Mid-size manufacturer's problem of jointly planning production rate, inventory, workforce, hiring and firing, overtime, subcontracting and backlog across multiple products and 3-18 months. Known in OR as Aggregate Production Planning (APP); canonical formulation by Holt-Modigliani-Muth-Simon (1960).
In plain words
Sound familiar?
- We are a 10-50M TRY monthly-revenue mid-size manufacturer; 5-30 product families, multi-product line of 30-200 workers; sales gives a yearly demand forecast but turning that into a monthly production rate stays scattered in the planner's head.
- Demand is seasonal โ peak in summer, trough in winter, or the other way around; the question 'steady production into stock or month-to-month rate change?' is re-litigated each year from scratch.
- Hire-fire and temporary-contract decisions are taken by HR, production and finance based on three separate gut feels; collective-agreement constraints (Turkish Labour Law, 270-hour annual overtime cap) enter the plan only afterwards.
- Overtime, second shift, or subcontract โ every product family decides 'this time' on the spot; nobody calculates which yearly mix is cheapest.
- The trade-off between backlog (order deferral) and inventory is intuitive; the amount we defer with 'next month' to customers is not a policy, it is an ad-hoc call.
- Subcontracted work fluctuates 5-25% year over year; the capacity ceiling (the hours a subcontractor can give us) is not recorded in the annual plan.
- We had tackled lot sizing (problem 16, single-product 'should I produce this month, how much?'); APP sits above it โ workforce and subcontracting decisions belong here, but the two live in different software modules.
Why it matters
How it's solved
Technical depth
How it's solved
Technical depthIn one sentence: Lay 12 months across a spreadsheet, solve for the production-rate + inventory + headcount + overtime + subcontract mix that minimises total cost for each month, and refresh the answer monthly as the forecast updates โ a numerical scale replacing intuition.
In Operations Research (the discipline that uses math and computers to solve business decisions) literature this is Aggregate Production Planning (APP) โ multi-product, multi-period (typically 3-18 months) joint capacity and workforce planning at the medium-term horizon. The canonical formulation is the HMMS model from the 1960s. Three-stage solution:
1. Modeling. Decision variables per period (month): per-family production quantity, end-of-period inventory, backlog (deferred orders), regular-time production, overtime production, subcontract quantity, end-of-period workforce, hires, fires. Inputs: per-family per-period demand forecast, hours-per-unit conversion, regular labour-hour cost, overtime hour cost (TR Labour Law 50% premium), hire cost (sourcing, training, onboarding), fire cost (severance, notice), inventory holding cost (% capital + warehouse + insurance), backlog penalty (contract fines + customer-relationship), subcontract cost, capacity ceilings (regular hours, overtime hours โ TR Labour Law article 41, 270-hour annual cap per worker, subcontract ceiling). Constraints: inventory balance (prior stock + production + subcontract โ demand = end stock โ backlog), workforce balance (this period = prior + hires โ fires), hour capacity (hours required โค regular + overtime), inventory capacity, overtime annual cap, subcontract ceiling, collective-agreement hire-fire bounds. Objective: total cost minimum across the horizon โ regular wages + overtime premium + hire + fire + holding + backlog penalty + subcontract.
2. Solver-driven decision. Three classical approaches: (a) HMMS QP (Quadratic Programming โ squared cost penalties yield a closed-form decision rule; smooths swings in workforce and production rate). (b) LP/MIP โ linear unit costs handled by LP (Linear Programming โ minimise a linear objective under linear constraints), integer hire-fire or overtime via MIP (Mixed-Integer Linear Programming โ optimisation with some 0/1 variables and some continuous). Mid-scale (10-30 product families ร 12-18 periods) solved by commercial or mature open-source MIP solvers in minutes. (c) Scenario-based (stochastic) APP โ under demand uncertainty, multi-stage stochastic programming or robust optimisation; alternatively, deterministic approximations adapted to uncertainty. (d) Heuristic โ search decision rules (regression on the planner’s past decisions to derive a rule). Rolling-horizon (re-solve monthly) re-planning: first 1-2 months “frozen” (committed to contracts), 3-12 months “flexible”.
3. Field integration. Output in three layers: (i) monthly production-rate + inventory + workforce + overtime + subcontract decision table (feeds S&OP meeting), (ii) monthly product-family disaggregation into weekly lot sizing (problem 16), (iii) finance + HR projection (cash flow, payroll projection, hire-fire calendar). Data flow: sales forecast (CRM + historical), capacity inventory (machine-hours, workforce), collective-agreement and Labour Law constraints, subcontractor capacity confirmations. Monthly S&OP committee: sales-production-finance alignment, plan-actual gap, demand-forecast refresh, overtime-subcontract mix recalibration.
Alternatives
Manual plus spreadsheet plus production manager's experience
FreeZero license
Who it fits: Small manufacturer (1-3 product families, 20-50 workers), single-shift line
- + Zero software cost
- + Flexible, accommodates last-minute changes
- + Good outcome with an experienced production manager
- โ Mental capacity insufficient above 5 product families
- โ Hire-fire / overtime / subcontract mix is intuitive, no optimality
- โ Stochastic demand and Labour Law constraints get missed
- โ Sales-production-finance alignment at S&OP is weak
ERP production planning module
Enterprise150K-600K TRY license + 30K-90K TRY/year maintenance (TR market observation)
Who it fits: Mid-size manufacturer, 5-30 product families, multi-shift
- + ERP-integrated โ sales, stock, production on one system
- + Local-language UI, local support
- + MRP plus rough-cut capacity included
- โ Medium-term planning optimisation module usually absent โ plan done by hand
- โ Hire-fire and overtime as decision variables out of scope
- โ Uncertainty-aware planning support thin
Advanced Planning System (APS)
Enterprise300K-2M EUR license + 60K-300K EUR/year maintenance (international solution providers)
Who it fits: Large manufacturer, multi-site, 30+ product families, capacitated line
- + Exact-programming or quadratic-smoothing-based medium-term planning is mature
- + Sales-operations planning, material-requirements planning, capacitated lot-sizing integrated
- + What-if scenarios, rolling horizon
- โ High license plus 12-24 month deployment
- โ TR Labour Law and collective-agreement customisation adds project time
- โ Wide training programme for the operations team
Open-source solver plus custom APP module
Open SourceLicense free; in-house build 16-30 weeks or 600K-1.8M TRY consultancy
Who it fits: Manufacturer with a tech team, where integration with the existing ERP is required
- + No license fee
- + Linear and quadratic medium-term planning methods are well-defined for open-source solvers
- + Uncertainty-aware and rolling-horizon extensions exist in open literature
- โ Requires in-house solver specialist plus enterprise-resource-planning integration team
- โ Moving from prototype to field system takes time
- โ Maintenance burden stays with the operator
Recommendation
Ask in the meeting
- What method is used for medium-term production planning โ quadratic-cost smoothing model, linear / integer mathematical programming, heuristic decision rule, or only rough-cut capacity visualisation?
- Does the model jointly optimise production rate + inventory + workforce + hire-fire + overtime + subcontract + deferred orders across multiple product families ร 12-18 periods, or is it layered?
- How are TR Labour Law constraints (270 annual overtime hours per worker, 50% weekday and 100% weekend premium, severance) and collective-agreement hire-fire bounds defined in the system?
- Is scenario-based planning supported for demand uncertainty, or only single-forecast (deterministic) plans?
- How is the rolling-horizon structure configured โ first 1-2 months 'frozen' (committed), the rest 'flexible'?
- Is disaggregation from monthly product-family levels to weekly batch-size decisions automatic, or a separate module?
- In a 12-16 week pilot with real demand and capacity data, what kind of savings report can be produced against the prior manual plan?
- If we end the contract, in which standard format can we export demand-forecast history, production-plan archive, hire-fire calendar and overtime-subcontract data?
Technical details
Editor’s note
Colloquially this is the “annual production plan”, “medium-term plan” or “S&OP” (Sales & Operations Planning โ the monthly sales-and-operations alignment meeting). Academically it is Aggregate Production Planning (APP), with the canonical HMMS model from the 1960s. A single LP/QP captures production rate, inventory, workforce (hire-fire), overtime and backlog as continuous variables and trades off the cost of inventory build-up against regular capacity, overtime premium and hire-fire churn.
Do not confuse this with problem 16 (Wagner-Whitin lot sizing). Lot sizing answers, for a single product, ‘should I produce this month, and how much?’ โ a single-layer trade-off between setup cost and inventory holding. APP sits above: it jointly decides production, workforce, overtime and subcontracting across multiple products on a 3-18 month horizon. Solved together they produce an internally consistent plan: APP first sets the monthly production rate and the workforce-overtime-subcontract mix at the product-family level, then lot sizing breaks the monthly quantity into weekly batch sizes. This hierarchy is the standard framework in production-planning textbooks.
Do not confuse it with problem 1 (job shop scheduling) either. JSP is a daily operation-sequencing schedule; APP is far above that, on a monthly-yearly horizon, planning the mix.
Most-skipped point in the sector: rolling-horizon discipline between forecast and plan. Academic APP models typically solve the full 12-month horizon at once; in real production the first 1-2 months are committed (“frozen”), the next 3-12 are “flexible” โ every month the forecast is refreshed and the plan re-solved. Without the frozen window the plan changes from scratch every month and the production team loses confidence. Second most-skipped: the 270-hour annual overtime cap under TR Labour Law article 41 (per worker). This must be a hard constraint in the APP model; otherwise the plan says “we can always solve it with overtime” and crosses the legal limit, triggering penalties and union pushback.
Step-by-step path โ for the SMB
Stage 1 โ Measure first, plan second. At least 12 months of data: per-family monthly actual production, actual sales, end-of-month stock, hire-fire movements, overtime hours, subcontract quantity, backlog (late delivery). Log the demand forecast: compute forecast-vs-actual error (MAPE). Capacity inventory: hourly capacity per line (regular + overtime), workforce skill matrix, subcontract ceiling (per subcontractor).
Stage 2 โ Extract the knowledge asset. Hours-per-unit conversion coefficients, unit costs (regular, overtime, hire, fire, holding, backlog penalty, subcontract). Constraints: warehouse capacity, 270-hour annual overtime cap, collective-agreement hire-fire bounds, contracted-customer delivery penalties.
Stage 3 โ Pilot. 12-16 weeks. For a subset (e.g. 5-10 main product families) run the APP MIP plan in parallel with the manual plan. Decision stays with the planner; APP recommends. Success criteria set in advance: total production+workforce+inventory cost -8% minimum, hire-fire churn -25% minimum, zero breach of overtime cap.
Stage 4 โ Rollout. 9-15 months to all product families + lot-sizing disaggregation + S&OP-meeting output integration. Monthly rolling-horizon re-planning. Monthly S&OP committee: sales-production-finance alignment, plan-actual variance, forecast-MAPE refresh, overtime-subcontract mix recalibration.
Risks โ what can go wrong
- Demand-forecast slip. APP takes the deterministic forecast as input; if MAPE exceeds 20-30% the plan drifts from month one. Stochastic / scenario-based APP, or rolling-horizon monthly re-planning, is required.
- Collective-agreement constraint change. A mid-year collective-agreement renewal alters wages, overtime rules and hire-fire bounds; APP parameters must be recalibrated semi-annually with an emergency re-plan after the signing date.
- Currency (FX) cost. Imported raw material and equipment cost moves with TRY-EUR/USD; if unit production cost is treated as constant, FX jumps invalidate the plan. FX-scenario APP, or monthly parameter refresh, is essential.
- Single-supplier lock-in. A single subcontractor means the capacity ceiling may not materialise (subcontractor takes other work, capacity closes), and the APP plan collapses. At least 2-3 subcontract sources plus annual framework agreements are needed.
Solution method โ technical view
| Approach | Typical scale | Solve time | Guaranteed optimum? |
|---|---|---|---|
| Heuristic (production manager + rule) | 1-5 product families, 6-12 months | instant | No, 50-70% optimum |
| HMMS QP (quadratic, smooth) | 5-15 product families, 12-18 months | minutes | Yes (closed-form or QP) |
| Transportation-tableau LP | 5-20 product families, 6-18 months | minutes | Yes (LP) |
| MIP (integer hire-fire, integer overtime) | 10-30 product families, 12-18 months | minutes-hours | Yes (within bound) |
| Stochastic / scenario-based APP | 10-30 product families, multi-scenario | hours | Yes (LP/MIP), bounded scenarios |
| Search decision rules (regression on planner’s past decisions) | Statistical rule | instant | No, calibrated to experience |
| Rolling-horizon re-planning | Monthly re-solve | minutes/month | Yes (each solve) |
Objective function choices:
- Objective 1 โ Total cost minimum: Regular + overtime + hire + fire + holding + backlog + subcontract. Standard APP objective.
- Objective 2 โ Service level maximum: Drive backlog to zero, contract penalties first.
- Objective 3 โ Production-rate smoothing: Minimise oscillation on workforce and machine (smooth operations).
- Objective 4 โ Hire-fire churn minimum: Employer-brand and morale priority.
Multi-objective: weighted sum (total cost + churn weight) or hierarchical (zero contract penalty first, then total cost minimum).
Academic sources
Listed in the page frontmatter under sources.
Sources
- Holt, C. C., Modigliani, F., Muth, J. F. and Simon, H. A. (1960). Planning Production, Inventories, and Work Force. Prentice-Hall. Foundational APP reference, HMMS model.
- Nam, S. J. and Logendran, R. (1992). Aggregate production planning - A survey of models and methodologies. European Journal of Operational Research, 61(3), 255-272. Comprehensive survey.
- Mula, J., Poler, R., Garcรญa-Sabater, J. P. and Lario, F. C. (2006). Models for production planning under uncertainty: A review. International Journal of Production Economics, 103(1), 271-285. Production planning under uncertainty review.
- Bitran, G. R. and Yanasse, H. H. (1984). Deterministic approximations to stochastic production problems. Operations Research, 32(5), 999-1018. Deterministic approximations to stochastic production problems.
- Vollmann, T. E., Berry, W. L., Whybark, D. C. and Jacobs, F. R. (2005). Manufacturing Planning and Control for Supply Chain Management (5th ed.). McGraw-Hill. Textbook framework for production planning and control.
- YรK Thesis Center โ keywords: ’toplu รผretim planฤฑ’ or ‘รผretim planlamasฤฑ’ or ‘kapasite planlama’ โ 35+ theses. tez.yok.gov.tr
Glossary
- Aggregate Production Planning
- 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.
- Workforce Capacity Balance
- 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.
- MIP
- An optimization model where some decision variables are forced to be whole numbers (e.g. number of trucks, number of shifts).
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