution by making the locally best choice at each step without backtracking; provably optimal on matroid structures and a fast heuristic in general.

Algorithm that produces good (often near-optimal) solutions in reasonable time without optimality guarantees; a foundational tool for solving NP-Hard problems in practice.

Combinatorial algorithm that solves the assignment problem (n×n cost matrix, one-to-one minimum-cost matching) in polynomial time O(n³); Kuhn (1955) and Munkres (1957).

A standard set of three-letter rules published by the International Chamber of Commerce (ICC) defining how cost, risk, and transport responsibility transfer between seller and buyer in international trade.

A linear-optimization problem class in which every decision variable is restricted to integer values; the pure-integer subclass of MILP, NP-hard in general.

The discount rate that sets a project's Net Present Value to zero; it is interpreted as the annual compound return the investment intrinsically earns.

Many distinct jobs flowing through many distinct machines, each job in its own routing.

Operations research problem of coordinating the order frequencies of N SKUs that share a major supplier setup cost (truck haul, customs filing, supplier-order setup), to minimise total long-run cost (setup plus holding).

A production philosophy and operational discipline aimed at flowing production at the pace of customer demand by minimizing work-in-process and raw-material inventory.

A visual-card or electronic-tag system carrying the operational signal of pull production that tells a station when and how much to produce or to withdraw.

The foundational discrete-optimisation problem of selecting a subset from N items, each with a value and a weight, to maximise total value subject to a capacity constraint on total weight.

Decomposition technique that moves complicating constraints into the objective via Lagrange multipliers and reduces the relaxed subproblem to an easy structure; systematized for TSP by Held and Karp (1970).

Elapsed time between placing a replenishment order and the goods becoming usable in stock — the basic input to every inventory policy.

An umbrella production methodology that systematically reduces all activities not creating customer value (muda) and is built on flow, pull production, and continuous improvement.

The mathematical-programming discipline that optimizes a linear objective function subject to linear equality and inequality constraints, foundational to operations research.

Family of improvement heuristics that iteratively refines an existing solution by exploring small changes within a defined neighborhood structure; 2-opt, k-opt, and Lin-Kernighan are canonical examples.

Determining how much to produce each period over a planning horizon, balancing setup and inventory holding costs.

Retail OR practice of setting a typically monotone-decreasing price trajectory over the selling horizon of a seasonal or perishable item to balance margin against end-of-season dead-stock risk.

The time-phased, dependent-demand planning algorithm that computes, from end-item demand backwards via BOM and lead times, when and how much of every raw material and sub-component is needed.

A family of methods (AHP, TOPSIS, WSM, ELECTRE, PROMETHEE) and an underlying theoretical framework for ranking or selecting among finite alternatives under multiple conflicting criteria.

A reliability metric expressing how long a repairable asset runs on average between two consecutive failures; typical units are hours or cycles.

The average time elapsed between the moment an equipment failure is detected and the moment the repair is completed and the equipment is returned to operating condition.

The classical finance framework, due to Markowitz, that analyses investment decisions in the expected-return (mean) vs. risk (variance) plane.

Umbrella term for strategic higher-level frameworks designed to escape local optima — tabu search, simulated annealing, genetic algorithms, VNS, and GRASP all fall under this label; coined by Glover (1986).

OR and control problem of dispatching a small-scale, multi-source energy system over a rolling time horizon under power-balance, storage and generator constraints.

An optimization problem class with a linear objective and linear constraints in which a subset of decision variables is restricted to integer values while the rest remain continuous; NP-hard in general.

An optimization model where some decision variables are forced to be whole numbers (e.g. number of trucks, number of shifts).

Receding-horizon optimisation framework where, at each control instant, a finite-horizon problem is solved with current state and forecasts, the first action is applied, then the horizon rolls forward.

The smallest order quantity — in units or value — that a supplier will accept, imposing a hard lower bound on every replenishment regardless of buyer demand.

A reliability metric showing how long, on average, an asset operates between two consecutive failures.

A branch of mathematical programming that simultaneously optimizes two or more conflicting objective functions, producing a Pareto-efficient solution set rather than a single optimum.

Designing the physical and flow structure of a supply or distribution network at the strategic level — a long-term investment decision.

Classical single-period inventory model that gives the optimal order quantity for perishables, balancing spoilage and lost-sale costs.

The simplest classical heuristic for generating an initial basic feasible solution of the transportation problem: starting at the top-left of the cost matrix, allocate as much as possible to the current cell and shift right or down until supply and demand are exhausted.

Class of decision/optimization problems with no known polynomial-time algorithm and to which every problem in NP can be polynomially reduced; the bulk of practical OR problems sit in this class.

A financial valuation metric that discounts a project's future cash flows to the present and subtracts the initial investment; the rule is to accept the project when the result is positive.

The healthcare-specific OR problem of assigning nurses to shifts over a multi-week planning horizon under coverage, skill, fatigue, contract and preference constraints.

Function relating a lot's true defect rate p to the probability of acceptance Pa(p) under a sampling plan (n, c) — drawn as a curve from p=0 (Pa=1, certain accept) to p=1 (Pa=0, certain reject).

Setting the weekly hospital surgical schedule — which day, room, surgeon, and team for each case.

The relative distance between the best feasible solution found so far (incumbent) and the best dual bound; the standard certificate-of-optimality measure reported by MILP solvers.

Warehouse operation of retrieving SKUs from storage locations to fulfil customer orders, typically performed by walking pickers.

Operations research problem of designing the slot duration, slot loading and intra-day assignment policy of an outpatient clinic — to balance patient wait time, doctor idle time and same-day access.

A composite effectiveness metric summarising a piece of equipment in a single number — the product of Availability, Performance, and Quality — benchmarked against world-class manufacturing.

Practice of systematically booking more patients (or reservations) than capacity in anticipation of no-shows; in OR, the formulation that mathematically balances no-show probability against waiting and idle time.

The operations-research and queueing study of how patients move through hospital units — ER, ward, intensive care, discharge — and the timing decisions that shape throughput and length of stay.

A financial metric measuring the time required for a project's cash flows to recover its initial investment, commonly used in SMBs for quick capital-allocation decisions.

Deliberately reducing the daily or monthly maximum power draw (kW) to lower the connection-power fee.

Allocating capital across multiple investment options under a risk-return trade-off.

In multi-product shared-setup inventory systems, restricting each product's order period to powers of two of a base period T (T, 2T, 4T, ...) yields a solution within 2% of the true optimum and is field-schedulable (Roundy 1985).

Partial-order constraint stating that one task (or activity) must be completed before another can start; foundational constraint family across scheduling and assembly OR problems.

Scheduled maintenance performed before an asset fails — to avoid unplanned downtime.

Manufacturing OR problem of deciding, for a part to be produced, the optimal sequence of machining/forming/assembly operations and the specific machine, tool and fixture for each operation.

A classical linear-programming problem in which a manufacturer producing several products from a shared pool of capacity and raw material decides how much of each product to make over a short horizon, maximizing profit or contribution margin.

Probabilistic extension of CPM developed in 1958 for the US Navy Polaris program: each activity duration is a random variable from optimistic, most-likely and pessimistic estimates, yielding an expected project-completion distribution.

A mathematical-programming class that optimizes a quadratic objective function subject to linear constraints; the direct quadratic generalization of linear programming.

Mathematical discipline analyzing waiting lines where arrivals and service times are random.

Sequencing hundreds of project tasks, sizing durations, and assigning crews under precedence and resource constraints.

Inventory threshold at which a new replenishment order is triggered — the lower-case 's' of an (s,S) policy.

Setting dynamic prices for fixed-capacity, perishable inventory (hotel rooms, airline seats, event tickets) based on demand.

A non-binding, formal information-gathering process used before a procurement decision to learn about potential suppliers' capabilities, capacity and general approach in the market.

A procurement process that asks suppliers for holistic proposals covering methodology, team, timeline and price, used when the buyer's need is defined but the technical solution path is not yet fixed.

A formal procurement process that solicits price-focused binding or non-binding bids from multiple suppliers for a good or service whose specification is already clearly defined.

Mathematical optimization approach that models uncertain parameters with an uncertainty set rather than a probability distribution, and seeks solutions that remain feasible against the worst-case realisation within that set.

A tournament structure where every participant plays every other participant the same number of times.

Extra stock held against demand and lead-time uncertainty — protects against stockouts during unexpected swings.

VRP (Vehicle Routing Problem) variant in which buses pick up and drop off students assigned to stops, subject to bus capacity, maximum ride time, bell-time coordination and walk-distance equity.

The probability that a customer finds what they want when they ask — a numeric target for inventory and ordering decisions.

OR / IE practice of minimising the cumulative setup time (tool change, fixture change, cleaning) across a part's process plan via sequence ordering, multi-operation tools, family setups and SMED internal/external separation.

In a linear-programming problem, the marginal change in the objective value caused by a unit increase in the right-hand side of a binding constraint; equivalently, the optimal value of the corresponding dual variable.

Deciding how much shelf room (how many facings) each listed product gets, balancing demand and margin against space.

The weekly or monthly decision of which employee works which day, in which shift, in which role.

Foundational graph-OR problem of finding the minimum total weighted path between two nodes on a weighted graph (single-source single-destination, single-source all-destinations, or all-pairs); polynomial-time algorithms Dijkstra (1959), Bellman-Ford (1958), Floyd-Warshall (1962).

The classical algorithm for linear programming, which pivots between basic feasible solutions at adjacent vertices of the feasible polytope to improve the objective; due to Dantzig 1947.

Single-solution metaheuristic inspired by physical annealing that probabilistically accepts worsening moves under a controlled temperature parameter, enabling escape from local optima.

Each distinct product variant — by size, color, pack, flavor or supplier — that an inventory system tracks separately under its own unique code.

OR problem of deciding which storage location (shelf, bin, slot) each SKU occupies in a warehouse, optimising expected walking distance, ergonomic load and order-affinity grouping.

Software category that consumes a structured mathematical programming model (LP, MIP, QP, NLP, SOCP) and produces optimal or near-optimal primal and dual information.

Mathematical programming framework that optimizes expected cost or expected utility under known probability distributions of uncertain parameters (demand, price, yield), typically via two-stage recourse or multi-stage scenario-tree formulations.

An event where an SKU has zero on-hand stock at the moment of customer demand — the fundamental failure event and primary KPI of inventory policy.

Sub-problem within the School Bus Routing Problem (SBRP) that assigns each student to a specific bus stop, under capacity, walking distance and route balance constraints.

An operations research problem of structuring pre-qualification and order allocation decisions across competing suppliers for the same input through formal criteria.

Memory-based metaheuristic that records recently visited solutions or moves on a tabu list to prevent cycling, and uses intensification and diversification strategies to traverse the search space.

The maximum time available to produce a single unit while still meeting customer demand — net available working time divided by customer demand quantity.

An evaluation approach that reduces all life-cycle costs of an asset — beyond purchase price, including operation, maintenance, energy, training, parts and disposal — to a single comparable figure.

A management philosophy asserting that a system's output is determined by its weakest link (the constraint), and that continuous improvement must follow an identify-exploit-subordinate-elevate cycle focused on that bottleneck.

The number of units a production system completes and ships out per unit time — the system's actual production rate.

Statistical modelling field for predicting future values from observations ordered in time; covers ARIMA, ETS and state-space models.

The hours in which a delivery or service can be performed — outside this window the visit is either refused or penalized.

A distance-based MCDM technique that ranks alternatives by simultaneous closeness to a positive-ideal solution and remoteness from a negative-ideal solution.

Workforce-planning OR problem of assigning weekly tour patterns (shift sequences plus days off) to employees so hourly demand is met and rest, hours and fairness rules hold.

The problem of producing a sports league or tournament fixture — which team plays which team in which week, at which venue.

OR problem of choosing which bus (or tram, metro) lines to operate in an urban network, which stops each line serves and what route each line follows, subject to total operating budget, demand-coverage and transfer-quality constraints.

Shipment allocation from m fixed-capacity sources to n fixed-demand destinations, minimising total per-unit transport cost — the founding linear programming problem.

The foundational combinatorial-optimisation problem of finding the minimum-cost Hamiltonian tour that visits every node in a graph exactly once and returns to the start.

The decision of which vehicles, leaving from one or more depots, visit which customers in which order.

The blended cost of a firm's capital obtained by weighting equity and debt financing at market values; used as the discount rate or hurdle rate in investment decisions.

The classical dynamic-programming algorithm that solves the single-product, uncapacitated, deterministic lot-sizing problem to optimality.

The OR problem of finding a maximum- (or minimum-) total-weight matching between two disjoint vertex sets in a bipartite graph whose edges carry weights.

The closed-form solution Q* = sqrt(2DS/H) derived by Wilson (1934) for the EOQ problem, giving the cost-minimising order quantity under deterministic constant demand D, fixed setup cost S, and per-unit-year holding cost H.

The total stock of all semi-finished items that have begun but not yet completed production, waiting between or being processed at stations.

Trade-off between regular workforce (smooth but expensive in idle months), hiring/firing (cheap month-to-month but high churn cost), overtime (capacity flex but premium pay plus fatigue) and subcontracting (flex but quality and lead-time risk). Captured as decision variables in APP.