(a) (i) List the strategic objectives of aggregate planning. 5 (ii) Describe the chase and level strategies for aggregate…

(a) (i) Strategic objectives of aggregate planning:

• Match aggregate demand with available capacity at minimum total cost.
• Decide output rate, workforce size, inventory and backlog levels.
• Stabilise employment and production, avoiding frequent hiring, firing and idle time.
• Meet customer service and delivery targets.
• Use overtime, subcontracting and inventory efficiently.
• Maximise profit and give a basis for master production scheduling.

(a) (ii) Chase strategy varies output/capacity each period to match demand. It uses hiring, lay-off, overtime, idle time and subcontracting. It gives low inventory and close demand matching, but causes unstable workforce, morale and quality problems, and high hiring/firing costs. Level strategy keeps workforce/output constant and absorbs demand changes through inventory, backorders, queues or stockouts. It gives stable workforce and consistent quality, but creates inventory carrying, storage, obsolescence and backlog costs. Between the two, level strategy is generally preferred when demand fluctuations are moderate and inventory carrying cost is low, because it stabilises employment and quality. Chase is preferred when demand is highly seasonal and labour is flexible. In practice, a mixed/hybrid strategy based on least total cost that satisfies service policy is often best.

(a) (iii) Manufacturing aggregate planning can store output, so it uses finished-goods inventory, backorders, overtime, subcontracting and workforce changes. Service output is intangible and perishable; it cannot be inventoried except through customer waiting or appointments. Service capacity is usually labour/equipment at the point of contact, so planning uses scheduling, reservations, pricing, promotion, part-time staff, cross-training, queueing and yield management. Manufacturing can smooth production by inventory; services must manage demand and capacity at the same time. Service capacity units are rooms, seats or billable hours, not stored units.

(b) (i) Time and motion study is a systematic work-measurement and method-improvement technique. Time study determines the standard time for a qualified worker to perform a task at a defined performance level, including allowances. Motion study analyses movements to eliminate unnecessary motion and design the best method. Together they improve productivity and set time standards.

(b) (ii) Work study is the systematic examination of work methods and time to improve productivity and establish standards; it comprises method study and work measurement. Method study is the systematic recording and critical examination of existing or proposed methods of doing work, to develop easier, safer, cheaper and more effective methods and reduce waste.

(b) (iii) Steps in work study: select the job/process; record facts; examine critically; develop improved method; measure work to set standard time; install the method; maintain through audit and revision. Steps in method study: select; record using charts/diagrams; examine by questioning purpose, place, sequence, person and means; develop the best method; define and install it; maintain it. Thus method study supplies the improved method, while work measurement supplies the standard time within overall work study.

(c) (i) Control charts have a central line showing process average and upper/lower control limits, usually at ±3σ. They separate common-cause and special-cause variation. Control limits are based on process variation, not specification limits. Points are plotted over time; an in-control process shows random variation within limits. Out-of-control signals include points outside limits, runs, trends, cycles or unusual patterns near limits.

(c) (ii) A P-chart is an attributes control chart for the proportion defective, i.e. nonconforming. Centre line p̄ = total defectives/total inspected. For constant sample size n, limits are p̄ ± 3√(p̄(1−p̄)/n). For variable n, limits are computed for each nᵢ. If LCL is below zero, it is taken as zero. It assumes independent binomial samples.

(c) (iii) Total defectives = 25 + 30 + 35 + 40 + 45 + 35 + 40 + 30 + 20 + 50 = 350 defective pieces. Number of lots = 10; sample size n = 300 pieces per lot. Total inspected = 10 × 300 = 3000 pieces. Average fraction defective: p̄ = 350/3000 = 7/60 = 0.116667. Standard deviation of proportion: σₚ = √(p̄(1−p̄)/n) = √((7/60)(53/60)/300) = √(371/1,080,000) = 0.0185343. Three-sigma limits: UCL = p̄ + 3σₚ = 7/60 + 3√(371/1,080,000) = 0.172269 ≈ 0.1723. LCL = p̄ − 3σₚ = 7/60 − 3√(371/1,080,000) = 0.061064 ≈ 0.0611. Since LCL > 0, no truncation is needed. Lot fractions defective: 25/300 = 0.0833, 30/300 = 0.1000, 35/300 = 0.1167, 40/300 = 0.1333, 45/300 = 0.1500, 35/300 = 0.1167, 40/300 = 0.1333, 30/300 = 0.1000, 20/300 = 0.0667, 50/300 = 0.1667. All lie between 0.0611 and 0.1723, and no run signal is evident. Average fraction defective p̄ = 7/60 = 0.1167; three-sigma limits are UCL = 0.1723 and LCL = 0.0611; hence the process is in control. Validity: independent random lots, constant n = 300 pieces, binomial conditions, np̄ = 35 and n(1−p̄) = 265, both ≥ 5.