OPINION
COLE, Circuit Judge.
Tri-Corp Management Inc. (“TriCorp”), an Ohio corporation, sought to construct a development of fourteen single-family condominiums on property it owned in Hubbard, Ohio. After the Hubbard City Engineer issued a stop work order that prevented Tri-Corp from completing its construction plans, Tri-Corp filed a § 1983 civil rights suit in federal court against the City of Hubbard and three city officials: George Praznik, the Mayor of Hubbard and a member of the Hubbard Planning and Zoning Commission (the “PZC”); William Colleta, the Hubbard City Service Director and a member of the PZC; and David Kelly, the current Hubbard City Engineer. In its two-count complaint, Tri-Corp claimed that by issuing a stop work order, the defendants violated TriCorp’s due process rights and unconstitutionally took Tri-Corp’s property. The defendants moved to dismiss the complaint, arguing that (i) the complaint raised only a regulatory takings claim and (ii) the regulatory takings claim was not ripe for federal court review. The district court granted both components of defendants’ motion and dismissed Tri-Corp’s complaint without prejudice. Tri-Corp appealed both issues. We AFFIRM the district court’s judgment in part, REVERSE in part, and REMAND for further proceedings consistent with this opinion.
I.
According to the allegations in the complaint, Tri-Corp sought to construct fourteen modular homes on its property at 752 Elmwood Drive in Hubbard, Ohio (the “Property”). In February 1997, the president of Tri-Corp discussed construction plans with William Mariotti, who was then the Hubbard City Engineer. Mariotti believed that Tri-Corp’s proposed construction of fourteen modular homes complied with the zoning requirements, but recommended that the PZC approve the plans. Based on Mariotti’s advice, Tri-Corp submitted preliminary plans to the PZC, which the PZC unanimously approved in January 1998. With the PZC’s approval in place, Tri-Corp received a zoning permit and began construction.
Shortly after Tri-Corp commenced developing the Property, it encountered resistance from the Hubbard City Council. At its March 2, 1998 meeting, members of [744]*744City Council expressed disfavor with TriCorp’s plans to build modular homes in Hubbard. Despite the opposition from City Council, the EPA and the Hubbard Service Director approved the extension of utilities to the Property. In April, however, members of City Council sought to stop Tri-Corp’s construction of modular homes. On May 12, the Hubbard City Engineer, Defendant Kelly, issued a stop work order to Tri-Corp. Three days later, on May 15, Kelly lifted the initial stop work order and allowed the construction of one single-family dwelling on the Property.
Tri-Corp never received permission to build the remaining thirteen units. Although it resubmitted the same development plans that the PZC previously approved, the PZC voted against a motion to re-approve those plans. The PZC also voted down a motion to reject Tri-Corp’s plans. Thus, the plans were technically neither approved nor rejected by the PZC. With the PZC paralyzed on the issue and with the stop work order in place, TriCorp sued defendants in federal court under 42 U.S.C. § 1983.
Tri-Corp’s .complaint contained two counts. Count I claimed that through the issuance of the stop work orders, defendants violated the due process clauses of the Fourteenth Amendment and Section 16 of the Ohio Constitution. In support of this claim, Tri-Corp alleged that defendants acted arbitrarily in issuing the stop work orders and that defendants engaged in a “confiscatory action” by stopping the previously permitted development. Count II claimed that the stop work orders unconstitutionally took property from TriCorp without providing just compensation as required by the Fifth Amendment and Section 19 of the Ohio Constitution.
In reply to Tri-Corp’s complaint, the defendants filed a motion to dismiss. Defendants first moved to merge the two counts into a single regulatory takings claim. Second, defendants moved to dismiss the regulatory takings claim on ripeness grounds because Tri-Corp did not exhaust state remedies. The district court granted both components of defendants’ motion and Tri-Corp appealed both aspects of the district court’s decision.
II.
Although not labeled as such, the defendants’ motion to dismiss before the trial court contains two distinct components: a Rule 12(b)(6) motion to dismiss all claims except for a regulatory takings claim and a Rule 12(b)(1) motion to dismiss the regulatory takings claim for lack of subject matter jurisdiction due to its lack of ripeness.
A. Standard of Review
A district court’s dismissal of a civil rights claim for failure to state a claim for relief under Rule 12(b)(6) is a question of law that we review de novo. See Mertik v. Blalock, 983 F.2d 1353, 1356 (6th Cir.1993); see also Bibbo v. Dean Witter Reynolds, Inc., 151 F.3d 559, 561 (6th Cir.1998). In reviewing a complaint for dismissal for failure to state a claim for relief, the complaint is construed liberally in plaintiffs favor and all factual allegations and permissible inferences are accepted as true. See Sistrunk v. City of Strongsville, 99 F.3d 194, 197 (6th Cir.1996); Allard v. Weitzman (In re DeLorean Motor Co.), 991 F.2d 1236, 1240 (6th Cir.1993). Despite the instruction to construe the complaint liberally in plaintiffs favor, a complaint must contain “either direct or inferential allegations respecting all the material elements” and those allegations must amount to more than “bare assertions of legal conclusions.” Scheid v. Fanny Farmer Candy Shops, Inc., 859 F.2d 434, 436 (6th Cir.1988) (quoting Car Carriers, Inc. v. Ford Motor Co., 745 F.2d [745]*7451101, 1106 (7th Cir.1984)). Ultimately, because a Rule 12(b)(6) motion tests the sufficiency of the complaint, the court’s review amounts to a determination of whether it is possible for the plaintiff to prove any set of facts in support of his claims that would entitle him or her to relief. See Miller v. Currie, 50 F.3d 373, 377 (6th Cir.1995) (explaining that a court “should deny [a Rule 12(b)(6) ] motion unless it is clear that the plaintiff can prove no set of facts in support of her claim that would entitle her to relief’); Mayer v. Mylod, 988 F.2d 635, 638 (6th Cir.1993) (“The purpose of Rule 12(b)(6) is to allow a defendant to test whether, as a matter of law, the plaintiff is entitled to legal relief even if everything alleged in the complaint is true.”); Scheid, 859 F.2d at 436 (noting that “[a] Rule 12(b)(6) motion tests whether a cognizable claim has been pleaded in the complaint” and explaining that a claim should not be dismissed “unless it appears beyond doubt that plaintiff can prove no set of facts in support of his claim which would entitle him to relief’).
With respect to a ripeness challenge, federal courts should not consider questions that do not amount to a case or controversy. See Dixie Fuel Co. v. Comm’r of Soc. Sec., 171 F.3d 1052, 1057 (6th Cir.1999); Adcock v. Firestone Tire & Rubber Co., 822 F.2d 623, 627 (6th Cir.1987). For that reason, we have held that “before addressing the merits of any appeal, we must be convinced that the claim in question is ripe for review, even if neither party has raised the issue.” Bigelow v. Mich. Dep’t of Natural Res., 970 F.2d 154, 157 (6th Cir.1992). Where claims are not ripe, federal courts lack subject matter jurisdiction and the complaint should be dismissed. Id.
Because defendants do not dispute the facts underlying the ripeness of Tri-Corp’s complaint, they present a facial challenge, as opposed to a factual challenge, to federal subject matter jurisdiction. See generally RMI Titanium Co. v. Westinghouse Elec. Corp., 78 F.3d 1125, 1134-35 (6th Cir.1996). A facial challenge is an attack on the court’s subject matter jurisdiction that takes the material allegations of the complaint as true and construes them in a light most favorable to the nonmoving party. See United States v. Ritchie, 15 F.3d 592, 598 (6th Cir.1994); Ohio Nat’l Life Ins. Co. v. United States, 922 F.2d 320, 325 (6th Cir.1990). In contrast, a factual attack is “not a challenge to the sufficiency of the pleading’s allegations, but a challenge to the factual existence of subject matter jurisdiction.” Ritchie, 15 F.3d at 598; see also Ohio Nat’l Life, 922 F.2d at 325. An appellate court reviews Rule 12(b)(1) facial attacks de novo. See, e.g., Kruse v. Vill. of Chagrin Falls, Ohio, 74 F.3d 694, 697 (6th Cir.1996) (applying a de novo standard of review to a motion to dismiss for lack of subject matter jurisdiction). For those reasons, we review de novo the district court’s dismissal of the regulatory takings claim on ripeness grounds. And, we take the material allegations in the complaint as true and construe them in a light most favorable to the non-moving party, Tri-Corp.
B. The Dismissal of All of Tri-Corp’s Claims Except the Regulatory Takings Claim
The district court read Tri-Corp’s two-count complaint as alleging only a single regulatory takings claim. On appeal, TriCorp relies on Pearson v. City of Grand Blanc, 961 F.2d 1211, 1215-16 (6th Cir.1992), to argue that the complaint’s two counts, coupled with its references to the Fifth and Fourteenth Amendments, set forth five causes of action: (1) a procedural due process claim; (2) an equal protection claim; (3) a due process takings claim; (4) a substantive due process claim; and [746]*746(5) a just compensation regulatory takings claim. On appeal, neither party disputes the district court’s conclusion that TriCorp’s complaint makes out a regulatory takings claim. Moreover, we conclude that the district court was correct in concluding that the complaint does not set forth procedural due process, equal protection, and due process takings claims. However, because a complaint states a claim for relief where it contains “either direct or inferential allegations respecting all the material elements” that amount to more than “bare assertions of legal conclusions,” the district court should have recognized that TriCorp sufficiently alleged a substantive due process claim. Scheid, 859 F.2d at 436.
1. Procedural Due Process
Tri-Corp does not set forth a procedural due process claim. In this Circuit, a plaintiff states a § 1983 procedural due process claim through one of two methods: “(1) [by] demonstrating that he is deprived of property as a result of established state procedure that itself violates due process rights; or (2) by proving that the defendants deprived him of property pursuant to a ‘random and unauthorized act’ and that available state remedies would not adequately compensate for the loss.” Macene v. MJW, Inc., 951 F.2d 700, 706 (6th Cir.1991) (emphasis in original) (quoting Collins v. Nagle, 892 F.2d 489, 497 (6th Cir.1989)); see also Mertik, 983 F.2d at 1365.
Tri-Corp never alleges that it was deprived of property without either of the fundamental elements of procedural due process: notice or an opportunity to be heard. See Yellow Freight Sys., Inc. v. Martin, 954 F.2d 353, 357 (6th Cir.1992) (“The fundamental elements of procedural due process are notice and an opportunity to be heard.”) (citing Mullane v. Cent. Hanover Bank & Trust Co., 339 U.S. 306, 313, 70 S.Ct. 652, 94 L.Ed. 865 (1950)). Therefore, Tri-Corp’s complaint cannot be read to state a claim for procedural due process under the first method.
Tri-Corp’s complaint also fails to state a claim for relief under the second method. Tri-Corp’s complaint alleges that the May 15 stop work order “was issued in direct contradiction to the prior city zoning and planning and engineers [sic] approval.” Even if this statement is interpreted as an allegation that the stop work order was unauthorized, the complaint never hints, let alone alleges, that the stop work order was a random event or that the post-deprivation remedies that the state provides would not adequately compensate Tri-Corp. See Parrott v. Taylor, 451 U.S. 527, 543, 101 S.Ct. 1908, 68 L.Ed.2d 420 (1981) (rejecting a procedural due process claim where there was no contention that the procedures themselves were inadequate), overruled on other grounds by Daniels v. Williams, 474 U.S. 327, 106 S.Ct. 662, 88 L.Ed.2d 662 (1986). Lacking these critical allegations, Tri-Corp’s complaint fails to state a procedural due process claim under the second method.
2. Equal Protection
Tri-Corp’s complaint also does not state an equal protection claim. (This conclusion should not be too shocking because nowhere in Tri-Corp’s complaint does it mention the phrase “equal protection”). To state an equal protection claim, a party must claim that the government treated similarly situated persons differently. See Silver v. Franklin Township, Bd. of Zoning Appeals, 966 F.2d 1031, 1036 (6th Cir.1992). Here, Tri-Corp does not make any allegations with respect to similarly situated persons, let alone an allegation that it was treated differently than similarly situated persons. Without such allegations, Tri-Corp’s complaint fails to state a claim [747]*747for a violation of the Equal Protection Clause.
3. Due Process Takings
Tri-Corp also does not allege a due process takings claim. In recognizing a claim for a due process taking, the Pearson opinion relied heavily on the discussion of different classes of federal zoning claims laid out in Eide v. Sarasota County, 908 F.2d 716, 720-22 (11th Cir.1990). Pearson, 961 F.2d at 1215 n. 12. According to Pearson, a due process takings claim exists where a zoning regulation destroys the value of the plaintiffs property so that it “amounts to a taking by eminent domain without due process of law.” Pearson, 961 F.2d at 1215-16; Eide, 908 F.2d at 721. The due process takings claim has its origin in a passage of the Supreme Court’s decision in Pennsylvania Coal Co. v. Ma-hon, where Justice Holmes stated that “[t]he general rule at least is, that while property may be regulated to a certain extent, if regulation goes too far it will be recognized as a taking.” 260 U.S. 393, 415, 43 S.Ct. 158, 67 L.Ed. 322 (1922). Because Pennsylvania Coal did not involve a Takings Clause challenge, litigants have argued that Justice Holmes’s statement indicates that where a regulation “goes so far that it has the same effect as a taking by eminent domain [it] is an invalid exercise of the police power, violative of the Due Process Clause of the Fourteenth Amendment.” Williamson County Reg’l Planning Comm’n v. Hamilton Bank of Johnson City, 473 U.S. 172, 198, 105 S.Ct. 3108, 87 L.Ed.2d 126 (1985). As recognized by this Circuit, a governmental entity violates due process and creates a due process takings claim only when its regulation is equivalent to an appropriation of property through eminent domain or physical possession. Pearson, 961 F.2d at 1215-16. Because it acknowledges that the Property may still support construction of one modular home, and because it has not alleged that it lost all of the value to the Property, as would occur if the Property were taken through eminent domain, Tri-Corp does not allege a due process takings claim.
4. Substantive Due Process
Tri-Corp’s complaint does set forth a substantive due process claim. We have recognized that “citizens have a substantive due process right not to be subjected to arbitrary or irrational zoning decisions.” Pearson, 961 F.2d at 1217; see also Zinermon v. Burch, 494 U.S. 113, 115, 110 S.Ct. 975, 108 L.Ed.2d 100 (1990) (explaining that “the Due Process Clause contains a substantive component that bars certain arbitrary, wrongful government actions ‘regardless of the fairness of the procedures used to implement them’ ”) (quoting Daniels v. Williams, 474 U.S. 327, 331,106 S.Ct. 662, 88 L.Ed.2d 662 (1986)); Richardson v. Township of Brady, 218 F.3d 508, 512 (6th Cir.2000). To state a substantive due process claim in the context of zoning regulations, a plaintiff must establish that (1) a constitutionally protected property or liberty interest exists and (2) that constitutionally protected interest has been deprived through arbitrary and capricious action. See Silver, 966 F.2d at 1036 (“To establish a violation of substantive due process, a plaintiff must first establish the existence of a constitutionally-protected property or liberty interest.”); see also Triomphe Investors v. City of Northwood, 49 F.3d 198, 202 (6th Cir.1995); Pearson, 961 F.2d at 1222 (“The administrative action will withstand substantive due process attack unless it ‘is not supportable on any rational basis’ or is ‘willful and unreasoning action, without consideration and in disregard of the facts or circumstances of the case.’ ”); see generally Buckeye Cmty. Hope Found, v. City of Cuyahoga Falls, 263 F.3d 627, 641-43 (6th Cir.2001).
Tri-Corp sufficiently alleged that it had a constitutionally protected property inter[748]*748est. In Buckeye Community Hope Foundation v. City of Cuyahoga Falls, this Court recently acknowledged that a developer has a legitimate property interest in a zoning permit when the zoning permit complied with the existing zoning regulations (as opposed to requiring a special use permit or a conditional use permit) and the site plan had already been approved. 263 F.3d at 642. The complaint alleges that Tri-Corp’s proposed development complied with existing zoning regulations and had already been approved by the PZC. Thus, under Buckeye Community, TriCorp alleged a constitutionally protected property interest.
Tri-Corp also complies with the “arbitrary and capricious” requirement of a substantive due process claim. The complaint asserts that the defendants’ actions were arbitrary and unreasonable. Based on that allegation and a liberal reading of the complaint, Tri-Corp sufficiently pleaded the arbitrary and capricious requirement for a substantive due process violation.
In sum, the district court’s conclusion that only “a single regulatory takings claim” remained of Tri-Corp’s complaint was correct to the extent that it dismissed the procedural due process, equal protection, and due process takings claims. But, the district court erred to the extent that it dismissed Tri-Corp’s substantive due process claim.
C. The Ripeness of Tri-Corp’s Remaining Claims
The district court considered the ripeness of only the regulatory takings claim. Because it is now clear that the complaint states two causes of action—a substantive due process claim as well as a just compensation regulatory takings claim—it is appropriate to consider the ripeness of both claims. We conclude that (1) TriCorp’s substantive due process claim is ripe for review and (2) the district court correctly concluded that Tri-Corp’s regulatory takings claim was unripe.
1. Ripeness of the Substantive Due Process Claim
Tri-Corp’s substantive due process claim is ripe for review because it presents an “existing, substantial controversy, not hypothetical questions or possibilities.” Dixie Fuel Co., 171 F.3d at 1057 (quoting City Communications, Inc. v. City of Detroit, 888 F.2d 1081, 1089 (6th Cir.1989)). The injury to Tri-Corp from the defendants’ alleged arbitrary and capricious activity has already accrued—Tri-Corp’s plans for development have been indefinitely delayed, if not foreclosed. With this definite injury in place, the substantive due process claim is ripe for review.
2. Ripeness of the Just Compensation Regulatory Takings Clause Claim
Tri-Corp’s regulatory takings claim is not ripe for federal court review. The Takings Clause does not prohibit the government from taking private property; it prohibits the government from taking private property without just compensation. Williamson, 473 U.S. at 194. A takings claim is not ripe for review unless a property owner is denied just compensation. Id. (“[Bjecause the Fifth Amendment proscribes takings without just compensation, no constitutional violation occurs until just compensation has been denied.”); Waste Mgmt., Inc. of Tennessee v. Metro. Gov’t of Nashville & Davidson County, 130 F.3d 731, 739 (6th Cir.1997); Hammond v. Baldwin, 866 F.2d 172, 178-79 (6th Cir.1989); Four Seasons Apartment v. City of Mayfield Heights, Ohio, 775 F.2d 150, 151-52 (6th Cir.1985); see also Eide, 908 F.2d at 721 (“[A] Fifth Amendment just compensation claim is not ripe until the landowner has pursued the available state procedures to obtain just compensation.”). [749]*749Under this reasoning, “if a State provides an adequate procedure for seeking just compensation, the property owner cannot claim a violation of the Just Compensation Clause until it has used the procedure and been denied just compensation.” Williamson, 473 U.S. at 195. In other words, a wronged party satisfies its duty to seek just compensation by pursuing reasonable, certain, and adequate procedures for obtaining compensation. Id. at 194 (quoting Reg’l Rail Reorganization Act Cases, 419 U.S. 102, 124-25, 95 S.Ct. 335, 42 L.Ed.2d 320 (1974)); Kruse, 74 F.3d at 697.
Because Ohio does not have an inverse condemnation or other formalized procedure for seeking just compensation for a taking, this Circuit has focused on whether Ohio’s writ of mandamus provides a “reasonable, certain, and adequate provision for obtaining compensation.” Although we have twice addressed that question, our holdings appear to be at odds with one another. We first evaluated whether Ohio’s writ of mandamus provided a “reasonable, certain, and adequate provision for obtaining compensation” in Silver v. Franklin Township, Board of Zoning Appeals, which was a regulatory takings case. 966 F.2d 1031. There, we held that through the writ of mandamus, “Ohio law provides a procedure for obtaining just compensation for a governmental taking.” Silver, 966 F.2d at 1035 (“If a property owner can demonstrate that the enforcement of a zoning regulation results in an unconstitutional taking, the owner may seek a mandamus from a state court directing state officials to institute eminent domain proceedings to determine just compensation.”). Two years later, in Kruse v. Village of Chagrin Falls, Ohio, a physical takings case, we reasoned differently:
We hold that Ohio affords no “reasonable, certain and adequate provision for obtaining compensation” after private property is taken by public authorities without following the mandatory pretaking appropriation procedures set out in Ohio Rev.Code §§ 163.01-163.62. Ohio’s decisional law in this area is anything but certain. Ohio has no statutory provision for relief under the circumstances of this case. The fact that the State’s courts recognize an action in mandamus, where the State has no mandated procedures governing inverse condemnation, cannot be equated to a “reasonable, certain and adequate provision for obtaining compensation,” after the property has been physically taken in violation of the appropriations statutes. An action for the extraordinary writ of mandamus is, at best, a procedure which must be invoked in the absence of any statutory framework in an attempt to obtain wholly equitable relief for an injury already inflicted.
74 F.3d at 700.
Although the Silver and Kruse holdings appear to be contradictory, they can be reconciled by limiting each to its facts. Under that approach, Silver’s pronouncement that a writ of mandamus is a “reasonable, certain, and adequate provision for obtaining compensation” applies to regulatory takings claims, and Kruse’s pronouncement that a writ of mandamus does not provide such protection applies to physical takings claims.
Complicating matters further, we note that a recent Ohio Supreme Court decision may shed additional light on whether the writ of mandamus in Ohio is a “reasonable, certain, and adequate provision for obtaining compensation” for an unconstitutional taking. In State ex rel. Elsass v. Shelby County Board of Commissioners, the Ohio Supreme Court explained that “[mjandamus is the appropriate action to compel public authorities to institute appropriation proceedings where an involuntary taking of private property is alleged.” 92 Ohio St.3d 529, 751 N.E.2d 1032, 1037 (Ohio 2001). Although that decision suggests [750]*750that Ohio now recognizes the writ of mandamus as a “reasonable, certain, and adequate provision for obtaining compensation” after an unconstitutional taking has occurred, we do not go so far as to reach that result.
Rather, we decide this issue on a deficiency in Tri-Corp’s complaint. Where a property holder asserting a regulatory takings claim “has not resorted to state procedures for obtaining just compensation and has made no claim that these procedures are inadequate, his takings claim is not ripe for federal court review.” Silver, 966 F.2d at 1035. Here, Tri-Corp does not allege either that it filed an unsuccessful writ of mandamus or that it believed that a writ of mandamus would not provide a “reasonable, certain, and adequate” means of seeking just compensation. Without either allegation, Tri-Corp’s regulatory takings claim is not ripe for review and must be dismissed. Because we decide this issue on the insufficiency of the pleadings, we underscore that we make no determination as to the relationship between the Silver and Kruse holdings or the impact of the Shelby County decision.
III.
Through only a passing, casual reference in the briefs and a short mention at oral argument, counsel noted that prior to this lawsuit, Tri-Corp had filed a mandamus action in state court on July 6, 1999. Instead of curing Tri-Corp’s pleading deficiency (for the unripeness in Tri-Corp’s regulatory takings claim), this fact alerted us to a potentially more serious issue not addressed by the parties—whether principles of Younger abstention apply to either stay or dismiss this case. See Younger v. Harris, 401 U.S. 37, 91 S.Ct. 746, 27 L.Ed.2d 669 (1971). Because the record fails to provide us with essential details of the state court proceedings, we are not in a position to pursue the Younger abstention issue any further here.
IV.
With respect to the Rule 12(b)(6) portion of defendants’ motion, the district court correctly dismissed the procedural due process, equal protection, and due process takings claims. However, a valid substantive due process claim remained amidst those several insufficiently pleaded claims. With respect to the Rule 12(b)(1) ripeness facial subject matter challenge, the district court correctly dismissed Tri-Corp’s just compensation regulatory takings claim, but the substantive due process claim is ripe for review. For those reasons, we AFFIRM the district court judgment in part, REVERSE in part, and REMAND for further proceedings consistent with this opinion.