43. The expected monthly demand for gardening tools made by a company is: 80, 100, 120, 110, 100 and 90. The company wants to level the production for each month in the planning horizon. The beginning inventory is zero and backorders are allowed. Which months have a backorder and what is the size of those backorders?
Answer: D
Months 4 and 5 have a backorder of 10 each
To level the production for each month while managing the expected demand of gardening tools, the analysis shows that both months 4 and 5 will incur a backorder of 10 units each.
A) Months 4 and 5 have a backorder of 20 each
This option is incorrect because the calculated demand for months 4 and 5 does not support a backorder of 20 units. The demand for month 4 is 110 and for month 5 is 100, which only results in a backorder of 10 units each when the monthly production level is set to meet the average demand.
B) Months 2 and 3 have a backorder of 10 each
This option is incorrect as the analysis indicates that months 2 and 3 have sufficient production capacity to meet the demand. The production level set would align closely with the demand of 100 for month 2 and 120 for month 3, resulting in no backorders.
C) Months 2 and 3 have a backorder of 20 each
This option is incorrect since there is no basis for a backorder of 20 units in months 2 and 3. The demand in these months can be satisfied without incurring significant backorders, particularly with the average production level set to accommodate the overall demand.
D) Months 4 and 5 have a backorder of 10 each
This option is correct as the production level, when averaged out, results in a backorder of 10 units for both months 4 and 5. The demand for these months exceeds the average monthly production capacity, leading to the specified backorder situation.
Conclusion
The analysis concludes that the correct option is D, indicating that months 4 and 5 will each have a backorder of 10 units. Other options fail to accurately reflect the demand and production capabilities during those months, demonstrating the importance of balancing production levels with expected demand to avoid excess backorders.