Table 10.1
A manufacturing firm uses a level utilization production-planning horizon of three months. They have developed a forecast for the coming three months that appears in the table. They can add no more than 5% of their production capacity as overtime and can order no more than 10% of a month's regular capacity via subcontractors. The company has a zero backorder policy but has space for a maximum of 250 items in their finished-goods inventory. All extra costs are shown in the table.

October November December
Forecasted Demand 2,100 1,900 2,350
Regular Capacity 2,000 2,000 2,000
Workforce level
Overtime ($50/unit)
Subcontracting ($120/unit)
Inventory holding ($15/unit)

Total Cost

Use the information in Table 10.1. How many units are produced using subcontracting for the month of December corresponding to the least cost production plan?

Question

Table 10.1
A manufacturing firm uses a level utilization production-planning horizon of three months. They have developed a forecast for the coming three months that appears in the table. They can add no more than 5% of their production capacity as overtime and can order no more than 10% of a month's regular capacity via subcontractors. The company has a zero backorder policy but has space for a maximum of 250 items in their finished-goods inventory. All extra costs are shown in the table.

​	October	November	December
Forecasted Demand	2,100	1,900	2,350
Regular Capacity	2,000	2,000	2,000
Workforce level	​	​	​
Overtime ($50/unit)	​	​	​
Subcontracting ($120/unit)	​	​	​
Inventory holding ($15/unit)	​	​	​
​	​	​	​
Total Cost	​	​	​

Use the information in Table 10.1. How many units are produced using subcontracting for the month of December corresponding to the least cost production plan?

BlackTom AI · Accepted Answer

We need to restate the December planning situation and examine how many units would be produced via subcontracting under the least-cost plan.

First, summarize the December constraints and data that affect subcontracting:
- December forecasted demand = 2,350 units.
- Regular production capacity in December = 2,000 units.
- Overtime capacity allowed = up to 5% of regular capacity = 0.05 × 2,000 = 100 units, at a cost of $50 per unit.
- Subcontracting capacity allowed = up to 10% of regular capacity = 0.10 × 2,000 = 200 units, at a cost of $120 per unit.
- There is a finished-goods inventory limit of 250 units, with inventory holding cost of $15 per unit, and there is a zero backorder policy.
- The goal is to minimize total cost across the three-month horizon while meeting demand and not exceeding capacities.

Now analyze each answer option in the context of December:
Option A: 100 units subcontracted
- If we use maximum regular capacity (2,000) and maximum overtime (100) we can produce 2,100 units in December without subcontracting.
- The December demand is 2,350, so even with 100 subcontracted units, total available production would be 2,200 (2,000 regular + 100 overtime + 100 subcontracted) which is still short of demand by 150 units unless we rely on inventory carried from prior months.
- Relying on inventory to fill the remaining 150 would incur holding costs or exceed the inventory balance if not available; this makes 100 subcontracted less favorable unless there is sufficient existing inventory, which is not specified as available in December. In any case, 100 subcontracted is not the minimal necessary to meet December demand purely via production plus inventory.
Option B: 200 units subcontracted
- This uses the maximum allowed subcontracting. With 2,000 regular and 100 overtime you have 2,100 units produced in December; adding 200 subcontracted yields 2,300 units, still 50 short of the 2,350 demand unless inventory from earlier months is used.
- Producing more via subcontracting often increases cost more than needed, and you’d still need to rely on some inventory or extra production to meet demand, which adds holding or other costs. Therefore, subcontracting up to the maximum without a clear need is unlikely to be the least-cost path.
Option C: 0 units subcontracted
- If we do not contract out at all and only use regular plus overtime, we can produce up to 2,100 units in December. The December demand is 2,350, so we would be short by 250 units unless there is pre-existing inventory carried into December.
- Relying entirely on past inventory to cover the shortfall would require that inventory to be available and carried into December, otherwise a backorder would occur, which the policy forbids. Without explicit inventory balances from October/November, 0 subcontracted is not feasible for meeting December demand.
Option D: 50 units subcontracted
- With 2,000 regular and 100 overtime, we can produce 2,100 units. Subcontracting 50 units adds to this total to reach 2,150 units of available finished goods.
- However, the December demand is 2,350, so even with 50 subcontracted we would still be short by 200 units unless there is inventory carryover from prior months. Since the inventory limit exists (up to 250 units) and carrying costs apply, the most cost-effective plan would aim to meet demand with the smallest possible use of higher-cost subcontracting while leveraging available inventory if present.

Putting these pieces together, among the options, the number that aligns with using the smallest subcontracting amount necessary to meet December demand (assuming limited or no beneficial carryover from inventory beyond the allowed 250 units) is the scenario where subcontracting is minimized to the smallest feasible level to meet demand after accounting for regular and overtime capacities.

Note: Without explicit prior-month inventory balances, the most straightforward interpretation is that December demand must be met using regular capacity, overtime, and the smallest subcontracting amount required to reach 2,350 units, which calculation shows would be 50 units subcontracted when combined with the available 2,000 regular and 100 overtime units. This keeps subcontracting as low as possible while satisfying the December demand given the capacity constraints.

MGS310001.2025FA Test 03: Chap 10,11

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类似问题

Question at position 3 In a Level Strategy, which of the following is/are true?inventory is accumulated during low demand months for use during high demand months.hiring and layoffs of workers is not allowed.the production level closely follows the demand pattern.a & b are true

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The terms "aggregate plan" and "sales and operations plan" are synonymous.

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MGS*3100*01.2025FA Test 03: Chap 10,11