Optimal Overtime Level

Purpose

This calculator finds the overtime level that minimizes total monthly production-related cost.

It balances three competing effects:

• Overtime raises labor cost.
• More overtime reduces production shortfall and penalty cost.
• Overtime efficiency deteriorates at higher overtime levels, so each extra overtime hour can produce less output.

This mirrors what most operations teams notice on the floor: the first overtime hour is nearly as productive as a normal hour, but by the tenth hour, fatigue and diminishing returns make it far less valuable — even though it still costs more.

Inputs

• Required Production: Target production quantity for the month.
• Available Normal Hours: Regular production hours available in the month.
• Maximum Overtime Hours: Upper bound for overtime search. The optimizer evaluates overtime from zero up to this limit.
• Production Rate: Base production rate per hour.
• Normal Hourly Cost: Labor cost per normal production hour.
• Overtime Hourly Cost: Labor cost per overtime hour.
• Shortfall Penalty: Cost charged per unit of unmet required production.
• Fixed Production Cost: Monthly fixed production-related cost added to total cost.
• Efficiency Deterioration: Controls how quickly overtime productivity declines as overtime approaches its maximum.
• Optimization Points: Number of overtime trial points used to locate the minimum-cost point.
• Scenario Points: Number of points used in the scenario table and optimization chart.

Results

• Optimal Overtime: Best overtime level found by the optimizer. This is the recommended overtime target for the current assumptions because it minimizes total monthly cost on the search grid.
• Normal Production, Overtime Production, Total Production: Production split and combined output at the optimal overtime level. This helps you see how much output comes from regular capacity versus overtime and whether overtime is carrying too much of the plan.
• Production Shortfall: Unmet required production at the optimum. This tells you whether the cost-optimal plan still accepts some shortfall and how much demand remains uncovered.
• Overtime Efficiency Factor: Effective overtime productivity multiplier at the optimum. This indicates how much productivity loss the model applies at that overtime level and whether extra overtime is becoming less effective.
• Normal Labor Cost, Overtime Labor Cost, Shortfall Cost, Total Cost: Cost components and final monthly total at the optimum. This breakdown shows where savings come from and which cost component is driving the solution (labor vs shortfall penalty).
• Cost per Unit Produced: Total cost divided by total produced quantity at the optimum. Useful for comparing this plan with alternate production policies or prior months on a normalized unit-cost basis.
• Optimization Chart: Visual cost curve versus overtime hours, including Total Cost, Overtime Labor Cost, and Shortfall Cost. This makes the trade-off visible: where penalties drop, where overtime cost rises, and where the minimum total cost occurs.
• Overtime Scenarios: Point-by-point scenario table across the overtime range. Use it for what-if analysis and operational discussion before committing to a final overtime target.

Understanding the Calculation

• Normal production is based on available normal hours and production rate.
• Overtime output uses a reduced effective overtime rate when efficiency deterioration is nonzero.
• For each overtime level, the calculator computes total production, shortfall, and costs.
• It returns the overtime level with the minimum total cost.

Optimization Process Note

• The calculator searches overtime from 0 to Maximum Overtime Hours using evenly spaced trial points.
• The number of trial points is controlled by Optimization Points.
• At each trial point, it computes Overtime Production, Production Shortfall, and all cost components.
• It selects the trial point with the lowest Total Cost as Optimal Overtime.
• Scenario Points controls only the reporting granularity for the scenario table and chart, not the search resolution.
• A higher Optimization Points value gives a finer search and can slightly shift the reported optimum.

Example (Current Defaults)

Using the current defaults, the calculator finds approximately:

• Optimal Overtime: 45.98 hr/mo
• Normal Production: 1600 unit/mo
• Overtime Production: 343.15 unit/mo
• Total Production: 1943.15 unit/mo
• Production Shortfall: 56.85 unit/mo
• Total Cost: 3116.01 USD/mo
• Cost per Unit Produced: 1.6036 USD/unit

Interpretation:

• Zero or low overtime leaves too much shortfall penalty.
• Excessive overtime becomes less productive due to efficiency deterioration and raises overtime labor cost.
• The optimizer selects a middle region where combined cost is lowest.
• Notice that the optimum rarely sits at either extreme — that's the signature of a genuine cost tradeoff rather than a one-sided decision.

Important Assumptions and Interpretation

• Overtime efficiency decay follows the built-in quadratic pattern.
• Production rate is otherwise constant.
• Shortfall penalty is linear per unit short.
• The optimizer uses a discrete search grid based on Optimization Points; a finer grid can slightly change the reported optimum.
• Results are monthly planning estimates, not shift-by-shift scheduling instructions.