Project Management and Supply Chain Management
Projects and networks
A project is a temporary, unique endeavour with defined scope, time and cost. The work breakdown structure (WBS) decomposes scope; CPM/PERT networks show dependencies. For each activity: ES = max EF of predecessors; EF = ES + duration; LF = min LS of successors; LS = LF - duration; float = LS - ES. The critical path has zero float and determines duration. Crashing shortens duration by adding resources, choosing the cheapest critical activity per day saved. PERT uses three time estimates: te = (o + 4m + p)/6.
Supply chains integrate suppliers, operations, distribution and customers. The bullwhip effect is demand amplification upstream, caused by forecast updating, order batching, price promotions and rationing; remedies include information sharing, everyday low pricing and shorter lead times.
Worked example
A (3 days) and B (4 days) start together. C (2 days) follows A; D (5 days) follows B and C. Paths: A-C-D = 3+2+5 = 10; B-D = 4+5 = 9. Critical path A-C-D, duration 10. B has ES 0, EF 4, LS = LF 5 - 4 = 1, so float 1 day. Delaying B by one day is safe; delaying A by one day delays the project.
Traps
Float belongs to non-critical activities; the critical path can change after crashing. PERT is probabilistic, CPM deterministic. Do not crash the cheapest activity overall, only a critical one. Earned value: CPI = EV/AC and SPI = EV/PV; CPI below 1 means over budget.