Investments in Nonconsolidated Affiliates - Narrative (Details) $ in Millions		3 Months Ended
Aug. 31, 2018 USD ($)	Jun. 03, 2023 USD ($) affiliate
Schedule of Equity Method Investments
Number of nonconsolidated affiliates \| affiliate		2
Global Holdings Netherlands B.V. (Maars) \| MAARS
Schedule of Equity Method Investments
Ownership interest (percent)	100.00%
Global Holdings Netherlands B.V. (Maars)
Schedule of Equity Method Investments
Difference between investment value versus Company's proportionate share of underlying net assets	$ 3.1	$ 1.0
Amortizable difference between investment value versus Company's proportionate share of underlying net assets	2.7
Permanent difference between investment value versus Company's proportionate share of underlying net assets	$ 0.4
Equity method investment impairment		$ 1.0
Global Holdings Netherlands B.V. (Maars)
Schedule of Equity Method Investments
Outstanding equity interest acquired (percent)	48.20%
Cash payment to acquire equity interest	$ 6.1

Equity Method Investment, Permanent Difference Between Carrying Amount and Underlying Equity, Permanent

No definition available.

Name:	mlkn_EquityMethodInvestmentPermanentDifferenceBetweenCarryingAmountAndUnderlyingEquityPermanent
Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Equity Method Investment, Temporary Difference Between Carrying Amount and Underlying Equity, Amortized

+ References

No definition available.

+ Details

Name:	mlkn_EquityMethodInvestmentTemporaryDifferenceBetweenCarryingAmountAndUnderlyingEquityAmortized
Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Number Of Equity Method Investments

+ References

No definition available.

+ Details

Name:	mlkn_NumberOfEquityMethodInvestments
Namespace Prefix:	mlkn_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of voting equity interests acquired at the acquisition date in the business combination.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479328/805-10-50-2

+ Details

Name:	us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Difference between amount at which an investment accounted for under the equity method of accounting is carried (reported) on the balance sheet and amount of underlying equity in net assets the reporting Entity has in the investee.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481687/323-10-50-3

+ Details

Name:	us-gaap_EquityMethodInvestmentDifferenceBetweenCarryingAmountAndUnderlyingEquity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

This item represents an other than temporary decline in value that has been recognized against an investment accounted for under the equity method of accounting. The excess of the carrying amount over the fair value of the investment represents the amount of the write down which is or was reflected in earnings. The written down value is a new cost basis with the adjusted value of the investment becoming its new carrying value subject to the equity accounting method. Evidence of a loss in value might include, but would not necessarily be limited to, absence of an ability to recover the carrying amount of the investment or inability of the investee to sustain an earnings capacity which would justify the carrying amount of the investment.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481664/323-10-45-1

+ Details

Name:	us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The parent entity's interest in net assets of the subsidiary, expressed as a percentage.

+ References

No definition available.

+ Details

Name:	us-gaap_MinorityInterestOwnershipPercentageByParent
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The cash outflow associated with the acquisition of business during the period. The cash portion only of the acquisition price.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479581/805-30-50-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 13
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-13

+ Details

Name:	us-gaap_PaymentsToAcquireBusinessesGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(g)(1)(ii))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481687/323-10-50-3

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482907/825-10-50-28

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481687/323-10-50-3

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481687/323-10-50-3

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481687/323-10-50-3

+ Details

Name:	us-gaap_ScheduleOfEquityMethodInvestmentsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	dei_LegalEntityAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_OwnershipAxis=mlkn_MAARSMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: