Operations Management: Strategies, Processes, and Sustainability

Operations Management (OM) Overview Definition: OM involves planning, designing, coordinating, and executing processes to produce goods or services.Core Activities: Managing inputs (materials, equipment, etc.), transformations (physical, informational, etc.), and outputs (finished products/services).Why Study OM? Backbone of organizations, affecting all functions.Interrelated with areas like finance, HR, and marketing. Vital for corporate strategy; 20% of Canadian jobs in goods-producing sectors.Key Components of OM 6Ps of Operational Systems: Plant: Facilities.Parts: Raw materials/components.

People

Workforce.

Partners

Suppliers/collaborators.

Protocols

Standards/rules.

Processes

Workflows.

Competitive Priorities (CoPs)Cost

Minimizing expenses while supporting strategy.

Quality

Ensuring high performance and consistency.

Time

Meeting demands quickly and on schedule.

Flexibility

Offering variety and adjusting volumes.

Corporate Strategy and OM AlignmentOrder Qualifiers vs. Winners

Order Qualifiers:
Minimum requirements to enter the market.

Order Winners

Features that differentiate and give a competitive edge.

Strategic Priorities in OM

Aligning the 6Ps with competitive priorities to meet corporate goals.

Sustainability in OM Definition

Managing resources to meet current needs without hindering future generations.

Triple Bottom Line

Balancing social, environmental, and economic goals.

Sustainability Perspectives

Efficiency

Reduce waste and improve resource use.

Differentiator

Eco-labeling and green inputs.

Driver

Innovating for societal benefits and responding to crises.

Sustainability PracticesPollution Management

Prevention

Eliminate waste at the source.

Control

Add systems to treat and reduce pollution.

Transparency

Disclosing environmental and social practices.Using IoT, audits, and certifications for supply chain visibility.

Goods vs. Services Services

Intangible, high customer interaction, labor-intensive.

Goods

Tangible, standardized, often automated. 

Process Management

Four Major Process Decisions

Process Structure

: Determines how activities are organized and executed.

Customer Involvement

: Degree of customer interaction during the process.

Resource Flexibility

: Ability of resources to adapt to various tasks.

Capital Intensity

: Investment in equipment vs. Labor.

Process Types

Based on Product Flow

:

Project

: Unique, custom specifications.

Job Shop

: Small orders; flexible to customer needs.

Batch

: Small/medium production in batches.

Assembly Line

: High volume, standardized products.

Continuous

: Very high volume, fully standardized.

Intermittent Operations

: High product variety, flexible equipment, labor-intensive.

Repetitive Operations

: Low product variety, specialized equipment, capital-intensive.

Facility Layouts

Process Layout

: Grouping similar tasks (e.G., hospital).

Product Layout

: Sequential tasks (e.G., assembly lines).

Cell Layout

: Hybrid; groups similar processes.

Fixed-Position Layout

: Product remains stationary (e.G., construction).

Retail Layout

: Space allocation based on customer behavior.

Manufacturing Technologies

Group Technology

: Machines grouped for similar parts.

Flexible Manufacturing Systems (FMS)

: Automated, adaptable systems.

Robotics

: Automated machines for complex tasks.

Computer-Aided Manufacturing (CAM)

: Computers control production.

Computer-Integrated Manufacturing (CIM)

: Integration of design, planning, and production.

Key Metrics

Inventory (I)

: Total units in the system.

Flow Time (T)

: Total time a unit spends in the system.

Flow Rate (R)

: Units processed per time period.

Little’s Law

: I=R×TI = R \times TI=R×T(Average Inventory = Flow Rate × Flow Time)

Inventory Turnover (IT)

: IT=ThroughputAverageInventoryIT = \frac{Throughput}{Average Inventory}IT=AverageInventoryThroughput​ Processes Matching Corporate Strategy

Intermittent

: Customized products. Delivery, flexibility, and innovation. Make-to-order strategy.

Repetitive

:Mass-market, standardized products.Cost efficiency, speed, and consistency. Make-to-stock strategy.  Key Capacity Management
ConceptsCapacity: Maximum output rate for a process. Effective Capacity: Maximum sustainable output under normal conditions.Peak Capacity: Maximum output under ideal conditions.Capacity Cushion: Extra capacity to manage variability.Effective Capacity Unit Load: Ti = Average time required to process one unit Effective Capacity of a Resource Unit: EC_unit = 1 / Ti :Effective Capacity of a Resource Pool: EC_pool = ci / Ti :  ci = Number of resource units in the pool. Ti = Unit load. Bottleneck: Bottleneck = Resource pool with the lowest EC_pool  Capacity Utilization Utilization of a Resource Pool: ui = R / EC_pool : ui = R / (ci * Ti).  R = Throughput (output rate). EC_pool = Effective capacity of the resource pool. Utilization of the Process: u_process = u_bottleneck. Setup Times and Total Unit Load. Total Unit Load: T_total = Ti + (Si / Qi). Ti = Unit load. Si = Setup time. Qi = Batch size. Effective Capacity with Setup Time: EC_pool = ci / T_total. Little’s Law I = R * T. I = Inventory. R = Flow rate (throughput). T = Flow time. Theory of Constraints. Identify the bottleneck.  Exploit the bottleneck.  Support the bottleneck.  Elevate the bottleneck.  Maintain the process flow.  Capacity Expansion Strategies. Capacity Lead: Expand before demand increase.  Capacity Lag: Expand after demand increase.  Incremental (Step-Wise): Gradual expansion.  Big Bang: One-time significant expansion. Pros and Cons  Capacity Expansion Strategies. Big Bang Strategy:
Pros:
Achieves economies of scale, may increase market share.

Cons

Requires significant resources upfront, risk of overexpansion. 

Step-Wise Strategy

Pros

Less costly upfront, reduced risk of overexpansion, allows learning from mistakes.

Cons

Slower response to market demand, potential loss of customers and sales.

Examples Hospital Bottleneck

Bottleneck = Resource pool with the lowest EC_pool Example: Receptionist EC_pool = 12 patients/hour. Nurse EC_pool = 15 patients/hour. Doctor EC_pool = 10 patients/hour. Bottleneck = Doctor.

Setup Time Example

T_total = Ti + (Si / Qi). For Si = 5 min, Qi = 10, and Ti = 1 min/unit:  T_total = 1 + (5 / 10) = 1.5 min/unit. 

Supply Chain

Basics. Supply Chain: Network to produce and deliver products/services from suppliers to customers.  Supply Chain Management (SCM): Coordinates material, service, and information flows to meet demand. Supply Chain Designs Efficient: Focus: Low cost, inventory minimization. Use: Predictable demand, limited variety. Responsive: Focus: Fast response, flexibility. Use: Unpredictable demand, high variety. Make-or-Buy Decision Break-even formula:Q = (Fm – Fb) / (cb – cm) Where: Fm = Fixed cost for making. Fb = Fixed cost for buying. Cm = Variable cost per unit for making. Cb = Variable cost per unit for buying.Q = Break-even quantity. Inventory Strategies Inventory Pooling: Centralized storage, lower safety stock, slower delivery. Forward Placement: Inventory near customers, faster delivery, higher safety stock. Supplier Selection. Overall score formula: Overall Score = (w1 * s1) + (w2 * s2) + … + (wk * sk) Where: w1, w2, … Wk = Weights for each criterion (sum = 1). S1, s2, … Sk = Supplier scores for each criterion. Bullwhip Effect Definition: Variability in demand increases as you move upstream in the supply chain. Causes: Inaccurate demand forecasts. Order batching. Price fluctuations. Long lead times. 
Forecasting is the method used to predict future events using past and present data. In operations management, forecasting can be strategic for future products and markets or for planning the demand of products and services. Forecasting can use mathematical models, historical data, simulations, or expert opinions.Forecasting horizons are categorized as long-range (more than two years, used for strategy), mid-range (weekly or monthly up to two years, used for planning), and short-range (hourly or daily up to several months, used for scheduling). Time series forecasting involves repeated observations of demand over time and assumes past demand is a predictor of future demand and that records of past demand are available. There are five basic demand patterns in time series data. Stable demand shows consistent averages over time. Trend demand demonstrates systematic increases or decreases. Seasonal demand shows repeatable patterns based on periods like months or seasons. Cyclical demand involves less predictable, longer-term periodic behavior. Random variation represents unexplained and unforecastable variability. Managing demand can involve complementary services to smooth demand, promotional pricing to shift demand, prescheduled appointments to level demand, or revenue management to adjust prices in real time.The forecasting process includes identifying the purpose of the forecast, collecting required inputs, selecting appropriate techniques, checking model accuracy, and planning over the forecasting horizon. Collaborative Planning, Forecasting, and Replenishment (CPFR) involves collaboration with suppliers and customers to align forecasts. Qualitative forecasting is subjective and incorporates diverse information but can be biased. Quantitative forecasting is objective, handles large datasets, and relies on mathematical models but requires numerical data. Time-series methods predict future demand using past data. The naïve method uses the demand from the most recent period as the forecast for the next period. The simple moving average calculates the forecast by averaging demand over the most recent n periods. The weighted moving average gives different weights to recent periods, with weights summing to one. Exponential smoothing applies a smoothing parameter (alpha) to give more weight to recent observations. The formula for the naïve method is Ft+1 = Dt, where Ft+1 is the forecast for the next period and Dt is the actual demand for the most recent period. For the simple moving average, the formula is Ft+1 = (Dt + Dt-1 + … + Dt-N+1) / N, where N is the number of periods. The weighted moving average formula is Ft+1 = (Wt * Dt) + (Wt-1 * Dt-1) + … + (Wt-N+1 * Dt-N+1), where Wt are weights assigned to each period’s demand. The exponential smoothing formula is Ft+1 = αDt + (1 – α)Ft, where α is the smoothing parameter. Forecast error is the difference between actual demand and forecasted demand, calculated as Et = Dt – Ft. Measures of forecast error include cumulative sum of forecast errors (CFE), mean squared error (MSE), mean absolute deviation (MAD), and mean absolute percentage error (MAPE). Seasonality adjustment uses the multiplicative seasonal method. Seasonal factors are calculated by dividing demand by average demand per season, then multiplying the forecast by the seasonal index. Inventory refers to the stock of items, including materials, orders, information, and people, used to satisfy demand. Inventory management aims to balance inventory costs while aligning policies with competitive priorities.Inventory costs include holding costs (e.G., storage, taxes, insurance), ordering costs (fixed costs per order), and set-up costs (for production batches). Little’s Law explains that flow time increases with work-in-progress (WIP). Inventory pressures arise from the need to ensure quick delivery, avoid stockouts, and improve productivity. Larger batch sizes can reduce set-up costs, and higher inventory levels can optimize transportation efficiency.Functions of inventory include safety stock (buffer against uncertainties), cycle inventory (varies with order size), pipeline inventory (in transit), and anticipation inventory (for predictable demand). The reorder point formula is R = dL, where d is daily demand and L is lead time.The Economic Order Quantity (EOQ) minimizes total inventory costs. The formula is: EOQ = sqrt((2DS) / H), where D is annual demand, S is order cost, and H is annual holding cost per unit. Total annual inventory cost is calculated as: TC = (Q/2)H + (D/Q)S, where Q is the order quantity.Inventory management systems include the Q system (continuous review) and the P system (periodic review). In the Q system, replenishment occurs when inventory hits the reorder point (R = dL + safety stock). In the P system, orders are placed at fixed intervals, with a target inventory level T = d(P + L) + safety stock.The ABC system categorizes inventory into A-items (high priority, frequent reviews), B-items (moderate priority), and C-items (low priority, simple control). A-items account for the highest value but the smallest percentage of units, while C-items are the opposite.Safety stock is used in both systems to prevent stockouts. For the Q system, the reorder point formula with safety stock is R = dL + safety stock. For the P system, the target inventory formula is T = d(P + L) + safety stock.  Scheduling and Planning Cheat Sheet. Planning is the process of organizing resources to meet production and workforce demands across various time horizons. Long-term plans span 2-10 years and focus on strategic goals like new products or facility locations. Medium-term plans cover 6-18 months, focusing on aggregate demand and workforce capacity. Short-term plans address weekly or daily adjustments to schedules and operations.Aggregate Planning (S&OP) is a medium-term production plan designed to meet aggregate demand by grouping similar products (product families) or workforce needs. It involves inputs from operations (capacity and workforce planning), marketing (customer needs and forecasts), accounting (costs and financial data), human resources (training and availability), and materials (inventory and storage capacities). Demand management adjusts operational variables to meet demand.Inventory can be built as anticipation inventory during slow periods. Workforce levels are adjusted through hiring, firing, overtime, or undertime. Capacity utilization is modified by shutting down plants during slow periods or scheduling vacations.Subcontracting handles short-term capacity shortages. Level strategy maintains a constant production rate regardless of demand fluctuations. It provides workforce stability and predictable schedules but risks inventory buildup, stockouts, and higher holding costs. Demand variability can be handled using inventory, backorders, or overtime. Chase strategy matches production rates to demand by adjusting workforce levels. It minimizes inventory costs but involves high hiring and firing costs and can impact employee morale.Workforce size is increased or decreased to match demand.Mixed strategy combines Level and Chase approaches for flexibility. A base workforce level is maintained, with overtime or subcontracting used to manage demand peaks. Regular capacity is the standard production capacity within normal working hours.Overtime capacity is additional capacity achieved by extending working hours, typically capped at a percentage like 20 percent.Workforce level refers to the number of workers needed to meet production requirements.Overtime capacity is calculated as regular capacity multiplied by 1.2.Regular capacity is calculated as overtime capacity divided by 1.2.Cost elements in planning include production costs such as regular time, overtime, and subcontracting; inventory costs such as holding and backorder costs; and labour costs like hiring and termination costs. A practical example of cost comparison shows the Level Strategy with a total cost of $164,000. The Chase Strategy cost is $173,500. Other considerations when choosing a strategy include employee morale, operational flexibility, and long-term efficiency. 

Resource Planning

Cheat SheetResource planning combines aggregate planning (S&OP) with detailed information like processing time, routing, and production requirements to determine input needs for a given period.Enterprise Resource Planning (ERP) systems integrate business processes across the entire organization using a shared database. ERP modules include accounting, marketing, supply chain management, and manufacturing. ERP systems provide access to real-time data, process transactions, and generate reports to support decision-making across departments.Material Requirements Planning (MRP) ensures the availability of materials required for production. It is used for managing dependent demand inventory, where the required quantity depends on the demand for other items. Capacity Requirements Planning (CRP) ensures that labor and machine hours are sufficient to meet production needs. MRP and CRP must align to ensure both materials and capacity are available.The Bill of Materials (BOM) specifies parent-component relationships, including quantities needed for each component. Examples include end items (final products), intermediate items (items with both parents and components), subassemblies (assembled intermediate items), and purchased items (items with no components, sourced externally). Part commonality refers to components shared by multiple parents, increasing production efficiency.Master Production Schedule (MPS) specifies the requirements for individual end items by date and quantity, based on the aggregate production plan. Inventory records include details like lot-size policies, lead times, gross requirements, scheduled receipts, projected on-hand inventory, planned receipts, and planned order releases.Lot-sizing rules determine the timing and quantity of orders. Fixed Order Quantity (FOQ) uses a consistent order size, Periodic Order Quantity (POQ) varies order sizes based on predetermined intervals, and Lot-for-Lot (L4L) matches order size to gross requirements for each period. FOQ creates higher average inventory but provides a buffer, while POQ and L4L minimize inventory costs but are less adaptable to sudden demand changes.MRP Explosion disassembles end products into their components to calculate material needs. For example, calculating spring steel for 500 clipboards would consider the component hierarchy and usage quantities, identifying the total required. Quality Cheat SheetTotal Quality Management (TQM) is a philosophy focusing on customer satisfaction, employee involvement, and continuous improvement. Quality is defined as the degree of excellence in meeting or exceeding customer expectations. It can be viewed from three perspectives: the product perspective, which evaluates the design; the producer perspective, which assesses conformance to specifications; and the consumer perspective, which considers customer satisfaction and value.Quality is achieved by aligning customer expectations with organizational capabilities. High-performance design focuses on delivering reliability, durability, and features that differentiate products. Conformance ensures consistency by meeting specifications with minimal variability.The costs of quality are divided into control costs and failure costs. Control costs include prevention costs (e.G., training and quality planning) and appraisal costs (e.G., inspection and testing). Failure costs include internal failures (e.G., rework, scrap) and external failures (e.G., warranty claims, reputational damage).Employee involvement is essential for quality. Employees should be empowered through organizational culture, quality circles, special-purpose teams, and self-managing teams. Quality at the source encourages correcting defects where they occur.Continuous improvement tools include the Deming Wheel (plan, do, check, act cycle), which removes non-value-adding activities. Six Sigma focuses on minimizing defects and variability using the DMAIC process (define, measure, analyze, improve, control).Quality evaluation tools include check sheets, histograms, Pareto charts, cause-and-effect diagrams, scatter diagrams, flowcharts, and statistical process control (SPC) charts. SPC distinguishes between common cause variation (random, unavoidable) and assignable cause variation (identifiable, eliminable). Sampling plans determine when and how to inspect processes.SPC charts include p-charts for proportions, c-charts for defect counts, R-charts for variability, and x̄-charts for monitoring averages. Control limits are calculated to identify variations exceeding normal expectations. 

Lean Operations

Cheat Sheet. Lean systems aim to maximize value by removing unnecessary activities and delays, improving processes by eliminating waste. Waste, referred to as “muda,” includes overproduction, extra inventory, inappropriate use of resources, waiting time, unnecessary transportation, defects, and inefficient methods. Just-in-Time (JIT) is a philosophy from the Toyota Production System that meets demand while eliminating waste. The objective is to produce only what is needed when it is needed. JIT benefits include shorter customer wait times, higher productivity, lower inventory costs, and improved process efficiency. However, poor quality, long setup times, or unreliable suppliers can disrupt JIT systems.Lean supply chains focus on close supplier ties and small batch sizes. Close supplier ties require frequent, smaller deliveries with minimal safety stock. Small batch sizes reduce cycle inventory and holding costs, though they may increase setup costs. The pull method activates production based on actual demand, unlike the push method, which relies on forecasts and builds inventory.Workforce flexibility supports lean systems by allowing workers to shift between tasks, reducing bottlenecks and improving customization. Job rotation increases process understanding and reduces boredom. Ensuring quality at the source involves employees acting as quality inspectors using techniques like poka-yoke (mistake-proofing), jidoka (automation to prevent defects), and andon (visual signals for assistance).Uniform loading aligns production schedules with daily demand, reducing variability. Takt time defines the maximum time per unit to meet demand, while heijunka levels production by volume and product mix. Mixed-model assembly produces various models in small batches to enhance flexibility. Standardization supports lean efficiency by optimizing repetitive operations and increasing employee learning. Improvements come from employees rather than management. The Five S’s of JIT—sort, set in order, shine, standardize, and sustain—maintain organized and productive workstations.Total preventative maintenance minimizes downtime by scheduling regular maintenance tasks. Employees may handle minor maintenance to reduce disruptions.Lean work cells use cellular layouts, often U-shaped, to eliminate inefficiencies and improve productivity. Workers operate multiple machines, enhancing utilization and flexibility.The transition from traditional to lean systems includes reducing inventory, shifting to pull manufacturing, achieving zero defects, minimizing setup times, and fostering team-oriented employee involvement. Suppliers are treated as partners rather than independent entities.Challenges with lean systems include the need for a disciplined workforce, stable production schedules, and reliable suppliers. Small batches require frequent setups, and organizations must balance employee engagement with continuous improvement.

Project Management

Cheat Sheet  A project is an interrelated set of activities with a definite start and end point, resulting in a unique outcome with specific resources. The scope defines the boundaries of the project. Clear scope planning and concrete deliverables are essential. All decisions should be assessed against the project’s scope to prevent scope creep.Project Human Resource Management involves creating a project team, defining roles and responsibilities, and establishing communication and reporting tools. Staff can be sourced internally or externally, with skills and timelines aligned to project needs. Team development includes training, meetings, and team-building activities. A Work Breakdown Structure (WBS) outlines all work to be completed by breaking the project into specific activities. Each activity has a clearly designated responsibility. Network diagrams visually represent relationships between project activities using nodes (activities) and arcs (dependencies). Techniques like PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) allow managers to plan, estimate completion times, identify critical activities, and analyze resource trade-offs. The critical path is the sequence of activities that takes the longest time to complete. Any delay in critical path activities delays the entire project. Slack measures the maximum time an activity can be delayed without delaying the project and is calculated as Slack = Latest Start – Earliest Start or Latest Finish – Earliest Finish. Activities on the critical path have zero slack.Scheduling involves estimating activity times and determining start and finish times. Earliest Start (ES) is the latest Earliest Finish (EF) of preceding activities. Earliest Finish (EF) is calculated as ES + duration. Latest Finish (LF) is the earliest Latest Start (LS) of succeeding activities. Latest Start (LS) is calculated as LF – duration. Trade-offs in project management include balancing quality, cost, time, and scope. Improving quality often increases cost or time. Reducing cost may require reducing scope or extending time. Expanding scope typically requires more time or higher costs. Project managers track progress by addressing open issues and risks, monitoring schedule status, and ensuring critical activities remain on schedule. Resources should be reallocated to manage timing, focusing on activities with the earliest start. Deviation from the project budget and plan must be reported and analyzed. Projects often serve as opportunities for human resource development. Monitoring and control ensure efficient use of financial, physical, and human resources. Project managers address scheduling crunches and allocate resources effectively. The project closeout phase provides opportunities to learn from execution and improve future projects. Formulas and how to solve Process Management Little’s Law (I = RT)
Identify inventory (I), throughput rate (R), or flow time (T). Rearrange the formula as needed to find the unknown variable.

Takt Time = 1 / R

Calculate the maximum time per unit using the production rate (R).

Inventory Turnover = R / I

Find how often inventory is replenished by dividing throughput (R) by inventory (I).

Capacity Management Effective Capacity = c / T

Calculate capacity per resource unit by dividing resources (c) by time per unit (T).

Utilization = R / EC

Determine how much capacity is used by dividing throughput (R) by effective capacity (EC).

Effective Capacity (with setup) = c / [T + (S / Q)]

Add setup time (S) divided by batch size (Q) to the time per unit (T) to adjust capacity.

Supply Chain Management Make-or-Buy Decision (Q = (Fm – Fb) / (cb – cm))

Subtract fixed costs (Fb and Fm) and divide by the difference in variable costs (cb and cm) to find the break-even quantity.

Sourcing Score = w1s1 + w2s2 + … + wksk

Multiply weights (wi) by scores (si) for each criterion and sum the results.

Forecasting. Naive Forecast (Ft+1 = Dt)

Use the most recent demand (Dt) as the next period’s forecast.

Simple Moving Average (Ft+1 = (Dt + Dt-1 + … + Dt-N+1) / N)

Average demand from the past N periods.

Weighted Moving Average (Ft+1 = W1D1 + W2D2 + … + WnDn)

Multiply weights (Wi) by demands (Di) and sum the results. Ensure weights sum to 1.

Exponential Smoothing (Ft+1 = αDt + (1 – α)Ft)

Multiply recent demand (Dt) by α and previous forecast (Ft) by (1 – α), then sum.

Error Measures

Forecast Error: E = Dt – Ft. Mean Absolute Deviation: MAD = ∑|E| / n. Mean Squared Error: MSE = ∑E² / n. Mean Absolute Percentage Error: MAPE = ∑(|E| / Dt) / n × 100.

Inventory Management. EOQ = √(2DS / H)

Calculate the optimal order quantity using demand (D), order cost (S), and holding cost (H). 

Reorder Point (R = dL)

Multiply daily demand (d) by lead time (L). Add safety stock for Q systems (R = dL + safety stock). 

P System Target Inventory = d(P + L) + safety stock

Multiply daily demand (d) by the review period plus lead time (P + L), then add safety stock. 

Resource Planning. Lot-for-Lot (L4L) = gross requirements – on-hand inventory

Calculate production size to exactly meet demand.

Periodic Order Quantity (POQ) = total gross requirements over P weeks – projected inventory

Use gross requirements over a fixed period (P weeks).

Quality & SPC p-Chart

Center Line: p̅ (average proportion defective) UCL = p̅ + z√[p̅(1 – p̅) / n]. LCL = p̅ – z√[p̅(1 – p̅) / n].

C-Chart

Center Line: c̅ (average defect count). UCL = c̅ + z√c̅. LCL = c̅ – z√c̅.

R-Chart

Center Line: R̄ (average range). UCL = D4R̄, LCL = D3R̄.

X̄-Chart

Center Line: x̄ (average value). UCL = x̄ + A2R̄, LCL = x̄ – A2R̄.

Project Management. Slack

Slack = LS – ES or LF – EF. Use the latest and earliest start/finish times to find slack. 

Critical Path

Sequence activities with the longest duration. Activities on the critical path have zero slack.