5.1Project Management

Project management is the discipline of quantitatively managing a project so it finishes as planned. In the AP morning exam, date arithmetic on arrow diagrams (the critical path, earliest/latest start dates) and EVM cost and progress metric calculations are recurring calculation domains. Applying the formulas mechanically is not enough--understanding why each formula holds is what lets you handle exam variants that simply change the numbers.

5.1.1PMBOK and WBS

• PMBOK (Project Management Body of Knowledge) is an internationally recognized standard guide that systematizes project management knowledge, organized into knowledge areas such as scope, schedule, cost, quality, risk, procurement, and stakeholders.
• WBS (Work Breakdown Structure) hierarchically decomposes a project's deliverables and work down to manageable units (work packages). It is used to exhaustively surface scope and forms the basis for estimation, progress tracking, and staff assignment. Decomposing too coarsely produces large estimation error, while decomposing too finely raises management overhead, so stopping at an appropriate level is a practical judgment call.

5.1.2Date arithmetic on arrow diagrams, PERT, and the critical path

• Arrow diagrams represent activities as arrows and junctions (events/nodes) as circles, visualizing the sequencing of work and its duration as a network diagram. PERT is the umbrella term for the technique of analyzing and managing the overall project schedule using this diagram.
• Earliest start (ES) is the earliest possible point at which an activity can begin. It is computed with a forward pass from the start node, and at a node where multiple paths converge, the maximum among the converging paths is taken (because a successor cannot begin until every predecessor activity is done). Latest start (LS) is the latest point at which an activity can begin without delaying the project's overall completion. It is computed with a backward pass from the end node, and at a node where paths diverge, the minimum among the diverging paths is taken.
• The critical path is the path with the longest total duration among all paths from start to finish (equivalently, the path where ES equals LS everywhere--zero slack). If work on this path slips by one day, the project's overall completion also slips by the same number of days. Work not on the critical path has float (slack), and a delay within that float does not affect the overall schedule. Float = the longest duration among all paths (the critical path's duration) minus that path's own total duration.

5.1.3Cost and progress management with EVM

• EVM (Earned Value Management) manages progress and cost together using a common metric expressed in money. PV (Planned Value) is the budgeted amount of work that should have been completed by now per the plan. EV (Earned Value) is the budgeted amount of work actually completed (progress expressed in money). AC (Actual Cost) is the actual cost incurred so far. BAC (Budget At Completion) is the project's total original budget.
• Variance metrics: SV (Schedule Variance) = EV − PV (negative means behind schedule). CV (Cost Variance) = EV − AC (negative means over budget). Index (ratio) metrics: SPI (Schedule Performance Index) = EV ÷ PV (below 1 means behind schedule). CPI (Cost Performance Index) = EV ÷ AC (below 1 means over budget). Distinguish that variances express performance in money, while indexes express it as a ratio.
• EAC (Estimate At Completion) is the estimated total cost to complete the project, assuming the current cost efficiency (CPI) continues going forward. The most basic formula is EAC = BAC ÷ CPI (if CPI is below 1--a cost-overrun trend--EAC exceeds BAC). The worse CPI gets, the further EAC diverges from the original budget, giving grounds for judging whether additional budget is needed.

Take a core-system rebuild project as an example of working through schedule and cost calculations concretely. Suppose the arrow diagram has three paths from start to finish. Path A, "requirements (4 days) -> development (12 days) -> testing (6 days)," totals 22 days; path B, "environment setup (5 days) -> data migration prep (9 days)," totals 14 days; and path C, "procurement (3 days) -> equipment delivery (8 days) -> acceptance inspection (2 days)," totals 13 days. After computing all three paths, the longest, 22-day path A is determined to be the critical path. Path B's float is 22 − 14 = 8 days, and path C's float is 22 − 13 = 9 days--a modest delay on either does not affect overall completion. On the cost side, suppose at some point after the project starts, the plan called for 5,000,000 yen of work to be complete by now (PV = 5,000,000 yen). In practice only 4,000,000 yen of work has actually been completed (EV = 4,000,000 yen), and 5,000,000 yen of cost has been incurred so far (AC = 5,000,000 yen). From these: SV = EV − PV = 4,000,000 − 5,000,000 = -1,000,000 yen (behind schedule), CV = EV − AC = 4,000,000 − 5,000,000 = -1,000,000 yen (over budget), SPI = EV ÷ PV = 4,000,000 ÷ 5,000,000 = 0.8 (only 80% of planned progress achieved), and CPI = EV ÷ AC = 4,000,000 ÷ 5,000,000 = 0.8 (only 80% of earned value obtained per unit of cost spent). Assuming the project's original total budget (BAC = 10,000,000 yen) is unchanged and this cost efficiency (CPI = 0.8) continues, EAC = BAC ÷ CPI = 10,000,000 ÷ 0.8 = 12,500,000 yen--indicating the project is on track to cost 2,500,000 yen more than originally budgeted. Building on these numbers, risk management identifies early the risk that "the budget overrun will keep widening at this rate," and a response--adding staff, adjusting scope--is coordinated with stakeholders, completing the management cycle.

5.1.4Quality, risk, procurement, and stakeholder management

• Quality management plans, assures, and controls whether deliverables meet the required standard. Risk management identifies possible problems in advance and prepares responses--avoidance, mitigation, transfer, or acceptance--according to their probability and impact. Procurement management decides what scope is purchased or outsourced externally and manages contracting, ordering, and acceptance. Stakeholder management identifies parties with a stake in the project and manages their expectations and involvement.

5.1.5Section summary

• The critical path is the longest-duration path among all paths (zero float). Earliest start takes the maximum at a converging node; latest start takes the minimum at a diverging node. Float = the critical path's duration minus that path's own total.
• EVM: SV = EV − PV / CV = EV − AC (negative = behind/over budget); SPI = EV ÷ PV / CPI = EV ÷ AC (below 1 = behind/over budget); EAC = BAC ÷ CPI (a worse CPI pushes EAC above BAC)
• WBS hierarchically and exhaustively surfaces scope. Quality, risk, procurement, and stakeholders are also major PMBOK knowledge areas (risk responses = avoidance, mitigation, transfer, acceptance)