Choose a Product Mix When Machine Time and Finishing Labor Both Bind

Count the complete route through production

A small workshop can choose the wrong product mix even after calculating contribution per machine hour correctly. A product that uses the machine efficiently may consume so much finishing labor that the machine later sits idle. The decision needs the complete route from raw material to sale, including shared people, equipment and demand limits. Ranking products by one ratio works only while the other requirements remain slack. Here the question is a weekly allocation, with existing rent and salaried supervision unchanged.

NIST describes value stream mapping as a way to examine production and information flows. Our application is an original numerical scheduling exercise. The workshop should measure actual good units per resource hour, including ordinary rework, before using a spreadsheet to sell the resulting capacity. A precise solution to an incomplete routing sheet can make commitments the floor cannot fulfill. Keep a separate list of delivery promises that take priority over this illustrative contribution ranking.

Supporting references: 1. NIST: Value Stream Mapping

Build a feasible set before comparing earnings

Suppose a basic display contributes USD 60 after avoidable materials and production costs and needs two machine hours plus one finishing hour. A premium display contributes USD 90 and needs one machine hour plus three finishing hours. There are 100 machine hours and 90 finishing hours available this week. Demand can absorb every unit in the plans below. Units must be whole, and setup losses are already reflected in available hours.

Producing only basic displays gives 50 units and USD 3,000 of contribution, leaving 40 finishing hours unused. Producing only premium displays gives 30 units and USD 2,700, leaving 70 machine hours unused. Premium looks superior at USD 90 per machine hour versus USD 30 for basic, yet the premium-only plan earns less. Its finishing requirement is the reason. Neither unused resource can automatically substitute for the other, and their hours must not be added into a single undifferentiated capacity total.

Find the mix that uses both constraints

A plan with 42 basic and 16 premium displays uses 100 machine hours and 90 finishing hours. Contribution is USD 2,520 plus USD 1,440, or USD 3,960. This is USD 960 above the basic-only alternative. It is also optimal within these stated assumptions: valuing each machine hour at USD 18 and each finishing hour at USD 24 exactly accounts for each product contribution. Two machine hours plus one finishing hour explain USD 60; one plus three explain USD 90.

Those resource values provide an upper bound of USD 3,960 for every feasible plan because available hours are fixed. The mixed plan reaches that bound. They are local opportunity values, not wages or accounting allocations. SBA discusses comparing business costs and benefits; the values here come entirely from our case. If a customer limit or another production step changes, these same hour values may cease to describe the best alternative.

Supporting references: 2. SBA: Manage your business — finances

Buy capacity only where it releases output

Buying ten additional finishing hours permits a different whole-unit mix: 40 basic and 20 premium displays use 100 machine and 100 finishing hours. Contribution rises to USD 4,200 before the capacity purchase, a USD 240 increase. A hypothetical USD 180 all-in charge therefore leaves USD 60 of incremental benefit. Paying USD 260 instead would reduce the result below the original plan despite increasing production capability.

The ten-hour block is worth at most USD 240 in this narrow range. Purchasing another resource must be tested against a fresh feasible plan, rather than priced with the finishing-hour value by analogy. Extra machine hours, a different package size, or a mandatory overtime minimum can produce different gains. Verify that the person providing finishing capacity has the relevant skills and that inspection time has not been excluded from the hours being bought.

Let demand and imperfect output change the answer

Now cap premium demand at ten units. A feasible plan is 45 basic plus ten premium, consuming all 100 machine hours but only 75 finishing hours and earning USD 3,600. Additional finishing capacity has no immediate value because finishing is already slack. The earlier USD 24 estimate is no longer an appropriate purchasing limit. This counterexample shows why a resource price must travel with its active constraints and customer demand assumptions.

Yield deterioration has a similar effect. If premium finishing routinely takes four hours rather than three, the original 42-and-16 schedule requires 106 finishing hours and is infeasible. Rebuild the routing assumptions before investigating price changes. Contribution should also reflect scrap and variable energy, while already committed overhead stays separate. A product that creates a follow-on service obligation may need another future-period constraint even if its current production route fits.

Make the weekly decision auditable

Record the chosen quantities, resource usage, demand evidence and the alternative rejected. A workable schedule needs room for random interruptions; using every theoretical hour can leave no recovery time. The contribution-maximizing plan is a benchmark for the stated deterministic week, not a service guarantee. Management may deliberately reserve capacity for contracted repairs or an important customer, but should identify the contribution given up rather than hiding it in a blended average margin.

At the end of the week, compare actual hours and good units with the routing sheet. Investigate which constraint moved and whether the purchased hours produced saleable units. The practical boundary is to buy a capacity block only when a feasible, sellable revised mix produces more incremental contribution than its complete cost. When assumptions remain uncertain, use several explicit schedules and keep the commitments within the capacity that can actually be delivered.

Limits of this analysis

• Resource values apply locally to the stated routing and unconstrained demand.
• No legal labor-hour limits, overtime rules or employment costs are estimated.
• Integer quantities work for these examples; other orders can require explicit enumeration.
• Full utilization provides no allowance for unexpected downtime.